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<hr />
<div>In [[mathematics]], <b>Algebraic number theory</b> is the study of [[algebraic numbers]] and structures involving them, especially [[algebraic number fields]]. <br />
<br />
=Introduction=<br />
Algebraic number theory is a branch of [[number theory]] that, in a nutshell, extends various properties of the [[integer|integers]] to more general [[rings]] and [[fields]]. In doing so, many questions concerning [[Diophantine equations]] are resolved, including the celebrated [[quadratic reciprocity]] theorem. More recently, the field has been linked to the theory of [[elliptic curves]], and its ideas are responsible for the successful attack on [[Fermat's Last Theorem]]. This field is extremely rich and advanced (indeed, prerequisites to courses in this topic often include first-year graduate school material), and this article gives no more than a brief introduction.<br />
<br />
=The basics=<br />
<br />
==Motivation==<br />
Interest in the field was largely motivated by the desire to understand numbers of the form <math>x^2+ny^2</math> for some fixed, [[squarefree]] <math>n</math> (if <math>n=x^2y</math> is not [[squarefree]], the case is equivalent to <math>n=y</math>). More specifically, the question at hand was what numbers could be expressed in that form. Since <math>k=x^2+ny^2 \implies x^2 \equiv k \pmod n</math>, there was a natural connection to [[quadratic residues]] in play. In the ring of integers, this is a difficult question to analyze, but it becomes much easier when considering the [[field]] <math>Q[-\sqrt{n}]</math> because then <math>x^2+ny^2=(x+y\sqrt{-n})(x-y\sqrt{-n})</math> is the product of two elements - and the [[norm]] of one. The case of <math>n=1</math>, in particular, leads to [[factorization]] in the [[Gaussian integers]].<br />
<br />
This extension of the concept of [[factorization]] quickly spilled into other problems as well, most notably [[Fermat's Last Theorem]]. In the <math>n=3</math> case, a simple solution exists by taking <math>y^3=z^3-x^3=(z-x)(z^2+xz+z^2)</math> and using an [[infinite descent]] argument. However, this does not extend well to larger <math>n</math> because analogous factorizations contain terms of degree larger than 2. Early attempts at proof factored <math>y^p=z^p-x^p</math> into <math>y^p=\prod_{i=0}^{p-1}(z-\omega^ix)</math>, where <math>\omega</math> is a <math>p</math>th root of unity. However, though this was not well-understood at the time, the implicit assumption was that <math>\mathbb{Z}[\omega]</math> was a [[principal ideal domain]], later shown to be false. <br />
<br />
==Algebraic Numbers==<br />
An [[algebraic number]] is a number that is the root of some nonzero integer [[polynomial]] (i.e. a polynomial with integer coefficients). When that polynomial is [[monic]], the number is said to be an [[algebraic integer]]. For example, all [[rational]] numbers are algebraic integers (and thus an [[algebraic number]] as well), as the [[linear]] polynomial <math>nx-m</math> has root <math>\frac{m}{n}</math> for any [[integers]] <math>m,n</math> (with <math>n \neq 0</math>). When such a [[polynomial]] exists, it is called the <b>minimal polynomial</b> of the [[algebraic number]] in question. It can be shown that a number is an algebraic integer if and only if its minimal polynomial has integer coefficients. <br />
<br />
The sum, difference, product, and quotient of any two algebraic numbers is itself an [[algebraic number]]; as a result, the algebraic numbers form a [[field]]. In this article, <math>K</math> will denote an arbitrary [[algebraic number field]]; for example, <math>\mathbb{Q}[\sqrt{-5}]</math>, which consists of the numbers of the form <math>a+b\sqrt{-5}</math> where <math>a,b</math> are rational. As a sidenote, this shows that the sum of any two algebraic integers is itself an algebraic integer, and furthermore any [[rational]] algebraic integer is obviously also an [[integer]]. This gives an easy way to show that sums similar to <math>\sqrt{2}+\sqrt{3}+\sqrt{5}+\sqrt{7}</math> are [[irrational]] - as all of these terms are algebraic integers (they are roots of <math>x^2-k</math> for <math>k=2,3,5,7</math>), the sum is an algebraic integer as well, and so must be an [[integer]] if [[rational]]. But any old [[approximation]] is sufficient to determine that this sum is not an [[integer]], hence it is [[irrational]]. <br />
<br />
==Unique factorization==<br />
In the ring of [[integer|integers]], all numbers have unique factorizations by the [[Fundamental theorem of arithmetic]], up to multiplication by the [[unit|units]] 1 and -1. We will extend this notion to an [[integral domain]] <math>A</math>; in other words, a [[commutative ring]] in which the product of two nonzero elements is nonzero. An element <math>a \in A</math> is a [[unit]] if <math>a</math> is [[invertible]] in <math>A</math>; i.e. there exists an inverse <math>b \in A</math> such that <math>ab=ba=1</math> (where 1 is the [[multiplicative identity]]). An element <math>p \in A</math> is [[prime]] if it is not zero, not a unit, and <math>p \mid ab \implies p \mid a</math> or <math>p \mid b</math>. In a [[principal ideal domain]], any element <math>a \in A</math> can be unique factored as the product of primes, up to order and [[multiplication]] by [[unit|units]]. The first order of business is to explore when unique factorization holds.<br />
<br />
Of course, we first need to define the term <b>factorization</b>. An element <math>a \in A</math> is <b>irreducible</b> if it is not a unit and cannot be written as the product of two nonunits; obviously, [[prime]]s are irreducible (but not necessarily vice versa). A factorization of an element is its expression as a product of irreducible elements, and a ring is a <b>unique factorization domain</b> (or [[UFD]]) if this factorization is unique (up to order and multiplication by units). <br />
<br />
As previously mentioned, <math>K</math> is an arbitrary [[algebraic number field]]; as a field, factorization only makes sense in the presence of a subring. Fortunately, can be shown that the algebraic integers form a subring of <math>K</math>; however, though it can be shown that algebraic integers can always be factored, they do not generally form a [[UFD]]. For example, if <math>K=\mathbb{Q}[\sqrt{-5}]</math>, we have<br />
<cmath>6=2 \cdot 3=(1+\sqrt{-5})(1-\sqrt{-5})</cmath><br />
and so the [[factorization]] is not unique. <br />
<br />
It can be shown that unique factorization occurs when irreducibles are necessary primes. When this is not the case, the concept can be largely recovered through the use of [[ideal|ideals]]. The general idea is to consider entities that "divide" irreducibles, for the purpose of recovering unique factorization. This may sound contrived, but in fact it is a very important idea. In the above example,<br />
<cmath>6=2 \cdot 3=(1+\sqrt{-5})(1-\sqrt{-5})</cmath><br />
we define ideals <math>\mathfrak{a}, \mathfrak{b}, \mathfrak{c}, \mathfrak{d}</math> such that<br />
<cmath>6=(\mathfrak{a} \cdot \mathfrak{b}) \cdot (\mathfrak{c} \cdot \mathfrak{d})=(\mathfrak{a} \cdot \mathfrak{c}) \cdot (\mathfrak{b} \cdot \mathfrak{d})</cmath><br />
which is not unlike writing <math>210=6 \cdot 35=14 \cdot 15</math> (or <math>210=(2 \cdot 3) \cdot (5 \cdot 7)=(2 \cdot 7) \cdot (3 \cdot 5)</math>). The usual divisibility rules - namely <math>\mathfrak{a} \mid a \implies \mathfrak{a} \mid ab</math>, <math>\mathfrak{a} \mid a, \mathfrak{a} \mid b \implies \mathfrak{a} \mid a+b</math>, <math>\mathfrak{a} \mid 0</math> - still hold for ideals. When we define <math>\mathfrak{a}, \mathfrak{b}</math> by the set of irreducibles they divide, we can extend the notion to multiplication as well:<br />
<cmath>\mathfrak{a}\mathfrak{b}=\{a_nb_m : \mathfrak{a}\mid a_n, \mathfrak{b} \mid b_m\}</cmath><br />
this recovers unique factorization, as we can write <math>a=\mathfrak{a}\mathfrak{b}\mathfrak{c}\hdots</math> for all <math>a \in A</math>. When we have to resort to this definition, <math>K</math> is a <b>principal ideal domain</b>.<br />
<br />
==The norm map==<br />
We skated over a key detail in the above section: how do we know that <math>2, 3, 1+\sqrt{-5}</math>, and <math>1-\sqrt{-5}</math> are themselves irreducibles? To show this, we use the <b>norm map</b> <math>N:\mathbb{Q}[\sqrt{-5}] \rightarrow \mathbb{Q}</math>, <math>N(a+b\sqrt{-5})=a^2+5b^2</math>. It can be shown that the [[norm]] is [[multiplicative]], and so if <math>1+\sqrt{-5}=ab</math> for some <math>a,b \in K</math>, we have <math>N(ab)=N(a)N(b)=6</math>. We can immediately discard the cases where <math>N(a)=1</math>, as this implies <math>a\overline{a}=1 \implies a</math> is a [[unit]], and we can easily verify that the other two cases do not occur. There is one final detail to process: we must show that no two of these irreducibles are <b>associates</b>; i.e. they do not differ only by [[unit|units]]. Fortunately, it is easy to verify that <math>1+\sqrt{-5}=(a+b\sqrt{-5})(1-\sqrt{-5})</math> has no solutions in <math>a,b \in \mathbb{Z}</math>.<br />
<br />
=Major results=<br />
==Quadratic reciprocity==<br />
The discovery of [[Quadratic reciprocity]] was an early success of this research, stating the impressive formula<br />
<cmath>\left(\frac{p}{q}\right)\left(\frac{q}{p}\right)=(-1)^{\frac{p-1}{2}\frac{q-1}{2}}</cmath><br />
where <math>\left(\frac{p}{q}\right)</math> is the [[Legendre symbol]], equal to 1 if <math>p</math> is a [[quadratic residue]] modulo <math>q</math> and -1 otherwise (or 0 when <math>p \equiv 0 \pmod q</math>, but this clearly does not occur for [[primes]]). In other words, unless <math>p \equiv q \equiv 3 \pmod 4</math>, <math>p</math> is a [[quadratic residue]] modulo <math>q</math> if and only if <math>q</math> is a [[quadratic residue]] modulo <math>p</math>.<br />
<br />
==Finiteness of the class number==<br />
<br />
==Dirichlet's unit theorem==</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=Algebraic_number_theory&diff=70704Algebraic number theory2015-06-09T11:29:15Z<p>BOGTRO: </p>
<hr />
<div>In [[mathematics]], <b>Algebraic number theory</b> is the study of [[algebraic numbers]] and structures involving them, especially [[algebraic number fields]]. <br />
<br />
=Introduction=<br />
Algebraic number theory is a branch of [[number theory]] that, in a nutshell, extends various properties of the [[integer|integers]] to more general [[rings]] and [[fields]]. In doing so, many questions concerning [[Diophantine equations]] are resolved, including the celebrated [[quadratic reciprocity]] theorem. More recently, the field has been linked to the theory of [[elliptic curves]], and its ideas are responsible for the successful attack on [[Fermat's Last Theorem]]. This field is extremely rich and advanced, and this article gives no more than a brief introduction.<br />
<br />
=The basics=<br />
<br />
==Motivation==<br />
Interest in the field was largely motivated by the desire to understand numbers of the form <math>x^2+ny^2</math> for some fixed, [[squarefree]] <math>n</math> (if <math>n=x^2y</math> is not [[squarefree]], the case is equivalent to <math>n=y</math>). More specifically, the question at hand was what numbers could be expressed in that form. Since <math>k=x^2+ny^2 \implies x^2 \equiv k \pmod n</math>, there was a natural connection to [[quadratic residues]] in play. In the ring of integers, this is a difficult question to analyze, but it becomes much easier when considering the [[field]] <math>Q[-\sqrt{n}]</math> because then <math>x^2+ny^2=(x+y\sqrt{-n})(x-y\sqrt{-n})</math> is the product of two elements - and the [[norm]] of one. The case of <math>n=1</math>, in particular, leads to [[factorization]] in the [[Gaussian integers]].<br />
<br />
This extension of the concept of [[factorization]] quickly spilled into other problems as well, most notably [[Fermat's Last Theorem]]. In the <math>n=3</math> case, a simple solution exists by taking <math>y^3=z^3-x^3=(z-x)(z^2+xz+z^2)</math> and using an [[infinite descent]] argument. However, this does not extend well to larger <math>n</math> because analogous factorizations contain terms of degree larger than 2. Early attempts at proof factored <math>y^p=z^p-x^p</math> into <math>y^p=\prod_{i=0}^{p-1}(z-\omega^ix)</math>, where <math>\omega</math> is a <math>p</math>th root of unity. However, though this was not well-understood at the time, the implicit assumption was that <math>\mathbb{Z}[\omega]</math> was a [[principal ideal domain]], later shown to be false. <br />
<br />
==Algebraic Numbers==<br />
An [[algebraic number]] is a number that is the root of some nonzero integer [[polynomial]] (i.e. a polynomial with integer coefficients). When that polynomial is [[monic]], the number is said to be an [[algebraic integer]]. For example, all [[rational]] numbers are algebraic integers (and thus an [[algebraic number]] as well), as the [[linear]] polynomial <math>nx-m</math> has root <math>\frac{m}{n}</math> for any [[integers]] <math>m,n</math> (with <math>n \neq 0</math>). When such a [[polynomial]] exists, it is called the <b>minimal polynomial</b> of the [[algebraic number]] in question. It can be shown that a number is an algebraic integer if and only if its minimal polynomial has integer coefficients. <br />
<br />
The sum, difference, product, and quotient of any two algebraic numbers is itself an [[algebraic number]]; as a result, the algebraic numbers form a [[field]]. In this article, <math>K</math> will denote an arbitrary [[algebraic number field]]; for example, <math>\mathbb{Q}[\sqrt{-5}]</math>, which consists of the numbers of the form <math>a+b\sqrt{-5}</math> where <math>a,b</math> are rational. As a sidenote, this shows that the sum of any two algebraic integers is itself an algebraic integer, and furthermore any [[rational]] algebraic integer is obviously also an [[integer]]. This gives an easy way to show that sums similar to <math>\sqrt{2}+\sqrt{3}+\sqrt{5}+\sqrt{7}</math> are [[irrational]] - as all of these terms are algebraic integers (they are roots of <math>x^2-k</math> for <math>k=2,3,5,7</math>), the sum is an algebraic integer as well, and so must be an [[integer]] if [[rational]]. But any old [[approximation]] is sufficient to determine that this sum is not an [[integer]], hence it is [[irrational]]. <br />
<br />
==Unique factorization==<br />
In the ring of [[integer|integers]], all numbers have unique factorizations by the [[Fundamental theorem of arithmetic]], up to multiplication by the [[unit|units]] 1 and -1. We will extend this notion to an [[integral domain]] <math>A</math>; in other words, a [[commutative ring]] in which the product of two nonzero elements is nonzero. An element <math>a \in A</math> is a [[unit]] if <math>a</math> is [[invertible]] in <math>A</math>; i.e. there exists an inverse <math>b \in A</math> such that <math>ab=ba=1</math> (where 1 is the [[multiplicative identity]]). An element <math>p \in A</math> is [[prime]] if it is not zero, not a unit, and <math>p \mid ab \implies p \mid a</math> or <math>p \mid b</math>. In a [[principal ideal domain]], any element <math>a \in A</math> can be unique factored as the product of primes, up to order and [[multiplication]] by [[unit|units]]. The first order of business is to explore when unique factorization holds.<br />
<br />
Of course, we first need to define the term <b>factorization</b>. An element <math>a \in A</math> is <b>irreducible</b> if it is not a unit and cannot be written as the product of two nonunits; obviously, [[prime]]s are irreducible (but not necessarily vice versa). A factorization of an element is its expression as a product of irreducible elements, and a ring is a <b>unique factorization domain</b> (or [[UFD]]) if this factorization is unique (up to order and multiplication by units). <br />
<br />
As previously mentioned, <math>K</math> is an arbitrary [[algebraic number field]]; as a field, factorization only makes sense in the presence of a subring. Fortunately, can be shown that the algebraic integers form a subring of <math>K</math>; however, though it can be shown that algebraic integers can always be factored, they do not generally form a [[UFD]]. For example, if <math>K=\mathbb{Q}[\sqrt{-5}]</math>, we have<br />
<cmath>6=2 \cdot 3=(1+\sqrt{-5})(1-\sqrt{-5})</cmath><br />
and so the [[factorization]] is not unique. <br />
<br />
It can be shown that unique factorization occurs when irreducibles are necessary primes. When this is not the case, the concept can be largely recovered through the use of [[ideal|ideals]]. The general idea is to consider entities that "divide" irreducibles, for the purpose of recovering unique factorization. This may sound contrived, but in fact it is a very important idea. In the above example,<br />
<cmath>6=2 \cdot 3=(1+\sqrt{-5})(1-\sqrt{-5})</cmath><br />
we define ideals <math>\mathfrak{a}, \mathfrak{b}, \mathfrak{c}, \mathfrak{d}</math> such that<br />
<cmath>6=(\mathfrak{a} \cdot \mathfrak{b}) \cdot (\mathfrak{c} \cdot \mathfrak{d})=(\mathfrak{a} \cdot \mathfrak{c}) \cdot (\mathfrak{b} \cdot \mathfrak{d})</cmath><br />
which is not unlike writing <math>210=6 \cdot 35=14 \cdot 15</math> (or <math>210=(2 \cdot 3) \cdot (5 \cdot 7)=(2 \cdot 7) \cdot (3 \cdot 5)</math>). The usual divisibility rules - namely <math>\mathfrak{a} \mid a \implies \mathfrak{a} \mid ab</math>, <math>\mathfrak{a} \mid a, \mathfrak{a} \mid b \implies \mathfrak{a} \mid a+b</math>, <math>\mathfrak{a} \mid 0</math> - still hold for ideals. When we define <math>\mathfrak{a}, \mathfrak{b}</math> by the set of irreducibles they divide, we can extend the notion to multiplication as well:<br />
<cmath>\mathfrak{a}\mathfrak{b}=\{a_nb_m : \mathfrak{a}\mid a_n, \mathfrak{b} \mid b_m\}</cmath><br />
this recovers unique factorization, as we can write <math>a=\mathfrak{a}\mathfrak{b}\mathfrak{c}\hdots</math> for all <math>a \in A</math>. When we have to resort to this definition, <math>K</math> is a <b>principal ideal domain</b>.<br />
<br />
==The norm map==<br />
We skated over a key detail in the above section: how do we know that <math>2, 3, 1+\sqrt{-5}</math>, and <math>1-\sqrt{-5}</math> are themselves irreducibles? To show this, we use the <b>norm map</b> <math>N:\mathbb{Q}[\sqrt{-5}] \rightarrow \mathbb{Q}</math>, <math>N(a+b\sqrt{-5})=a^2+5b^2</math>. It can be shown that the [[norm]] is [[multiplicative]], and so if <math>1+\sqrt{-5}=ab</math> for some <math>a,b \in K</math>, we have <math>N(ab)=N(a)N(b)=6</math>. We can immediately discard the cases where <math>N(a)=1</math>, as this implies <math>a\overline{a}=1 \implies a</math> is a [[unit]], and we can easily verify that the other two cases do not occur. There is one final detail to process: we must show that no two of these irreducibles are <b>associates</b>; i.e. they do not differ only by [[unit|units]]. Fortunately, it is easy to verify that <math>1+\sqrt{-5}=(a+b\sqrt{-5})(1-\sqrt{-5})</math> has no solutions in <math>a,b \in \mathbb{Z}</math>.<br />
<br />
=Major results=<br />
==Quadratic reciprocity==<br />
The discovery of [[Quadratic reciprocity]] was an early success of this research, stating the impressive formula<br />
<cmath>\left(\frac{p}{q}\right)\left(\frac{q}{p}\right)=(-1)^{\frac{p-1}{2}\frac{q-1}{2}}</cmath><br />
where <math>\left(\frac{p}{q}\right)</math> is the [[Legendre symbol]], equal to 1 if <math>p</math> is a [[quadratic residue]] modulo <math>q</math> and -1 otherwise (or 0 when <math>p \equiv 0 \pmod q</math>, but this clearly does not occur for [[primes]]). In other words, unless <math>p \equiv q \equiv 3 \pmod 4</math>, <math>p</math> is a [[quadratic residue]] modulo <math>q</math> if and only if <math>q</math> is a [[quadratic residue]] modulo <math>p</math>.<br />
<br />
==Finiteness of the class number==<br />
<br />
==Dirichlet's unit theorem==</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=Algebraic_number_theory&diff=70703Algebraic number theory2015-06-09T11:25:20Z<p>BOGTRO: Created page with "In mathematics, <b>Algebraic number theory</b> is the study of algebraic numbers and structures involving them, especially algebraic number fields. =Introduction..."</p>
<hr />
<div>In [[mathematics]], <b>Algebraic number theory</b> is the study of [[algebraic numbers]] and structures involving them, especially [[algebraic number fields]]. <br />
<br />
=Introduction=<br />
Algebraic number theory is a branch of [[number theory]] that, in a nutshell, extends various properties of the [[integer|integers]] to more general [[rings]] and [[fields]]. In doing so, many questions concerning [[Diophantine equations]] are resolved, including the celebrated [[quadratic reciprocity]] theorem. More recently, the field has been linked to the theory of [[elliptic curves]], and its ideas are responsible for the successful attack on [[Fermat's Last Theorem]]. This field is extremely rich and advanced, and this article gives no more than a brief introduction.<br />
<br />
=The basics=<br />
<br />
==Motivation==<br />
Interest in the field was largely motivated by the desire to understand numbers of the form <math>x^2+ny^2</math> for some fixed, [[squarefree]] <math>n</math> (if <math>n=x^2y</math> is not [[squarefree]], the case is equivalent to <math>n=y</math>). More specifically, the question at hand was what numbers could be expressed in that form. Since <math>k=x^2+ny^2 \implies x^2 \equiv k \pmod n</math>, there was a natural connection to [[quadratic residues]] in play. In the ring of integers, this is a difficult question to analyze, but it becomes much easier when considering the [[field]] <math>Q[-\sqrt{n}]</math> because then <math>x^2+ny^2=(x+y\sqrt{-n})(x-y\sqrt{-n})</math> is the product of two elements - and the [[norm]] of one. The case of <math>n=1</math>, in particular, leads to [[factorization]] in the [[Gaussian integers]].<br />
<br />
This extension of the concept of [[factorization]] quickly spilled into other problems as well, most notably [[Fermat's Last Theorem]]. In the <math>n=3</math> case, a simple solution exists by taking <math>y^3=z^3-x^3=(z-x)(z^2+xz+z^2)</math> and using an [[infinite descent]] argument. However, this does not extend well to larger <math>n</math> because analogous factorizations contain terms of degree larger than 2. Early attempts at proof factored <math>y^p=z^p-x^p</math> into <math>y^p=\prod_{i=0}^{p-1}(z-\omega^ix)</math>, where <math>\omega</math> is a <math>p</math>th root of unity. However, though this was not well-understood at the time, the implicit assumption was that <math>\mathbb{Z}[\omega]</math> was a [[principal ideal domain]], later shown to be false. <br />
<br />
==Algebraic Numbers==<br />
An [[algebraic number]] is a number that is the root of some nonzero integer [[polynomial]] (i.e. a polynomial with integer coefficients). When that polynomial is [[monic]], the number is said to be an [[algebraic integer]]. For example, all [[rational]] numbers are algebraic integers (and thus an [[algebraic number]] as well), as the [[linear]] polynomial <math>nx-m</math> has root <math>\frac{m}{n}</math> for any [[integers]] <math>m,n</math> (with <math>n \neq 0</math>). When such a [[polynomial]] exists, it is called the <b>minimal polynomial</b> of the [[algebraic number]] in question. It can be shown that a number is an algebraic integer if and only if its minimal polynomial has integer coefficients. <br />
<br />
The sum, difference, product, and quotient of any two algebraic numbers is itself an [[algebraic number]]; as a result, the algebraic numbers form a [[field]]. In this article, <math>K</math> will denote an arbitrary [[algebraic number field]]; for example, <math>\mathbb{Q}[\sqrt{-5}]</math>, which consists of the numbers of the form <math>a+b\sqrt{-5}</math> where <math>a,b</math> are rational. As a sidenote, this shows that the sum of any two algebraic integers is itself an algebraic integer, and furthermore any [[rational]] algebraic integer is obviously also an [[integer]]. This gives an easy way to show that sums similar to <math>\sqrt{2}+\sqrt{3}+\sqrt{5}+\sqrt{7}</math> are [[irrational]] - as all of these terms are algebraic integers (they are roots of <math>x^2-k</math> for <math>k=2,3,5,7</math>), the sum is an algebraic integer as well, and so must be an [[integer]] if [[rational]]. But any old [[approximation]] is sufficient to determine that this sum is not an [[integer]], hence it is [[irrational]]. <br />
<br />
==Unique factorization==<br />
In the ring of [[integer|integers]], all numbers have unique factorizations by the [[Fundamental theorem of arithmetic]], up to multiplication by the [[unit|units]] 1 and -1. We will extend this notion to an [[integral domain]] <math>A</math>; in other words, a [[commutative ring]] in which the product of two nonzero elements is nonzero. An element <math>a \in A</math> is a [[unit]] if <math>a</math> is [[invertible]] in <math>A</math>; i.e. there exists an inverse <math>b \in A</math> such that <math>ab=ba=1</math> (where 1 is the [[multiplicative identity]]). An element <math>p \in A</math> is [[prime]] if it is not zero, not a unit, and <math>p \mid ab \implies p \mid a</math> or <math>p \mid b</math>. In a [[principal ideal domain]], any element <math>a \in A</math> can be unique factored as the product of primes, up to order and [[multiplication]] by [[unit|units]]. The first order of business is to explore when unique factorization holds.<br />
<br />
Of course, we first need to define the term <b>factorization</b>. An element <math>a \in A</math> is <b>irreducible</b> if it is not a unit and cannot be written as the product of two nonunits; obviously, [[prime]]s are irreducible (but not necessarily vice versa). A factorization of an element is its expression as a product of irreducible elements, and a ring is a <b>unique factorization domain</b> (or [[UFD]]) if this factorization is unique (up to order and multiplication by units). <br />
<br />
As previously mentioned, <math>K</math> is an arbitrary [[algebraic number field]]; as a field, factorization only makes sense in the presence of a subring. Fortunately, can be shown that the algebraic integers form a subring of <math>K</math>; however, though it can be shown that algebraic integers can always be factored, they do not generally form a [[UFD]]. For example, if <math>K=\mathbb{Q}[\sqrt{-5}]</math>, we have<br />
<cmath>6=2 \cdot 3=(1+\sqrt{-5})(1-\sqrt{-5})</cmath><br />
and so the [[factorization]] is not unique. <br />
<br />
It can be shown that unique factorization occurs when irreducibles are necessary primes. When this is not the case, the concept can be largely recovered through the use of [[ideal|ideals]]. The general idea is to consider entities that "divide" irreducibles, for the purpose of recovering unique factorization. This may sound contrived, but in fact it is a very important idea. In the above example,<br />
<cmath>6=2 \cdot 3=(1+\sqrt{-5})(1-\sqrt{-5})</cmath><br />
we define ideals <math>p_1, p_2, p_3, p_4</math> such that<br />
<cmath>6=(p_1 \cdot p_2) \cdot (p_3 \cdot p_4)=(p_1 \cdot p_3) \cdot (p_2 \cdot p_4)</cmath><br />
which is not unlike writing <math>210=6 \cdot 35=14 \cdot 15</math> (or <math>210=(2 \cdot 3) \cdot (5 \cdot 7)=(2 \cdot 7) \cdot (3 \cdot 5)</math>). The usual divisibility rules - namely <math>p_i \mid a \implies p_i \mid ab</math>, <math>p_i \mid a, p_i \mid b \implies p_i \mid a+b</math>, <math>p_i \mid 0</math> - still hold for ideals. When we define <math>p_i, p_j</math> by the set of irreducibles they divide, we can extend the notion to multiplication as well:<br />
<cmath>p_ip_j=\{a_nb_m : p_i \mid a_n, p_j \mid b_m\}</cmath><br />
this recovers unique factorization, as we can write <math>a=p_1p_2\hdots p_n</math> for all <math>a \in A</math>. When we have to resort to this definition, <math>K</math> is a <b>principal ideal domain</b>.<br />
<br />
==The norm map==<br />
We skated over a key detail in the above section: how do we know that <math>2, 3, 1+\sqrt{-5}</math>, and <math>1-\sqrt{-5}</math> are themselves irreducibles? To show this, we use the <b>norm map</b> <math>N:\mathbb{Q}[\sqrt{-5}] \rightarrow \mathbb{Q}</math>, <math>N(a+b\sqrt{-5})=a^2+5b^2</math>. It can be shown that the [[norm]] is [[multiplicative]], and so if <math>1+\sqrt{-5}=ab</math> for some <math>a,b \in K</math>, we have <math>N(ab)=N(a)N(b)=6</math>. We can immediately discard the cases where <math>N(a)=1</math>, as this implies <math>a\overline{a}=1 \implies a</math> is a [[unit]], and we can easily verify that the other two cases do not occur. There is one final detail to process: we must show that no two of these irreducibles are <b>associates</b>; i.e. they do not differ only by [[unit|units]]. Fortunately, it is easy to verify that <math>1+\sqrt{-5}=(a+b\sqrt{-5})(1-\sqrt{-5})</math> has no solutions in <math>a,b \in \mathbb{Z}</math>.<br />
<br />
=Major results=<br />
==Quadratic reciprocity==<br />
The discovery of [[Quadratic reciprocity]] was an early success of this research, stating the impressive formula<br />
<cmath>\left(\frac{p}{q}\right)\left(\frac{q}{p}\right)=(-1)^{\frac{p-1}{2}\frac{q-1}{2}}</cmath><br />
where <math>\left(\frac{p}{q}\right)</math> is the [[Legendre symbol]], equal to 1 if <math>p</math> is a [[quadratic residue]] modulo <math>q</math> and -1 otherwise (or 0 when <math>p \equiv 0 \pmod q</math>, but this clearly does not occur for [[primes]]). In other words, unless <math>p \equiv q \equiv 3 \pmod 4</math>, <math>p</math> is a [[quadratic residue]] modulo <math>q</math> if and only if <math>q</math> is a [[quadratic residue]] modulo <math>p</math>.<br />
<br />
==Finiteness of the class number==<br />
<br />
==Dirichlet's unit theorem==</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=Greedy_algorithm&diff=70701Greedy algorithm2015-06-09T10:04:47Z<p>BOGTRO: Created page with "In mathematics and computer science, a <b>greedy algorithm</b> is one that selects for the maximal immediate benefit, without regard for how this selection affects fut..."</p>
<hr />
<div>In [[mathematics]] and [[computer science]], a <b>greedy algorithm</b> is one that selects for the maximal immediate benefit, without regard for how this selection affects future choices.<br />
<br />
=Introduction=<br />
As with all [[algorithm|algorithms]], greedy algorithms seek to maximize the overall utility of some process. They operate by making the immediately optimal choice at each sub-stage of the process, hoping that this will maximize the utility of the entire process. More formally, when we reframe the problem in terms of forming a [[set]] with a desired property, at each step a greedy algorithm will add the element into the [[set]] if and only it does not cause the [[set]] to lose the desired property.<br />
<br />
Greedy algorithms are among the simplest types of [[algorithm|algorithms]]; as such, they are among the first examples taught when demonstrating the subject. They have the advantage of being ruthlessly efficient, when correct, and they are usually among the most natural approaches to a problem. For this reason, they are often referred to as "naïve methods". In many cases, more complicated [[algorithm|algorithms]] are formed by adjusting the greedy process to be correct, often through the use of clever [[sorting]]. <br />
<br />
=Examples of greedy algorithms=<br />
Many real-life scenarios are good examples of greedy algorithms. For example, consider the problem of converting an arbitrary number of cents into standard coins; in other words, consider the problem of making change. The process you almost certainly follow, without consciously considering it, is first using the largest number of quarters you can, then the largest number of dimes, then nickels, then pennies. This is an example of working <b>greedily</b>: at each step, we chose the maximal immediate benefit (number of coins we could give).<br />
<br />
Some problems are not so obviously algorithmic processes. For example, the [[Rearrangement inequality]] states that if <math>(a_1, a_2, \hdots, a_n)</math> and <math>(b_1, b_2, \hdots, b_n)</math> are [[increasing sequences]], we have<br />
<cmath>a_1b_n+a_2b_{n-2}+\hdots+a_nb_1\leq a_{\sigma(1)}b_{\sigma(1)}+a_{\sigma(2)}b_{\sigma(2)}+\hdots+a_{\sigma(n)}b_{\sigma(n)} \leq a_1b_1+a_2b_2+\hdots+a_nb_n</cmath><br />
where <math>\sigma</math> denotes any [[permutation]] of <math>a</math> and <math>b</math> (so <math>\sigma(1), \sigma(2), \hdots, \sigma(n)</math> are the numbers <math>1, 2, 3, \hdots, n</math> in any order). This may have an intimidating looking statement, but it is equivalent to saying that, in the particular scenario it deals with, the greedy algorithm is the best! This is because we can view the situation algorithmically: for each of the <math>a_i</math>, we are selecting a <math>b_j</math> to pair it with - with the caveat that each <math>b_j</math> must be used exactly once. The [[Rearrangement inequality]] states that the largest <math>a_i</math> should be paired with the largest <math>b_j</math> to achieve the maximal [[dot product]]. <br />
<br />
This idea of transforming problems into algorithmic process is a very important one. Take the following example:<br />
{| class="wikitable"<br />
|-<br />
| Given a 10 by 10 grid of unit squares, what is the maximum number of squares that can be shaded such that no row and no column is completely shaded?<br />
|}<br />
The first step is to transform this into an algorithmic process, which we can do as follows: for each row, in order, shade in some (but not all) of the 10 squares. <br />
<br />
=Proving correctness=<br />
Of course, greedy algorithms are not generally very interesting unless they're <i>correct</i>; in other words, they always produce the maximal overall benefit. In order to prove the correctness of a greedy algorithm, we must show that it is never beneficial to take less than the maximal benefit at any step of the process. This is most often done by focusing on two specific steps, and showing that if the benefit of one decreases and the benefit of the other increases, the overall benefit is decreased, and so taking the maximal benefit at the first step is most beneficial.<br />
<br />
For example, let's prove the correctness of the [[rearrangement inequality]] mentioned above. Suppose we have two sequences, <math>a</math> and <math>b</math>. We now want to prove that <math>a_1b_1+a_2b_2+\hdots+a_nb_n</math> is maximized when <math>a</math> and <math>b</math> are similarly sorted; i.e. they are either both [[increasing sequence|increasing]] or both [[decreasing sequence|decreasing]]. More formally, we wish to show that the [[dot product]] <math>a \cdot b</math> is maximized when the sequences are similarly sorted. We first reformat the problem algorithmically: we consider the <math>a_i</math> in order, at each step choosing a <math>b_j</math> to pair it with.<br />
<br />
We claim that the greedy algorithm produces the best result; i.e. if <math>a_1 \geq a_2 \geq \hdots a_n</math> and <math>b_1 \geq b_2 \geq \hdots \geq b_n</math>, then <math>a_1b_1+a_2b_2+\hdots+a_nb_n</math> is the maximal possible answer. Suppose that there exists a better [[algorithm]]. Consider the <b>first</b> step <math>i</math> in which we pair <math>a_i</math> with <math>b_j</math> such that <math>i<j</math> (in other words, <math>a_i</math> is in a "higher position" than <math>b_j</math> is) - if this step didn't exist, we'd always be pairing <math>a_i</math> with <math>b_i</math>, and be done immediately. Then, at some step <math>k</math>, we pair <math>a_k</math> with <math>b_i</math> - we also know that <math>k>i</math>, since we've already done the steps where <math>k \leq i</math>.<br />
<br />
We want to show that the result of this process is no better than if we simply paired <math>a_i</math> and <math>b_i</math> (note that it is not necessary to prove that it is <i>worse</i>, only that it cannot be <i>better</i>). In other words, we need to show that <math>a_ib_j+a_kb_i\leq a_ib_i+a_kb_j</math>. But this [[factoring|factors]] nicely: we want to show <math>(a_i-a_k)(b_j-b_i)\leq 0</math>. Fortunately, this is quite easy: we know that <math>i<j</math>, so <math>b_i \geq b_j</math>, but we also know that <math>i<k</math>, so <math>a_i \geq a_k</math>. Thus <math>a_i-a_k</math> is [[nonnegative]], but <math>b_j-b_i</math> is [[nonpositive]], proving the statement.<br />
<br />
==Adjusting greedy algorithms==<br />
Of course, the immediate application of greedy algorithms does not always produce the optimal result. For example, if asked what the maximum number of elements in the set <math>\{0.6, 0.5, 0.4, 0.3, 0.2, 0.1\}</math> can be chosen with sum at most 1, a particularly naive greedy algorithm will conclude the answer is two, as it will put the <math>0.6</math> term into the "greedy [[set]]", not put the <math>0.5</math> term in, put the <math>0.4</math> term in, and put none of the remaining terms in. Obviously, this is not the correct result, as the [[set]] <math>\{0.4, 0.3, 0.2, 0.1\}</math> is much bigger and still has sum at most 1.<br />
<br />
What went wrong here is the ordering of the elements - we certainly don't want to be considering the largest elements first! Instead we should process the elements in the order of smallest to largest, and this will indeed give us the correct [[set]] (the proof is straightforward: why would we ever take a larger element when a smaller one is available?). This concept, of sorting the elements in a convenient way prior to processing, is <br />
key to all but the most basic of greedy algorithms, and much more complicated problems can be taken down using this strategy.<br />
<br />
==When greedy algorithms fail==<br />
Of course, greedy algorithms are not always the optimal process, even after adjusting the order of their processing. For example, there is no way to salvage a greedy algorithm to do the following classic problem: given the following triangle of numbers, at each step we will move either left or right, and add the number we reach to a running total. Our goal is to minimize the final total.<br />
{| class="wikitable"<br />
|-<br />
| <br />
|<br />
| * (start)<br />
|<br />
|<br />
|-<br />
|<br />
| 2<br />
|<br />
| 1<br />
|<br />
|-<br />
| 1<br />
|<br />
| over 9000<br />
|<br />
| over 9000<br />
|}<br />
<br />
Obviously, the optimal path is to go left twice - but a greedy algorithm will begin by moving to the right! This is an example of when <i>all</i> paths must be considered, and taking a shortcut by using a greedy algorithm is insufficient. As an aside, it may appear that, in the general version of this problem with <math>n</math> layers, we have to consider all <math>2^n</math> possible paths - but there is a much more clever approach to this problem, which - as a conclusion to this article - we offer as an exercise to the reader.</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=Searching_the_community&diff=70696Searching the community2015-06-08T06:00:20Z<p>BOGTRO: /* General searching tips */</p>
<hr />
<div>This article is an introduction to <b>searching</b> the [http://artofproblemsolving.com/community AoPS forums]. All searching takes place from one of three pages: the [http://artofproblemsolving.com/community main webpage], any of the specific forums, or from the [http://artofproblemsolving.com/community/search dedicated webpage]. <br />
=Searching methods=<br />
==Searching from the community==<br />
[[Image:search.png|thumb|right|300px|Searching from the community page]]<br />
<br />
The first of these two options is shown in the image to the right. It is primarily useful for quickly searching, especially when the search is of a general nature and without a specific post in mind. The method is simple: simply type your query into the "Search Community" field, click the magnifying glass (or press the Enter key), and posts containing terms matching your query will be shown to you. The parts of the posts that match your query will be <span style="background:yellow"> highlighted in yellow</span>. For example, when searching for problems involving a [[circle]], one would simply type "[[circle]]" into the indicated field, getting a result similar to the following image:<br />
<br />
[[Image:searchresult.png|thumb|right|300px|Result of searching "[[circle]]"]]<br />
<br />
Clicking on any of these results will open the full topic in which the post was made, starting from the post you clicked on. For example, if the post you clicked on was the fourth post in its topic, you would originally see that post and could scroll up (or down) to see the rest of the topic.<br />
<br />
If these are not the results you were looking for, you can click the "Edit search settings" link in the top right corner to adjust your search parameters. <br />
<br />
==Searching from a forum==<br />
<br />
It is possible to initiate a search from a specific forum, using the toolbar on its header. This will limit the search results to posts in that forum. <br />
<br />
[[Image:searchforum.png|thumb|right|500px|The header of a forum]]<br />
<br />
To search from a forum, click the magnifying glass on its header (see image to the right). This will redirect you to the main search webpage, with the forum information already filled in. <br />
<br />
==Searching from the main webpage==<br />
<br />
[[Image:search2.png|thumbnail|left|300px|Searching from the [http://artofproblemsolving.com/community/search webpage]]]<br />
<br />
This page can be reached in three ways: by clicking on the "Advanced search" button under the quick-search option shown above, through the Community drop-down menu, or directly through the link http://artofproblemsolving.com/community/search. Compared to the other options, the [http://artofproblemsolving.com/community/search webpage] gives you significantly more ways to customize your search. There are five different fields to be filled in, but any of them can be left blank. For example, to search for all posts by [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk] made within the last year, the "search term" and "Posted In forum" fields should be left blank, but the other fields should be filled out with the appropriate information. It is even possible to leave every field blank, in which case the search results will mimic the [[global feed]]. The five fields are:<br />
<br />
{| class="wikitable"<br />
|+ Search fields<br />
|-<br />
! Field<br />
! Function<br />
|-<br />
| Search term<br />
| Fairly self-explanatory: enter the term(s) that you are searching for. Note that titles, tags, posts, and sources are all simultaneously searched. To search these separately, click the indicated option. It is possible to search different places for different terms simultaneously; for example, to search for [[AMC]] problems using [[Simon's Favorite Factoring Trick]], search for posts containing "[[SFFT]]" in topics with source containing "[[AMC]]". The indicated option will also allow you the choice of restricting your search to opening posts. This field is blank by default, indicating that all posts are searched regardless of content.<br />
<br />
Searching for multiple terms will return posts matching at least one of those terms, prioritizing posts "closer" to the query as a whole. See the following section for ways to further customize these queries. Note that it is also possible to search for multiple tags, which will return posts under at least one of those tags.<br />
|-<br />
| Posted By User<br />
| Enter the name(s) of user(s) to restrict your search to. The search results will only contain posts posted by the user(s) you entered. Note that the posters of the original <i>topics</i> may be different from the users you enter here. You can also search by user ID instead of username, if you happen to know the ID of the user you are searching for (you can find this in their profile URL, which is of the form artofproblemsolving.com/community/user/<user ID>). Users entered must be valid users and will be authenticated prior to searching. This field is blank by default, indicating that posts by all users are searched.<br />
|-<br />
| Posted In Forum<br />
| Enter the name(s) of forum(s) to restrict your search to. The search results will only contain posts posted in the forum(s) you entered. If you reached this webpage through clicking on the magnifying glass in one of the forums, this field will be pre-populated with that forum. Forums entered must be valid forums and will be authenticated prior to searching. This field is blank by default, indicating that all forums are searched.<br />
<br />
Note: On the previous website, forums were associated with a unique ID that could be used in searching, similar to user ID numbers, but this is no longer the case; type in the name of the forum instead.<br />
|-<br />
| Dates<br />
| Select the timeframe in which posts you're searching for must have been made. The options are "Any" (default), "During the last 24 hours", "During the last week", "During the last month", "During the last year", or any manually entered date range.<br />
|-<br />
| Sorting<br />
| Select whether to sort results by "Relevance" (default), "Newest first", or "Oldest first". If "relevance" is selected, the posts will be sorted according to a scoring algorithm that approximates how well a post correlates to the search query. The other two options, "Newest first" and "Oldest first", are self-explanatory.<br />
|}<br />
<br />
[[Image:rrusczykposts.png|thumb|right|400px|Posts by rrusczyk in the last year]]<br />
For example, to search for the aforementioned posts made by [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk] within the last year, the "Search term" field should be blank, the "Posted by User" field should contain [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk], the "Posted in Forum" field should be blank, the "Dates" field should be set to "During the last year", and the "Sorting" field can be set according to how the searcher wishes the results to be presented. The image to the right shows how this search looks on the webpage.<br />
[[Image:rrusczykposts2.png|thumb|left|400px|Topics started by rrusczyk in the last year]] To search instead for <i>topics</i> that [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk] has started within the last year, the steps are the same, except that the "search only the first post of each topic" option should be selected. To reach that option, click first on the "Click here to search titles, posts, sources, and tags separately" text, then check the box indicated. The image on the left shows how this search looks on the webpage. Of course, in both searches it is possible to further narrow the results by including the forum it was posted in, text that should be present in returned posts, and so on. It is also possible to expand the search to posts by [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk] and [http://artofproblemsolving.com/community/user/copeland copeland], or even [http://artofproblemsolving.com/community/q2h581792p3437787 posts] <i>by</i> [http://artofproblemsolving.com/community/user/copeland copeland] <i>about</i> [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk].<br />
<br />
=Getting the most out of search=<br />
==Searching for a specific post==<br />
One of the most common uses of search is to find a specific post that you remember some details about, but cannot find. For example, you might recall having once read a particularly well-written solution, a very nice question, or an important announcement, but you can't remember quite where you saw it before. How frustrating!<br />
<br />
Obviously, the more details you remember about the post, the more likely you are to find it. If you remember that, for example, the post was written sometime in the summer of 2013, you can set the date range from (for example) May to September of that year. If you remember the author, that narrows down the possibilities significantly, but even remembering that it was one of several authors is a good way to whittle the possibilities down. Finally, remembering the forum that it was posted in would be excellent, but even if you only vaguely remember the post, you can make some educated guesses. For example, if the post was about a new and exciting technique for the [[USAMO]], it was probably posted in either the [http://artofproblemsolving.com/community/c5_contests_amp_programs Contests & Programs] forum or the [http://artofproblemsolving.com/community/c6_high_school_olympiads High School Olympiads] forum. If the post was a collection of [[MATHCOUNTS]] strategies, it's almost certainly in [http://artofproblemsolving.com/community/c3_middle_school_math Middle School Math]. <br />
<br />
==General searching tips==<br />
<br />
Of course, the above strategies are helpful, but still leave a lot of posts to sift through - unless you remember some of the language used in the post. You might remember, for example, a particularly memorable phrase in the post, or perhaps they used a math problem as reference that you remember a bit about. In these cases,<br />
<ul><br />
<li>Include, in your search query, unusual or uncommon words. For example, searching for just the word "[[circumcenter]]", along with the tips in the previous section, narrows down the possibilities significantly</li><br />
<li>Avoid common words such as "a", "the", "of", and so on, even if you remember a word-for-word phrase from the post containing these words. You'll get bogged down in posts matching those words - which there are a lot of!</li><br />
<li>Avoid searching words that are contained within another common word, as they will get matched to words you certainly didn't intend. For example, search queries containing the word "in" might return results for "logg<b>in</b>g", "<b>In</b>equality", and so on. The word "a" is particularly guilty of this, as it often returns words containing the letter "a".</li><br />
<li>Be sure to avoid searching for words that are special modifiers - see the below section. In particular, avoid searches containing the words "and" and "not". Similarly, do not include quotes ("), asterisks (*), question marks (?), plus signs (+), minus signs (-), or parentheses as these all represent special commands.<br />
<li> Search engines in general are not very good at searching for mathematical symbols or numbers, so you are generally better off searching for text instead. For example, searching the text of a problem rather than equations or expressions is likely to produce better results.<br />
</ul><br />
<br />
For example, if you remember a post contained the phrase "the three [[perpendicular bisector|perpendicular bisectors]] of a [[triangle]] intersect at the [[circumcenter]]", your search query should be something similar to "[[perpendicular bisector|perpendicular bisectors]] intersect [[circumcenter]]", as these are all specific words that limit the number of posts returned (unlike words like "of", "a", "the", and "at").<br />
<br />
==Customizing search queries==<br />
<br />
We've already mentioned that posts are matched to the search query using a scoring algorithm, which approximates how "close" a post is to the given query. However, especially when searching for multiple terms, this algorithm often weights certain factors in different ways than the user intended. As such, there are several ways to customize your search queries.<br />
<br />
{| class="wikitable"<br />
|+ Customizing search queries<br />
|-<br />
| Operator<br />
| Example<br />
| Result<br />
|-<br />
| <i>(no adjustment)</i> <br />
| incenter circumcenter<br />
| Returns posts containing the word "[[incenter]]" and/or the word "[[circumcenter]]", with higher weight given to posts containing both.<br />
|-<br />
| +<br />
| +incenter circumcenter<br />
| Returned posts <b>must</b> contain the word "[[incenter]]", but may or may not contain "[[circumcenter]]". Again, higher weight is given to posts containing both words.<br />
|-<br />
| -<br />
| -incenter circumcenter excenter<br />
| Returned posts <b>must not</b> contain the word "[[incenter]]". Returned posts will contain the word "[[circumcenter]]" and/or the word "[[excenter]]", with higher weight given to posts containing both.<br />
|-<br />
| AND<br />
| incenter AND circumcenter<br />
| Returned posts <b>must</b> contain <i>both</i> "[[incenter]]" and "[[circumcenter]]". This is equivalent to the query "+incenter +circumcenter".<br />
|-<br />
| NOT<br />
| incenter NOT circumcenter<br />
| Returned posts will contain "[[incenter]]", but will <b>not</b> contain "[[circumcenter]]". Equivalent to the "-" and "!" operators.<br />
|-<br />
| "" (quotes)<br />
| "incenter circumcenter"<br />
| Returns posts containing the phrase "[[incenter]] [[circumcenter]]". Punctuation is usually ignored in results, so posts containing "[[incenter]], [[circumcenter]]" or "[[incenter]]-[[circumcenter]]" will also be returned.<br />
|-<br />
| ? and *<br />
| te?t, inc*, in*e<br />
| Wildcard symbols. The ? symbol allows any character to replace it, so posts containing the words "test" or "text" will match the query "te?t". The * symbol allows any number of characters to replace it, so posts containing the words "[[incenter]]", "[[incircle]]", "[[inclusive]]", etc. will match the query "inc*". The * symbol can also be used in the middle of a word, so posts containing the words "interface", "[[incircle]]", "intermediate", "[[infinite]]", etc. will all match the query "in*e". <br />
|-<br />
| () (parentheses)<br />
| incenter AND (circumcenter OR excenter)<br />
| Grouping symbols to allow one boolean command (e.g. AND, NOT, +, -, !) to modify multiple elements. The example returns posts that contain both "[[incenter]]" and at least one of "[[circumcenter]]" or "[[excenter]]". Equivalent to the query (incenter AND circumcenter) OR (incenter AND excenter) ([[Boolean]] logic applies to search strings).<br />
|-<br />
| \ <br />
| \AND<br />
| An "escape" character that allows you to search for reserved keywords and symbols. For example, the above query will return posts containing the word "and". Without the escape character, the search engine would parse the query "AND" as a command linking two nonexistent terms, and would thus throw an error. Similarly, the search term "[[incenter]] \AND [[circumcenter]]" would include results containing the word "[[incenter]]" and the word "and", but not the word "[[circumcenter]]".<br />
<br />
Note: in order to search for terms containing backslashes, such as LaTeX commands, the somewhat non-intuitive \\ is necessary (the first backslash "escapes" the second one). <br />
|}<br />
<br />
Note that, when using search modifiers, the <span style="background:yellow"> yellow background</span> indicating words that match your query will not generally be entirely accurate; for example, searching for "[[incenter]] AND [[circumcenter]]" will return posts containing both words as expected, but the word "and" will also be highlighted. Don't get confused by this - the search engine is still searching according to your query (and is not searching for the word "and"), the highlighting is simply slightly misleading.<br />
<br />
=Searching for LaTeX and Asympotote=<br />
<br />
Searching for [[LaTeX]] or [[Asymptote]] can be complicated, as they are their own languages, but this can actually be a big advantage! Predicting what code they've used is usually quite easy, and since the keywords are generally quite unique, searching for them will often narrow results down to posts using [[LaTeX]]/[[Asymptote]] themselves. Below are some common commands that [[LaTeX]]/[[Asymptote]] users often use, to help you search for them.<br />
<br />
==Searching for LaTeX==<br />
[[LaTeX]] is a programming language for rendering mathematical statements, and is very popular on [[AoPS]] (and other mathematical sources). [[LaTeX]] commands are enclosed in dollar signs for rendering, but you should not generally include those while searching. If you are searching for "full" commands (e.g. \frac{1}{2}), it is highly recommended that you enclose the entire command with quotation marks (e.g. "\\frac{1}{2}"; recall double backslash is needed), as otherwise it may parse as three different search terms (\frac, 1, and 2).<br />
<br />
{| class="wikitable"<br />
|+ Common LaTeX commands<br />
| Command<br />
| Use<br />
| Example<br />
| Rendered<br />
|-<br />
| \frac<br />
| Creates fractions<br />
| \frac{1}{2}<br />
| <math>\frac{1}{2}</math><br />
|-<br />
| \sqrt<br />
| Creates square (or, more generally, <math>n</math>th) roots<br />
| \sqrt{3}, \sqrt[3]{3}<br />
| <math>\sqrt{3}</math>, <math>\sqrt[3]{3}</math><br />
|-<br />
| \leq, \neq, \geq<br />
| Less than or equal to, not equal to, greater than or equal to (respectively)<br />
| a \leq b, a \neq b, a \geq b<br />
| <math>a \leq b, a \neq b, a \geq b</math><br />
|-<br />
| \alpha<br />
| Renders greek letters (most often alpha, beta, epsilon, pi, theta, phi, and omega)<br />
| \alpha+\beta=\pi-\epsilon<br />
| <math>\alpha+\beta=\pi-\epsilon</math><br />
|-<br />
|\rightarrow, \implies, \iff<br />
| Used for implication, algorithms, etc.<br />
| a>b \implies a^2>b^2, a>b \iff a-b>0, A\rightarrow A+1<br />
| <math>a>b \implies a^2>b^2, a>b \iff a-b>0, A\rightarrow A+1</math><br />
|-<br />
|\sum, \prod, \int<br />
|Used for summation, product, and integration symbols<br />
|\sum_1^5 x=15, \prod_1^5x=120, \int_1^5x=12<br />
|<math>\sum_1^5 x=15, \prod_1^5x=120, \int_1^5x=12</math><br />
|}<br />
<br />
See [[LaTeX:Symbols]] for a more comprehensive list of LaTeX commands, and use the [http://artofproblemsolving.com/texer/ TeXeR] to test how commands look when rendered.<br />
<br />
==Searching for Asymptote==<br />
[[Asymptote (Vector Graphics Language)|Asymptote]] is a programming language for creating diagrams. Unlike [[LaTeX]], dollar signs are not necessary, and [[Asymptote (Vector Graphics Language)|Asymptote]] code is enclosed in [asy] tags. [[Asymptote (Vector Graphics Language)|Asymptote]] commands take the form of most modern programming languages; lines are generally of the form <i>command(param1, param2, ...)</i> (this is different from TeX, where each parameter is enclosed in separate brackets). <br />
<br />
"Unfortunately" (for our purposes), most [[Asymptote (Vector Graphics Language)|Asymptote]] commands are simply the word-for-word descriptors of their function; for example, the command that returns the [[midpoint]] of a path is simply "[[midpoint]]", and the command that returns the [[circumcenter]] of a triangle is "[[circumcenter]]". This is further complicated by the usage of [[variable|variables]], the names of which are entirely up to the posters (unlike TeX, in which [[variable|variables]] are generally not used). Below are commonly used [[Asymptote (Vector Graphics Language)|Asymptote]] commands that are not actual words, so they are less likely to be confused with other posts during searching.<br />
<br />
{| class="wikitable"<br />
|+ Common [[Asymptote (Vector Graphics Language)|Asymptote]] commands<br />
| Command<br />
| Purpose<br />
| Command<br />
| Purpose<br />
|-<br />
| defaultpen<br />
| Adjusts the default settings for the pen. Very likely for this command to be in an [[Asymptote (Vector Graphics Language)|Asymptote]] drawing.<br />
| orthographic<br />
| Adjust the "camera position" in [[dimension|3-D]] drawings. Very likely for this command to be in a [[dimension|3-D]] [[Asymptote (Vector Graphics Language)|Asymptote]] drawing.<br />
|-<br />
| filldraw<br />
| Colors a given shape in some manner. Useful for shading in parts of diagrams; used reasonably foten.<br />
| unitsize<br />
| Sets the default size of a "unit" to a specified value. Default is very small. Not used particularly often because defaultpen is more general.<br />
|-<br />
| intersectionpoint<br />
| Determines the [[intersection]] (if there is exactly one) of two [[path|paths]]. Very useful command, and thus in many drawings.<br />
| intersectionpoints<br />
| Determine all the intersections of two [[path|paths]]. Obviously very similar to the previous command, but slightly less used as we generally want to know the intersection point of lines (rather than arbitrary paths).<br />
|-<br />
| rightanglemark<br />
| Marks a given [[angle]] as [[right angle|right]]. Used, obviously, in diagrams containing [[right angle|right angles]]; there are many of these.<br />
| anglemark<br />
| Marks a given [[angle]] with a given value. Used surprisingly little, since directly marking [[angle|angles]] isn't generally that important, but angle chase solutions will make heavy use of it.<br />
|-<br />
| linewidth<br />
| Sets the (visual -- [[line|lines]] have no real [[width]]!) [[width]] of a [[line]]. Also little used because defaultpen is more general.<br />
| currentpicture<br />
| A reference to the current picture. Used as an auxiliary command in other commands. This is the default value, so it is used only in very complicated drawings (or as a formality/copied and pasted sections).<br />
|}<br />
<br />
Note that simply searching "asy" will generally turn up [[Asymptote (Vector Graphics Language)|Asymptote]] drawings or discussions of such; especially when combined with a username or date range, simply remembering a post had any [[Asymptote (Vector Graphics Language)|Asymptote]] in it whatsoever is usually a good way to find it. As [[Asymptote (Vector Graphics Language)|Asymptote]] becomes more and more popular, the previous statement will become less true ([[LaTeX]], for example, is in a huge number of posts these days), but for now the numbers are small enough that you can sift through them pretty quickly.</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=Searching_the_community&diff=70695Searching the community2015-06-08T05:52:48Z<p>BOGTRO: /* Searching from the main webpage */</p>
<hr />
<div>This article is an introduction to <b>searching</b> the [http://artofproblemsolving.com/community AoPS forums]. All searching takes place from one of three pages: the [http://artofproblemsolving.com/community main webpage], any of the specific forums, or from the [http://artofproblemsolving.com/community/search dedicated webpage]. <br />
=Searching methods=<br />
==Searching from the community==<br />
[[Image:search.png|thumb|right|300px|Searching from the community page]]<br />
<br />
The first of these two options is shown in the image to the right. It is primarily useful for quickly searching, especially when the search is of a general nature and without a specific post in mind. The method is simple: simply type your query into the "Search Community" field, click the magnifying glass (or press the Enter key), and posts containing terms matching your query will be shown to you. The parts of the posts that match your query will be <span style="background:yellow"> highlighted in yellow</span>. For example, when searching for problems involving a [[circle]], one would simply type "[[circle]]" into the indicated field, getting a result similar to the following image:<br />
<br />
[[Image:searchresult.png|thumb|right|300px|Result of searching "[[circle]]"]]<br />
<br />
Clicking on any of these results will open the full topic in which the post was made, starting from the post you clicked on. For example, if the post you clicked on was the fourth post in its topic, you would originally see that post and could scroll up (or down) to see the rest of the topic.<br />
<br />
If these are not the results you were looking for, you can click the "Edit search settings" link in the top right corner to adjust your search parameters. <br />
<br />
==Searching from a forum==<br />
<br />
It is possible to initiate a search from a specific forum, using the toolbar on its header. This will limit the search results to posts in that forum. <br />
<br />
[[Image:searchforum.png|thumb|right|500px|The header of a forum]]<br />
<br />
To search from a forum, click the magnifying glass on its header (see image to the right). This will redirect you to the main search webpage, with the forum information already filled in. <br />
<br />
==Searching from the main webpage==<br />
<br />
[[Image:search2.png|thumbnail|left|300px|Searching from the [http://artofproblemsolving.com/community/search webpage]]]<br />
<br />
This page can be reached in three ways: by clicking on the "Advanced search" button under the quick-search option shown above, through the Community drop-down menu, or directly through the link http://artofproblemsolving.com/community/search. Compared to the other options, the [http://artofproblemsolving.com/community/search webpage] gives you significantly more ways to customize your search. There are five different fields to be filled in, but any of them can be left blank. For example, to search for all posts by [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk] made within the last year, the "search term" and "Posted In forum" fields should be left blank, but the other fields should be filled out with the appropriate information. It is even possible to leave every field blank, in which case the search results will mimic the [[global feed]]. The five fields are:<br />
<br />
{| class="wikitable"<br />
|+ Search fields<br />
|-<br />
! Field<br />
! Function<br />
|-<br />
| Search term<br />
| Fairly self-explanatory: enter the term(s) that you are searching for. Note that titles, tags, posts, and sources are all simultaneously searched. To search these separately, click the indicated option. It is possible to search different places for different terms simultaneously; for example, to search for [[AMC]] problems using [[Simon's Favorite Factoring Trick]], search for posts containing "[[SFFT]]" in topics with source containing "[[AMC]]". The indicated option will also allow you the choice of restricting your search to opening posts. This field is blank by default, indicating that all posts are searched regardless of content.<br />
<br />
Searching for multiple terms will return posts matching at least one of those terms, prioritizing posts "closer" to the query as a whole. See the following section for ways to further customize these queries. Note that it is also possible to search for multiple tags, which will return posts under at least one of those tags.<br />
|-<br />
| Posted By User<br />
| Enter the name(s) of user(s) to restrict your search to. The search results will only contain posts posted by the user(s) you entered. Note that the posters of the original <i>topics</i> may be different from the users you enter here. You can also search by user ID instead of username, if you happen to know the ID of the user you are searching for (you can find this in their profile URL, which is of the form artofproblemsolving.com/community/user/<user ID>). Users entered must be valid users and will be authenticated prior to searching. This field is blank by default, indicating that posts by all users are searched.<br />
|-<br />
| Posted In Forum<br />
| Enter the name(s) of forum(s) to restrict your search to. The search results will only contain posts posted in the forum(s) you entered. If you reached this webpage through clicking on the magnifying glass in one of the forums, this field will be pre-populated with that forum. Forums entered must be valid forums and will be authenticated prior to searching. This field is blank by default, indicating that all forums are searched.<br />
<br />
Note: On the previous website, forums were associated with a unique ID that could be used in searching, similar to user ID numbers, but this is no longer the case; type in the name of the forum instead.<br />
|-<br />
| Dates<br />
| Select the timeframe in which posts you're searching for must have been made. The options are "Any" (default), "During the last 24 hours", "During the last week", "During the last month", "During the last year", or any manually entered date range.<br />
|-<br />
| Sorting<br />
| Select whether to sort results by "Relevance" (default), "Newest first", or "Oldest first". If "relevance" is selected, the posts will be sorted according to a scoring algorithm that approximates how well a post correlates to the search query. The other two options, "Newest first" and "Oldest first", are self-explanatory.<br />
|}<br />
<br />
[[Image:rrusczykposts.png|thumb|right|400px|Posts by rrusczyk in the last year]]<br />
For example, to search for the aforementioned posts made by [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk] within the last year, the "Search term" field should be blank, the "Posted by User" field should contain [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk], the "Posted in Forum" field should be blank, the "Dates" field should be set to "During the last year", and the "Sorting" field can be set according to how the searcher wishes the results to be presented. The image to the right shows how this search looks on the webpage.<br />
[[Image:rrusczykposts2.png|thumb|left|400px|Topics started by rrusczyk in the last year]] To search instead for <i>topics</i> that [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk] has started within the last year, the steps are the same, except that the "search only the first post of each topic" option should be selected. To reach that option, click first on the "Click here to search titles, posts, sources, and tags separately" text, then check the box indicated. The image on the left shows how this search looks on the webpage. Of course, in both searches it is possible to further narrow the results by including the forum it was posted in, text that should be present in returned posts, and so on. It is also possible to expand the search to posts by [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk] and [http://artofproblemsolving.com/community/user/copeland copeland], or even [http://artofproblemsolving.com/community/q2h581792p3437787 posts] <i>by</i> [http://artofproblemsolving.com/community/user/copeland copeland] <i>about</i> [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk].<br />
<br />
=Getting the most out of search=<br />
==Searching for a specific post==<br />
One of the most common uses of search is to find a specific post that you remember some details about, but cannot find. For example, you might recall having once read a particularly well-written solution, a very nice question, or an important announcement, but you can't remember quite where you saw it before. How frustrating!<br />
<br />
Obviously, the more details you remember about the post, the more likely you are to find it. If you remember that, for example, the post was written sometime in the summer of 2013, you can set the date range from (for example) May to September of that year. If you remember the author, that narrows down the possibilities significantly, but even remembering that it was one of several authors is a good way to whittle the possibilities down. Finally, remembering the forum that it was posted in would be excellent, but even if you only vaguely remember the post, you can make some educated guesses. For example, if the post was about a new and exciting technique for the [[USAMO]], it was probably posted in either the [http://artofproblemsolving.com/community/c5_contests_amp_programs Contests & Programs] forum or the [http://artofproblemsolving.com/community/c6_high_school_olympiads High School Olympiads] forum. If the post was a collection of [[MATHCOUNTS]] strategies, it's almost certainly in [http://artofproblemsolving.com/community/c3_middle_school_math Middle School Math]. <br />
<br />
==General searching tips==<br />
<br />
Of course, the above strategies are helpful, but still leave a lot of posts to sift through - unless you remember some of the language used in the post. You might remember, for example, a particularly memorable phrase in the post, or perhaps they used a math problem as reference that you remember a bit about. In these cases,<br />
<ul><br />
<li>Include, in your search query, unusual or uncommon words. For example, searching for just the word "[[circumcenter]]", along with the tips in the previous section, narrows down the possibilities significantly</li><br />
<li>Avoid common words such as "a", "the", "of", and so on, even if you remember a word-for-word phrase from the post containing these words. You'll get bogged down in posts matching those words - which there are a lot of!</li><br />
<li>Avoid searching words that are contained within another common word, as they will get matched to words you certainly didn't intend. For example, search queries containing the word "in" might return results for "logg<b>in</b>g", "<b>In</b>equality", and so on. The word "a" is particularly guilty of this, as it often returns words containing the letter "a".</li><br />
<li>Be sure to avoid searching for words that are special modifiers - see the below section. In particular, avoid searches containing the words "and" and "not". Similarly, do not include quotes ("), asterisks (*), question marks (?), plus signs (+), minus signs (-), or parentheses as these all represent special commands.<br />
</ul><br />
<br />
For example, if you remember a post contained the phrase "the three [[perpendicular bisector|perpendicular bisectors]] of a [[triangle]] intersect at the [[circumcenter]]", your search query should be something similar to "[[perpendicular bisector|perpendicular bisectors]] intersect [[circumcenter]]", as these are all specific words that limit the number of posts returned (unlike words like "of", "a", "the", and "at"). <br />
<br />
==Customizing search queries==<br />
<br />
We've already mentioned that posts are matched to the search query using a scoring algorithm, which approximates how "close" a post is to the given query. However, especially when searching for multiple terms, this algorithm often weights certain factors in different ways than the user intended. As such, there are several ways to customize your search queries.<br />
<br />
{| class="wikitable"<br />
|+ Customizing search queries<br />
|-<br />
| Operator<br />
| Example<br />
| Result<br />
|-<br />
| <i>(no adjustment)</i> <br />
| incenter circumcenter<br />
| Returns posts containing the word "[[incenter]]" and/or the word "[[circumcenter]]", with higher weight given to posts containing both.<br />
|-<br />
| +<br />
| +incenter circumcenter<br />
| Returned posts <b>must</b> contain the word "[[incenter]]", but may or may not contain "[[circumcenter]]". Again, higher weight is given to posts containing both words.<br />
|-<br />
| -<br />
| -incenter circumcenter excenter<br />
| Returned posts <b>must not</b> contain the word "[[incenter]]". Returned posts will contain the word "[[circumcenter]]" and/or the word "[[excenter]]", with higher weight given to posts containing both.<br />
|-<br />
| AND<br />
| incenter AND circumcenter<br />
| Returned posts <b>must</b> contain <i>both</i> "[[incenter]]" and "[[circumcenter]]". This is equivalent to the query "+incenter +circumcenter".<br />
|-<br />
| NOT<br />
| incenter NOT circumcenter<br />
| Returned posts will contain "[[incenter]]", but will <b>not</b> contain "[[circumcenter]]". Equivalent to the "-" and "!" operators.<br />
|-<br />
| "" (quotes)<br />
| "incenter circumcenter"<br />
| Returns posts containing the phrase "[[incenter]] [[circumcenter]]". Punctuation is usually ignored in results, so posts containing "[[incenter]], [[circumcenter]]" or "[[incenter]]-[[circumcenter]]" will also be returned.<br />
|-<br />
| ? and *<br />
| te?t, inc*, in*e<br />
| Wildcard symbols. The ? symbol allows any character to replace it, so posts containing the words "test" or "text" will match the query "te?t". The * symbol allows any number of characters to replace it, so posts containing the words "[[incenter]]", "[[incircle]]", "[[inclusive]]", etc. will match the query "inc*". The * symbol can also be used in the middle of a word, so posts containing the words "interface", "[[incircle]]", "intermediate", "[[infinite]]", etc. will all match the query "in*e". <br />
|-<br />
| () (parentheses)<br />
| incenter AND (circumcenter OR excenter)<br />
| Grouping symbols to allow one boolean command (e.g. AND, NOT, +, -, !) to modify multiple elements. The example returns posts that contain both "[[incenter]]" and at least one of "[[circumcenter]]" or "[[excenter]]". Equivalent to the query (incenter AND circumcenter) OR (incenter AND excenter) ([[Boolean]] logic applies to search strings).<br />
|-<br />
| \ <br />
| \AND<br />
| An "escape" character that allows you to search for reserved keywords and symbols. For example, the above query will return posts containing the word "and". Without the escape character, the search engine would parse the query "AND" as a command linking two nonexistent terms, and would thus throw an error. Similarly, the search term "[[incenter]] \AND [[circumcenter]]" would include results containing the word "[[incenter]]" and the word "and", but not the word "[[circumcenter]]".<br />
<br />
Note: in order to search for terms containing backslashes, such as LaTeX commands, the somewhat non-intuitive \\ is necessary (the first backslash "escapes" the second one). <br />
|}<br />
<br />
Note that, when using search modifiers, the <span style="background:yellow"> yellow background</span> indicating words that match your query will not generally be entirely accurate; for example, searching for "[[incenter]] AND [[circumcenter]]" will return posts containing both words as expected, but the word "and" will also be highlighted. Don't get confused by this - the search engine is still searching according to your query (and is not searching for the word "and"), the highlighting is simply slightly misleading.<br />
<br />
=Searching for LaTeX and Asympotote=<br />
<br />
Searching for [[LaTeX]] or [[Asymptote]] can be complicated, as they are their own languages, but this can actually be a big advantage! Predicting what code they've used is usually quite easy, and since the keywords are generally quite unique, searching for them will often narrow results down to posts using [[LaTeX]]/[[Asymptote]] themselves. Below are some common commands that [[LaTeX]]/[[Asymptote]] users often use, to help you search for them.<br />
<br />
==Searching for LaTeX==<br />
[[LaTeX]] is a programming language for rendering mathematical statements, and is very popular on [[AoPS]] (and other mathematical sources). [[LaTeX]] commands are enclosed in dollar signs for rendering, but you should not generally include those while searching. If you are searching for "full" commands (e.g. \frac{1}{2}), it is highly recommended that you enclose the entire command with quotation marks (e.g. "\\frac{1}{2}"; recall double backslash is needed), as otherwise it may parse as three different search terms (\frac, 1, and 2).<br />
<br />
{| class="wikitable"<br />
|+ Common LaTeX commands<br />
| Command<br />
| Use<br />
| Example<br />
| Rendered<br />
|-<br />
| \frac<br />
| Creates fractions<br />
| \frac{1}{2}<br />
| <math>\frac{1}{2}</math><br />
|-<br />
| \sqrt<br />
| Creates square (or, more generally, <math>n</math>th) roots<br />
| \sqrt{3}, \sqrt[3]{3}<br />
| <math>\sqrt{3}</math>, <math>\sqrt[3]{3}</math><br />
|-<br />
| \leq, \neq, \geq<br />
| Less than or equal to, not equal to, greater than or equal to (respectively)<br />
| a \leq b, a \neq b, a \geq b<br />
| <math>a \leq b, a \neq b, a \geq b</math><br />
|-<br />
| \alpha<br />
| Renders greek letters (most often alpha, beta, epsilon, pi, theta, phi, and omega)<br />
| \alpha+\beta=\pi-\epsilon<br />
| <math>\alpha+\beta=\pi-\epsilon</math><br />
|-<br />
|\rightarrow, \implies, \iff<br />
| Used for implication, algorithms, etc.<br />
| a>b \implies a^2>b^2, a>b \iff a-b>0, A\rightarrow A+1<br />
| <math>a>b \implies a^2>b^2, a>b \iff a-b>0, A\rightarrow A+1</math><br />
|-<br />
|\sum, \prod, \int<br />
|Used for summation, product, and integration symbols<br />
|\sum_1^5 x=15, \prod_1^5x=120, \int_1^5x=12<br />
|<math>\sum_1^5 x=15, \prod_1^5x=120, \int_1^5x=12</math><br />
|}<br />
<br />
See [[LaTeX:Symbols]] for a more comprehensive list of LaTeX commands, and use the [http://artofproblemsolving.com/texer/ TeXeR] to test how commands look when rendered.<br />
<br />
==Searching for Asymptote==<br />
[[Asymptote (Vector Graphics Language)|Asymptote]] is a programming language for creating diagrams. Unlike [[LaTeX]], dollar signs are not necessary, and [[Asymptote (Vector Graphics Language)|Asymptote]] code is enclosed in [asy] tags. [[Asymptote (Vector Graphics Language)|Asymptote]] commands take the form of most modern programming languages; lines are generally of the form <i>command(param1, param2, ...)</i> (this is different from TeX, where each parameter is enclosed in separate brackets). <br />
<br />
"Unfortunately" (for our purposes), most [[Asymptote (Vector Graphics Language)|Asymptote]] commands are simply the word-for-word descriptors of their function; for example, the command that returns the [[midpoint]] of a path is simply "[[midpoint]]", and the command that returns the [[circumcenter]] of a triangle is "[[circumcenter]]". This is further complicated by the usage of [[variable|variables]], the names of which are entirely up to the posters (unlike TeX, in which [[variable|variables]] are generally not used). Below are commonly used [[Asymptote (Vector Graphics Language)|Asymptote]] commands that are not actual words, so they are less likely to be confused with other posts during searching.<br />
<br />
{| class="wikitable"<br />
|+ Common [[Asymptote (Vector Graphics Language)|Asymptote]] commands<br />
| Command<br />
| Purpose<br />
| Command<br />
| Purpose<br />
|-<br />
| defaultpen<br />
| Adjusts the default settings for the pen. Very likely for this command to be in an [[Asymptote (Vector Graphics Language)|Asymptote]] drawing.<br />
| orthographic<br />
| Adjust the "camera position" in [[dimension|3-D]] drawings. Very likely for this command to be in a [[dimension|3-D]] [[Asymptote (Vector Graphics Language)|Asymptote]] drawing.<br />
|-<br />
| filldraw<br />
| Colors a given shape in some manner. Useful for shading in parts of diagrams; used reasonably foten.<br />
| unitsize<br />
| Sets the default size of a "unit" to a specified value. Default is very small. Not used particularly often because defaultpen is more general.<br />
|-<br />
| intersectionpoint<br />
| Determines the [[intersection]] (if there is exactly one) of two [[path|paths]]. Very useful command, and thus in many drawings.<br />
| intersectionpoints<br />
| Determine all the intersections of two [[path|paths]]. Obviously very similar to the previous command, but slightly less used as we generally want to know the intersection point of lines (rather than arbitrary paths).<br />
|-<br />
| rightanglemark<br />
| Marks a given [[angle]] as [[right angle|right]]. Used, obviously, in diagrams containing [[right angle|right angles]]; there are many of these.<br />
| anglemark<br />
| Marks a given [[angle]] with a given value. Used surprisingly little, since directly marking [[angle|angles]] isn't generally that important, but angle chase solutions will make heavy use of it.<br />
|-<br />
| linewidth<br />
| Sets the (visual -- [[line|lines]] have no real [[width]]!) [[width]] of a [[line]]. Also little used because defaultpen is more general.<br />
| currentpicture<br />
| A reference to the current picture. Used as an auxiliary command in other commands. This is the default value, so it is used only in very complicated drawings (or as a formality/copied and pasted sections).<br />
|}<br />
<br />
Note that simply searching "asy" will generally turn up [[Asymptote (Vector Graphics Language)|Asymptote]] drawings or discussions of such; especially when combined with a username or date range, simply remembering a post had any [[Asymptote (Vector Graphics Language)|Asymptote]] in it whatsoever is usually a good way to find it. As [[Asymptote (Vector Graphics Language)|Asymptote]] becomes more and more popular, the previous statement will become less true ([[LaTeX]], for example, is in a huge number of posts these days), but for now the numbers are small enough that you can sift through them pretty quickly.</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=Searching_the_community&diff=70694Searching the community2015-06-08T05:47:48Z<p>BOGTRO: </p>
<hr />
<div>This article is an introduction to <b>searching</b> the [http://artofproblemsolving.com/community AoPS forums]. All searching takes place from one of three pages: the [http://artofproblemsolving.com/community main webpage], any of the specific forums, or from the [http://artofproblemsolving.com/community/search dedicated webpage]. <br />
=Searching methods=<br />
==Searching from the community==<br />
[[Image:search.png|thumb|right|300px|Searching from the community page]]<br />
<br />
The first of these two options is shown in the image to the right. It is primarily useful for quickly searching, especially when the search is of a general nature and without a specific post in mind. The method is simple: simply type your query into the "Search Community" field, click the magnifying glass (or press the Enter key), and posts containing terms matching your query will be shown to you. The parts of the posts that match your query will be <span style="background:yellow"> highlighted in yellow</span>. For example, when searching for problems involving a [[circle]], one would simply type "[[circle]]" into the indicated field, getting a result similar to the following image:<br />
<br />
[[Image:searchresult.png|thumb|right|300px|Result of searching "[[circle]]"]]<br />
<br />
Clicking on any of these results will open the full topic in which the post was made, starting from the post you clicked on. For example, if the post you clicked on was the fourth post in its topic, you would originally see that post and could scroll up (or down) to see the rest of the topic.<br />
<br />
If these are not the results you were looking for, you can click the "Edit search settings" link in the top right corner to adjust your search parameters. <br />
<br />
==Searching from a forum==<br />
<br />
It is possible to initiate a search from a specific forum, using the toolbar on its header. This will limit the search results to posts in that forum. <br />
<br />
[[Image:searchforum.png|thumb|right|500px|The header of a forum]]<br />
<br />
To search from a forum, click the magnifying glass on its header (see image to the right). This will redirect you to the main search webpage, with the forum information already filled in. <br />
<br />
==Searching from the main webpage==<br />
<br />
[[Image:search2.png|thumbnail|left|300px|Searching from the [http://artofproblemsolving.com/community/search webpage]]]<br />
<br />
This page can be reached in three ways: by clicking on the "Advanced search" button under the quick-search option shown above, through the Community drop-down menu, or directly through the link http://artofproblemsolving.com/community/search. Compared to the other options, the [http://artofproblemsolving.com/community/search webpage] gives you significantly more ways to customize your search. There are five different fields to be filled in, but any of them can be left blank. For example, to search for all posts by [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk] made within the last year, the "search term" and "Posted In forum" fields should be left blank, but the other fields should be filled out with the appropriate information. It is even possible to leave every field blank, in which case the search results will mimic the [[global feed]]. The five fields are:<br />
<br />
{| class="wikitable"<br />
|+ Search fields<br />
|-<br />
! Field<br />
! Function<br />
|-<br />
| Search term<br />
| Fairly self-explanatory: enter the term(s) that you are searching for. Note that titles, tags, posts, and sources are all simultaneously searched. To search these separately, click the indicated option. It is possible to search different places for different terms simultaneously; for example, to search for [[AMC]] problems using [[Simon's Favorite Factoring Trick]], search for posts containing "[[SFFT]]" in topics with source containing "[[AMC]]". The indicated option will also allow you the choice of restricting your search to opening posts. This field is blank by default, indicating that all posts are searched regardless of content.<br />
<br />
Searching for multiple terms will return posts matching at least one of those terms, prioritizing posts "closer" to the query as a whole. See the following section for ways to further customize these queries.<br />
|-<br />
| Posted By User<br />
| Enter the name(s) of user(s) to restrict your search to. The search results will only contain posts posted by the user(s) you entered. Note that the posters of the original <i>topics</i> may be different from the users you enter here. You can also search by user ID instead of username, if you happen to know the ID of the user you are searching for (you can find this in their profile URL, which is of the form artofproblemsolving.com/community/user/<user ID>). Users entered must be valid users and will be authenticated prior to searching. This field is blank by default, indicating that posts by all users are searched.<br />
|-<br />
| Posted In Forum<br />
| Enter the name(s) of forum(s) to restrict your search to. The search results will only contain posts posted in the forum(s) you entered. If you reached this webpage through clicking on the magnifying glass in one of the forums, this field will be pre-populated with that forum. Forums entered must be valid forums and will be authenticated prior to searching. This field is blank by default, indicating that all forums are searched.<br />
<br />
Note: On the previous website, forums were associated with a unique ID that could be used in searching, similar to user ID numbers, but this is no longer the case; type in the name of the forum instead.<br />
|-<br />
| Dates<br />
| Select the timeframe in which posts you're searching for must have been made. The options are "Any" (default), "During the last 24 hours", "During the last week", "During the last month", "During the last year", or any manually entered date range.<br />
|-<br />
| Sorting<br />
| Select whether to sort results by "Relevance" (default), "Newest first", or "Oldest first". If "relevance" is selected, the posts will be sorted according to a scoring algorithm that approximates how well a post correlates to the search query. The other two options, "Newest first" and "Oldest first", are self-explanatory.<br />
|}<br />
<br />
[[Image:rrusczykposts.png|thumb|right|400px|Posts by rrusczyk in the last year]]<br />
For example, to search for the aforementioned posts made by [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk] within the last year, the "Search term" field should be blank, the "Posted by User" field should contain [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk], the "Posted in Forum" field should be blank, the "Dates" field should be set to "During the last year", and the "Sorting" field can be set according to how the searcher wishes the results to be presented. The image to the right shows how this search looks on the webpage.<br />
[[Image:rrusczykposts2.png|thumb|left|400px|Topics started by rrusczyk in the last year]] To search instead for <i>topics</i> that [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk] has started within the last year, the steps are the same, except that the "search only the first post of each topic" option should be selected. To reach that option, click first on the "Click here to search titles, posts, sources, and tags separately" text, then check the box indicated. The image on the left shows how this search looks on the webpage. Of course, in both searches it is possible to further narrow the results by including the forum it was posted in, text that should be present in returned posts, and so on. It is also possible to expand the search to posts by [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk] and [http://artofproblemsolving.com/community/user/copeland copeland], or even [http://artofproblemsolving.com/community/q2h581792p3437787 posts] <i>by</i> [http://artofproblemsolving.com/community/user/copeland copeland] <i>about</i> [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk].<br />
<br />
=Getting the most out of search=<br />
==Searching for a specific post==<br />
One of the most common uses of search is to find a specific post that you remember some details about, but cannot find. For example, you might recall having once read a particularly well-written solution, a very nice question, or an important announcement, but you can't remember quite where you saw it before. How frustrating!<br />
<br />
Obviously, the more details you remember about the post, the more likely you are to find it. If you remember that, for example, the post was written sometime in the summer of 2013, you can set the date range from (for example) May to September of that year. If you remember the author, that narrows down the possibilities significantly, but even remembering that it was one of several authors is a good way to whittle the possibilities down. Finally, remembering the forum that it was posted in would be excellent, but even if you only vaguely remember the post, you can make some educated guesses. For example, if the post was about a new and exciting technique for the [[USAMO]], it was probably posted in either the [http://artofproblemsolving.com/community/c5_contests_amp_programs Contests & Programs] forum or the [http://artofproblemsolving.com/community/c6_high_school_olympiads High School Olympiads] forum. If the post was a collection of [[MATHCOUNTS]] strategies, it's almost certainly in [http://artofproblemsolving.com/community/c3_middle_school_math Middle School Math]. <br />
<br />
==General searching tips==<br />
<br />
Of course, the above strategies are helpful, but still leave a lot of posts to sift through - unless you remember some of the language used in the post. You might remember, for example, a particularly memorable phrase in the post, or perhaps they used a math problem as reference that you remember a bit about. In these cases,<br />
<ul><br />
<li>Include, in your search query, unusual or uncommon words. For example, searching for just the word "[[circumcenter]]", along with the tips in the previous section, narrows down the possibilities significantly</li><br />
<li>Avoid common words such as "a", "the", "of", and so on, even if you remember a word-for-word phrase from the post containing these words. You'll get bogged down in posts matching those words - which there are a lot of!</li><br />
<li>Avoid searching words that are contained within another common word, as they will get matched to words you certainly didn't intend. For example, search queries containing the word "in" might return results for "logg<b>in</b>g", "<b>In</b>equality", and so on. The word "a" is particularly guilty of this, as it often returns words containing the letter "a".</li><br />
<li>Be sure to avoid searching for words that are special modifiers - see the below section. In particular, avoid searches containing the words "and" and "not". Similarly, do not include quotes ("), asterisks (*), question marks (?), plus signs (+), minus signs (-), or parentheses as these all represent special commands.<br />
</ul><br />
<br />
For example, if you remember a post contained the phrase "the three [[perpendicular bisector|perpendicular bisectors]] of a [[triangle]] intersect at the [[circumcenter]]", your search query should be something similar to "[[perpendicular bisector|perpendicular bisectors]] intersect [[circumcenter]]", as these are all specific words that limit the number of posts returned (unlike words like "of", "a", "the", and "at"). <br />
<br />
==Customizing search queries==<br />
<br />
We've already mentioned that posts are matched to the search query using a scoring algorithm, which approximates how "close" a post is to the given query. However, especially when searching for multiple terms, this algorithm often weights certain factors in different ways than the user intended. As such, there are several ways to customize your search queries.<br />
<br />
{| class="wikitable"<br />
|+ Customizing search queries<br />
|-<br />
| Operator<br />
| Example<br />
| Result<br />
|-<br />
| <i>(no adjustment)</i> <br />
| incenter circumcenter<br />
| Returns posts containing the word "[[incenter]]" and/or the word "[[circumcenter]]", with higher weight given to posts containing both.<br />
|-<br />
| +<br />
| +incenter circumcenter<br />
| Returned posts <b>must</b> contain the word "[[incenter]]", but may or may not contain "[[circumcenter]]". Again, higher weight is given to posts containing both words.<br />
|-<br />
| -<br />
| -incenter circumcenter excenter<br />
| Returned posts <b>must not</b> contain the word "[[incenter]]". Returned posts will contain the word "[[circumcenter]]" and/or the word "[[excenter]]", with higher weight given to posts containing both.<br />
|-<br />
| AND<br />
| incenter AND circumcenter<br />
| Returned posts <b>must</b> contain <i>both</i> "[[incenter]]" and "[[circumcenter]]". This is equivalent to the query "+incenter +circumcenter".<br />
|-<br />
| NOT<br />
| incenter NOT circumcenter<br />
| Returned posts will contain "[[incenter]]", but will <b>not</b> contain "[[circumcenter]]". Equivalent to the "-" and "!" operators.<br />
|-<br />
| "" (quotes)<br />
| "incenter circumcenter"<br />
| Returns posts containing the phrase "[[incenter]] [[circumcenter]]". Punctuation is usually ignored in results, so posts containing "[[incenter]], [[circumcenter]]" or "[[incenter]]-[[circumcenter]]" will also be returned.<br />
|-<br />
| ? and *<br />
| te?t, inc*, in*e<br />
| Wildcard symbols. The ? symbol allows any character to replace it, so posts containing the words "test" or "text" will match the query "te?t". The * symbol allows any number of characters to replace it, so posts containing the words "[[incenter]]", "[[incircle]]", "[[inclusive]]", etc. will match the query "inc*". The * symbol can also be used in the middle of a word, so posts containing the words "interface", "[[incircle]]", "intermediate", "[[infinite]]", etc. will all match the query "in*e". <br />
|-<br />
| () (parentheses)<br />
| incenter AND (circumcenter OR excenter)<br />
| Grouping symbols to allow one boolean command (e.g. AND, NOT, +, -, !) to modify multiple elements. The example returns posts that contain both "[[incenter]]" and at least one of "[[circumcenter]]" or "[[excenter]]". Equivalent to the query (incenter AND circumcenter) OR (incenter AND excenter) ([[Boolean]] logic applies to search strings).<br />
|-<br />
| \ <br />
| \AND<br />
| An "escape" character that allows you to search for reserved keywords and symbols. For example, the above query will return posts containing the word "and". Without the escape character, the search engine would parse the query "AND" as a command linking two nonexistent terms, and would thus throw an error. Similarly, the search term "[[incenter]] \AND [[circumcenter]]" would include results containing the word "[[incenter]]" and the word "and", but not the word "[[circumcenter]]".<br />
<br />
Note: in order to search for terms containing backslashes, such as LaTeX commands, the somewhat non-intuitive \\ is necessary (the first backslash "escapes" the second one). <br />
|}<br />
<br />
Note that, when using search modifiers, the <span style="background:yellow"> yellow background</span> indicating words that match your query will not generally be entirely accurate; for example, searching for "[[incenter]] AND [[circumcenter]]" will return posts containing both words as expected, but the word "and" will also be highlighted. Don't get confused by this - the search engine is still searching according to your query (and is not searching for the word "and"), the highlighting is simply slightly misleading.<br />
<br />
=Searching for LaTeX and Asympotote=<br />
<br />
Searching for [[LaTeX]] or [[Asymptote]] can be complicated, as they are their own languages, but this can actually be a big advantage! Predicting what code they've used is usually quite easy, and since the keywords are generally quite unique, searching for them will often narrow results down to posts using [[LaTeX]]/[[Asymptote]] themselves. Below are some common commands that [[LaTeX]]/[[Asymptote]] users often use, to help you search for them.<br />
<br />
==Searching for LaTeX==<br />
[[LaTeX]] is a programming language for rendering mathematical statements, and is very popular on [[AoPS]] (and other mathematical sources). [[LaTeX]] commands are enclosed in dollar signs for rendering, but you should not generally include those while searching. If you are searching for "full" commands (e.g. \frac{1}{2}), it is highly recommended that you enclose the entire command with quotation marks (e.g. "\\frac{1}{2}"; recall double backslash is needed), as otherwise it may parse as three different search terms (\frac, 1, and 2).<br />
<br />
{| class="wikitable"<br />
|+ Common LaTeX commands<br />
| Command<br />
| Use<br />
| Example<br />
| Rendered<br />
|-<br />
| \frac<br />
| Creates fractions<br />
| \frac{1}{2}<br />
| <math>\frac{1}{2}</math><br />
|-<br />
| \sqrt<br />
| Creates square (or, more generally, <math>n</math>th) roots<br />
| \sqrt{3}, \sqrt[3]{3}<br />
| <math>\sqrt{3}</math>, <math>\sqrt[3]{3}</math><br />
|-<br />
| \leq, \neq, \geq<br />
| Less than or equal to, not equal to, greater than or equal to (respectively)<br />
| a \leq b, a \neq b, a \geq b<br />
| <math>a \leq b, a \neq b, a \geq b</math><br />
|-<br />
| \alpha<br />
| Renders greek letters (most often alpha, beta, epsilon, pi, theta, phi, and omega)<br />
| \alpha+\beta=\pi-\epsilon<br />
| <math>\alpha+\beta=\pi-\epsilon</math><br />
|-<br />
|\rightarrow, \implies, \iff<br />
| Used for implication, algorithms, etc.<br />
| a>b \implies a^2>b^2, a>b \iff a-b>0, A\rightarrow A+1<br />
| <math>a>b \implies a^2>b^2, a>b \iff a-b>0, A\rightarrow A+1</math><br />
|-<br />
|\sum, \prod, \int<br />
|Used for summation, product, and integration symbols<br />
|\sum_1^5 x=15, \prod_1^5x=120, \int_1^5x=12<br />
|<math>\sum_1^5 x=15, \prod_1^5x=120, \int_1^5x=12</math><br />
|}<br />
<br />
See [[LaTeX:Symbols]] for a more comprehensive list of LaTeX commands, and use the [http://artofproblemsolving.com/texer/ TeXeR] to test how commands look when rendered.<br />
<br />
==Searching for Asymptote==<br />
[[Asymptote (Vector Graphics Language)|Asymptote]] is a programming language for creating diagrams. Unlike [[LaTeX]], dollar signs are not necessary, and [[Asymptote (Vector Graphics Language)|Asymptote]] code is enclosed in [asy] tags. [[Asymptote (Vector Graphics Language)|Asymptote]] commands take the form of most modern programming languages; lines are generally of the form <i>command(param1, param2, ...)</i> (this is different from TeX, where each parameter is enclosed in separate brackets). <br />
<br />
"Unfortunately" (for our purposes), most [[Asymptote (Vector Graphics Language)|Asymptote]] commands are simply the word-for-word descriptors of their function; for example, the command that returns the [[midpoint]] of a path is simply "[[midpoint]]", and the command that returns the [[circumcenter]] of a triangle is "[[circumcenter]]". This is further complicated by the usage of [[variable|variables]], the names of which are entirely up to the posters (unlike TeX, in which [[variable|variables]] are generally not used). Below are commonly used [[Asymptote (Vector Graphics Language)|Asymptote]] commands that are not actual words, so they are less likely to be confused with other posts during searching.<br />
<br />
{| class="wikitable"<br />
|+ Common [[Asymptote (Vector Graphics Language)|Asymptote]] commands<br />
| Command<br />
| Purpose<br />
| Command<br />
| Purpose<br />
|-<br />
| defaultpen<br />
| Adjusts the default settings for the pen. Very likely for this command to be in an [[Asymptote (Vector Graphics Language)|Asymptote]] drawing.<br />
| orthographic<br />
| Adjust the "camera position" in [[dimension|3-D]] drawings. Very likely for this command to be in a [[dimension|3-D]] [[Asymptote (Vector Graphics Language)|Asymptote]] drawing.<br />
|-<br />
| filldraw<br />
| Colors a given shape in some manner. Useful for shading in parts of diagrams; used reasonably foten.<br />
| unitsize<br />
| Sets the default size of a "unit" to a specified value. Default is very small. Not used particularly often because defaultpen is more general.<br />
|-<br />
| intersectionpoint<br />
| Determines the [[intersection]] (if there is exactly one) of two [[path|paths]]. Very useful command, and thus in many drawings.<br />
| intersectionpoints<br />
| Determine all the intersections of two [[path|paths]]. Obviously very similar to the previous command, but slightly less used as we generally want to know the intersection point of lines (rather than arbitrary paths).<br />
|-<br />
| rightanglemark<br />
| Marks a given [[angle]] as [[right angle|right]]. Used, obviously, in diagrams containing [[right angle|right angles]]; there are many of these.<br />
| anglemark<br />
| Marks a given [[angle]] with a given value. Used surprisingly little, since directly marking [[angle|angles]] isn't generally that important, but angle chase solutions will make heavy use of it.<br />
|-<br />
| linewidth<br />
| Sets the (visual -- [[line|lines]] have no real [[width]]!) [[width]] of a [[line]]. Also little used because defaultpen is more general.<br />
| currentpicture<br />
| A reference to the current picture. Used as an auxiliary command in other commands. This is the default value, so it is used only in very complicated drawings (or as a formality/copied and pasted sections).<br />
|}<br />
<br />
Note that simply searching "asy" will generally turn up [[Asymptote (Vector Graphics Language)|Asymptote]] drawings or discussions of such; especially when combined with a username or date range, simply remembering a post had any [[Asymptote (Vector Graphics Language)|Asymptote]] in it whatsoever is usually a good way to find it. As [[Asymptote (Vector Graphics Language)|Asymptote]] becomes more and more popular, the previous statement will become less true ([[LaTeX]], for example, is in a huge number of posts these days), but for now the numbers are small enough that you can sift through them pretty quickly.</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=Searching_the_community&diff=70693Searching the community2015-06-08T05:29:59Z<p>BOGTRO: /* Customizing search queries */</p>
<hr />
<div>This article is an introduction to <b>searching</b> the [http://artofproblemsolving.com/community AoPS forums]. All searching takes place from one of three pages: the [http://artofproblemsolving.com/community main webpage], any of the specific forums, or from the [http://artofproblemsolving.com/community/search dedicated webpage]. <br />
=Searching methods=<br />
==Searching from the community==<br />
[[Image:search.png|thumb|right|300px|Searching from the community page]]<br />
<br />
The first of these two options is shown in the image to the right. It is primarily useful for quickly searching, especially when the search is of a general nature and without a specific post in mind. The method is simple: simply type your query into the "Search Community" field, click the magnifying glass (or press the Enter key), and posts containing terms matching your query will be shown to you. The parts of the posts that match your query will be <span style="background:yellow"> highlighted in yellow</span>. For example, when searching for problems involving a [[circle]], one would simply type "[[circle]]" into the indicated field, getting a result similar to the following image:<br />
<br />
[[Image:searchresult.png|thumb|right|300px|Result of searching "[[circle]]"]]<br />
<br />
Clicking on any of these results will open the full topic in which the post was made, starting from the post you clicked on. For example, if the post you clicked on was the fourth post in its topic, you would originally see that post and could scroll up (or down) to see the rest of the topic.<br />
<br />
If these are not the results you were looking for, you can click the "Edit search settings" link in the top right corner to adjust your search parameters. <br />
<br />
==Searching from a forum==<br />
<br />
It is possible to initiate a search from a specific forum, using the toolbar on its header. This will limit the search results to posts in that forum. <br />
<br />
[[Image:searchforum.png|thumb|right|500px|The header of a forum]]<br />
<br />
To search from a forum, click the magnifying glass on its header (see image to the right). This will redirect you to the main search webpage, with the forum information already filled in. <br />
<br />
==Searching from the main webpage==<br />
<br />
[[Image:search2.png|thumbnail|left|300px|Searching from the [http://artofproblemsolving.com/community/search webpage]]]<br />
<br />
This page can be reached in three ways: by clicking on the "Advanced search" button under the quick-search option shown above, through the Community drop-down menu, or directly through the link http://artofproblemsolving.com/community/search. Compared to the other options, the [http://artofproblemsolving.com/community/search webpage] gives you significantly more ways to customize your search. There are five different fields to be filled in, but any of them can be left blank. For example, to search for all posts by [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk] made within the last year, the "search term" and "Posted In forum" fields should be left blank, but the other fields should be filled out with the appropriate information. It is even possible to leave every field blank, in which case the search results will mimic the [[global feed]]. The five fields are:<br />
<br />
{| class="wikitable"<br />
|+ Search fields<br />
|-<br />
! Field<br />
! Function<br />
|-<br />
| Search term<br />
| Fairly self-explanatory: enter the term(s) that you are searching for. Note that titles, tags, posts, and sources are all simultaneously searched. To search these separately, click the indicated option. It is possible to search different places for different terms simultaneously; for example, to search for [[AMC]] problems using [[Simon's Favorite Factoring Trick]], search for posts containing "[[SFFT]]" in topics with source containing "[[AMC]]". The indicated option will also allow you the choice of restricting your search to opening posts. This field is blank by default, indicating that all posts are searched regardless of content.<br />
<br />
Searching for multiple terms will return posts matching at least one of those terms, prioritizing posts "closer" to the query as a whole. See the following section for ways to further customize these queries.<br />
|-<br />
| Posted By User<br />
| Enter the name(s) of user(s) to restrict your search to. The search results will only contain posts posted by the user(s) you entered. Note that the posters of the original <i>topics</i> may be different from the users you enter here. You can also search by user ID instead of username, if you happen to know the ID of the user you are searching for (you can find this in their profile URL, which is of the form artofproblemsolving.com/community/user/<user ID>). Users entered must be valid users and will be authenticated prior to searching. This field is blank by default, indicating that posts by all users are searched.<br />
|-<br />
| Posted In Forum<br />
| Enter the name(s) of forum(s) to restrict your search to. The search results will only contain posts posted in the forum(s) you entered. If you reached this webpage through clicking on the magnifying glass in one of the forums, this field will be pre-populated with that forum. Forums entered must be valid forums and will be authenticated prior to searching. This field is blank by default, indicating that all forums are searched.<br />
<br />
Note: On the previous website, forums were associated with a unique ID that could be used in searching, similar to user ID numbers, but this is no longer the case; type in the name of the forum instead.<br />
|-<br />
| Dates<br />
| Select the timeframe in which posts you're searching for must have been made. The options are "Any" (default), "During the last 24 hours", "During the last week", "During the last month", "During the last year", or any manually entered date range.<br />
|-<br />
| Sorting<br />
| Select whether to sort results by "Relevance" (default), "Newest first", or "Oldest first". If "relevance" is selected, the posts will be sorted according to a scoring algorithm that approximates how well a post correlates to the search query. The other two options, "Newest first" and "Oldest first", are self-explanatory.<br />
|}<br />
<br />
For example, to search for the aforementioned posts made by [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk] within the last year, the "Search term" field should be blank, the "Posted by User" field should contain [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk], the "Posted in Forum" field should be blank, the "Dates" field should be set to "During the last year", and the "Sorting" field can be set according to how the searcher wishes the results to be presented. To search for topics that [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk] has started within the last year, the steps are the same, except that the "search only the first post of each topic" should be selected. See the images below.<br />
<br />
[[Image:rrusczykposts.png|thumb||530px|Posts by rrusczyk in the last year]]<br />
[[Image:rrusczykposts2.png|thumb|left|420px|Topics started by rrusczyk in the last year]]<br />
<br />
=Getting the most out of search=<br />
==Searching for a specific post==<br />
One of the most common uses of search is to find a specific post that you remember some details about, but cannot find. For example, you might recall having once read a particularly well-written solution, a very nice question, or an important announcement, but you can't remember quite where you saw it before. How frustrating!<br />
<br />
Obviously, the more details you remember about the post, the more likely you are to find it. If you remember that, for example, the post was written sometime in the summer of 2013, you can set the date range from (for example) May to September of that year. If you remember the author, that narrows down the possibilities significantly, but even remembering that it was one of several authors is a good way to whittle the possibilities down. Finally, remembering the forum that it was posted in would be excellent, but even if you only vaguely remember the post, you can make some educated guesses. For example, if the post was about a new and exciting technique for the [[USAMO]], it was probably posted in either the [http://artofproblemsolving.com/community/c5_contests_amp_programs Contests & Programs] forum or the [http://artofproblemsolving.com/community/c6_high_school_olympiads High School Olympiads] forum. If the post was a collection of [[MATHCOUNTS]] strategies, it's almost certainly in [http://artofproblemsolving.com/community/c3_middle_school_math Middle School Math]. <br />
<br />
==General searching tips==<br />
<br />
Of course, the above strategies are helpful, but still leave a lot of posts to sift through - unless you remember some of the language used in the post. You might remember, for example, a particularly memorable phrase in the post, or perhaps they used a math problem as reference that you remember a bit about. In these cases,<br />
<ul><br />
<li>Include, in your search query, unusual or uncommon words. For example, searching for just the word "[[circumcenter]]", along with the tips in the previous section, narrows down the possibilities significantly</li><br />
<li>Avoid common words such as "a", "the", "of", and so on, even if you remember a word-for-word phrase from the post containing these words. You'll get bogged down in posts matching those words - which there are a lot of!</li><br />
<li>Avoid searching words that are contained within another common word, as they will get matched to words you certainly didn't intend. For example, search queries containing the word "in" might return results for "logg<b>in</b>g", "<b>In</b>equality", and so on. The word "a" is particularly guilty of this, as it often returns words containing the letter "a".</li><br />
<li>Be sure to avoid searching for words that are special modifiers - see the below section. In particular, avoid searches containing the words "and" and "not". Similarly, do not include quotes ("), asterisks (*), question marks (?), plus signs (+), minus signs (-), or parentheses as these all represent special commands.<br />
</ul><br />
<br />
For example, if you remember a post contained the phrase "the three [[perpendicular bisector|perpendicular bisectors]] of a [[triangle]] intersect at the [[circumcenter]]", your search query should be something similar to "[[perpendicular bisector|perpendicular bisectors]] intersect [[circumcenter]]", as these are all specific words that limit the number of posts returned (unlike words like "of", "a", "the", and "at"). <br />
<br />
==Customizing search queries==<br />
<br />
We've already mentioned that posts are matched to the search query using a scoring algorithm, which approximates how "close" a post is to the given query. However, especially when searching for multiple terms, this algorithm often weights certain factors in different ways than the user intended. As such, there are several ways to customize your search queries.<br />
<br />
{| class="wikitable"<br />
|+ Customizing search queries<br />
|-<br />
| Operator<br />
| Example<br />
| Result<br />
|-<br />
| <i>(no adjustment)</i> <br />
| incenter circumcenter<br />
| Returns posts containing the word "[[incenter]]" and/or the word "[[circumcenter]]", with higher weight given to posts containing both.<br />
|-<br />
| +<br />
| +incenter circumcenter<br />
| Returned posts <b>must</b> contain the word "[[incenter]]", but may or may not contain "[[circumcenter]]". Again, higher weight is given to posts containing both words.<br />
|-<br />
| -<br />
| -incenter circumcenter excenter<br />
| Returned posts <b>must not</b> contain the word "[[incenter]]". Returned posts will contain the word "[[circumcenter]]" and/or the word "[[excenter]]", with higher weight given to posts containing both.<br />
|-<br />
| AND<br />
| incenter AND circumcenter<br />
| Returned posts <b>must</b> contain <i>both</i> "[[incenter]]" and "[[circumcenter]]". This is equivalent to the query "+incenter +circumcenter".<br />
|-<br />
| NOT<br />
| incenter NOT circumcenter<br />
| Returned posts will contain "[[incenter]]", but will <b>not</b> contain "[[circumcenter]]". Equivalent to the "-" and "!" operators.<br />
|-<br />
| "" (quotes)<br />
| "incenter circumcenter"<br />
| Returns posts containing the phrase "[[incenter]] [[circumcenter]]". Punctuation is usually ignored in results, so posts containing "[[incenter]], [[circumcenter]]" or "[[incenter]]-[[circumcenter]]" will also be returned.<br />
|-<br />
| ? and *<br />
| te?t, inc*, in*e<br />
| Wildcard symbols. The ? symbol allows any character to replace it, so posts containing the words "test" or "text" will match the query "te?t". The * symbol allows any number of characters to replace it, so posts containing the words "[[incenter]]", "[[incircle]]", "[[inclusive]]", etc. will match the query "inc*". The * symbol can also be used in the middle of a word, so posts containing the words "interface", "[[incircle]]", "intermediate", "[[infinite]]", etc. will all match the query "in*e". <br />
|-<br />
| () (parentheses)<br />
| incenter AND (circumcenter OR excenter)<br />
| Grouping symbols to allow one boolean command (e.g. AND, NOT, +, -, !) to modify multiple elements. The example returns posts that contain both "[[incenter]]" and at least one of "[[circumcenter]]" or "[[excenter]]". Equivalent to the query (incenter AND circumcenter) OR (incenter AND excenter) ([[Boolean]] logic applies to search strings).<br />
|-<br />
| \ <br />
| \AND<br />
| An "escape" character that allows you to search for reserved keywords and symbols. For example, the above query will return posts containing the word "and". Without the escape character, the search engine would parse the query "AND" as a command linking two nonexistent terms, and would thus throw an error. Similarly, the search term "[[incenter]] \AND [[circumcenter]]" would include results containing the word "[[incenter]]" and the word "and", but not the word "[[circumcenter]]".<br />
<br />
Note: in order to search for terms containing backslashes, such as LaTeX commands, the somewhat non-intuitive \\ is necessary (the first backslash "escapes" the second one). <br />
|}<br />
<br />
Note that, when using search modifiers, the <span style="background:yellow"> yellow background</span> indicating words that match your query will not generally be entirely accurate; for example, searching for "[[incenter]] AND [[circumcenter]]" will return posts containing both words as expected, but the word "and" will also be highlighted. Don't get confused by this - the search engine is still searching according to your query (and is not searching for the word "and"), the highlighting is simply slightly misleading.<br />
<br />
=Searching for LaTeX and Asympotote=<br />
<br />
Searching for [[LaTeX]] or [[Asymptote]] can be complicated, as they are their own languages, but this can actually be a big advantage! Predicting what code they've used is usually quite easy, and since the keywords are generally quite unique, searching for them will often narrow results down to posts using [[LaTeX]]/[[Asymptote]] themselves. Below are some common commands that [[LaTeX]]/[[Asymptote]] users often use, to help you search for them.<br />
<br />
==Searching for LaTeX==<br />
[[LaTeX]] is a programming language for rendering mathematical statements, and is very popular on [[AoPS]] (and other mathematical sources). [[LaTeX]] commands are enclosed in dollar signs for rendering, but you should not generally include those while searching. If you are searching for "full" commands (e.g. \frac{1}{2}), it is highly recommended that you enclose the entire command with quotation marks (e.g. "\\frac{1}{2}"; recall double backslash is needed), as otherwise it may parse as three different search terms (\frac, 1, and 2).<br />
<br />
{| class="wikitable"<br />
|+ Common LaTeX commands<br />
| Command<br />
| Use<br />
| Example<br />
| Rendered<br />
|-<br />
| \frac<br />
| Creates fractions<br />
| \frac{1}{2}<br />
| <math>\frac{1}{2}</math><br />
|-<br />
| \sqrt<br />
| Creates square (or, more generally, <math>n</math>th) roots<br />
| \sqrt{3}, \sqrt[3]{3}<br />
| <math>\sqrt{3}</math>, <math>\sqrt[3]{3}</math><br />
|-<br />
| \leq, \neq, \geq<br />
| Less than or equal to, not equal to, greater than or equal to (respectively)<br />
| a \leq b, a \neq b, a \geq b<br />
| <math>a \leq b, a \neq b, a \geq b</math><br />
|-<br />
| \alpha<br />
| Renders greek letters (most often alpha, beta, epsilon, pi, theta, phi, and omega)<br />
| \alpha+\beta=\pi-\epsilon<br />
| <math>\alpha+\beta=\pi-\epsilon</math><br />
|-<br />
|\rightarrow, \implies, \iff<br />
| Used for implication, algorithms, etc.<br />
| a>b \implies a^2>b^2, a>b \iff a-b>0, A\rightarrow A+1<br />
| <math>a>b \implies a^2>b^2, a>b \iff a-b>0, A\rightarrow A+1</math><br />
|-<br />
|\sum, \prod, \int<br />
|Used for summation, product, and integration symbols<br />
|\sum_1^5 x=15, \prod_1^5x=120, \int_1^5x=12<br />
|<math>\sum_1^5 x=15, \prod_1^5x=120, \int_1^5x=12</math><br />
|}<br />
<br />
See [[LaTeX:Symbols]] for a more comprehensive list of LaTeX commands, and use the [http://artofproblemsolving.com/texer/ TeXeR] to test how commands look when rendered.<br />
<br />
==Searching for Asymptote==<br />
[[Asymptote (Vector Graphics Language)|Asymptote]] is a programming language for creating diagrams. Unlike [[LaTeX]], dollar signs are not necessary, and [[Asymptote (Vector Graphics Language)|Asymptote]] code is enclosed in [asy] tags. [[Asymptote (Vector Graphics Language)|Asymptote]] commands take the form of most modern programming languages; lines are generally of the form <i>command(param1, param2, ...)</i> (this is different from TeX, where each parameter is enclosed in separate brackets). <br />
<br />
"Unfortunately" (for our purposes), most [[Asymptote (Vector Graphics Language)|Asymptote]] commands are simply the word-for-word descriptors of their function; for example, the command that returns the [[midpoint]] of a path is simply "[[midpoint]]", and the command that returns the [[circumcenter]] of a triangle is "[[circumcenter]]". This is further complicated by the usage of [[variable|variables]], the names of which are entirely up to the posters (unlike TeX, in which [[variable|variables]] are generally not used). Below are commonly used [[Asymptote (Vector Graphics Language)|Asymptote]] commands that are not actual words, so they are less likely to be confused with other posts during searching.<br />
<br />
{| class="wikitable"<br />
|+ Common [[Asymptote (Vector Graphics Language)|Asymptote]] commands<br />
| Command<br />
| Purpose<br />
| Command<br />
| Purpose<br />
|-<br />
| defaultpen<br />
| Adjusts the default settings for the pen. Very likely for this command to be in an [[Asymptote (Vector Graphics Language)|Asymptote]] drawing.<br />
| orthographic<br />
| Adjust the "camera position" in [[dimension|3-D]] drawings. Very likely for this command to be in a [[dimension|3-D]] [[Asymptote (Vector Graphics Language)|Asymptote]] drawing.<br />
|-<br />
| filldraw<br />
| Colors a given shape in some manner. Useful for shading in parts of diagrams; used reasonably foten.<br />
| unitsize<br />
| Sets the default size of a "unit" to a specified value. Default is very small. Not used particularly often because defaultpen is more general.<br />
|-<br />
| intersectionpoint<br />
| Determines the [[intersection]] (if there is exactly one) of two [[path|paths]]. Very useful command, and thus in many drawings.<br />
| intersectionpoints<br />
| Determine all the intersections of two [[path|paths]]. Obviously very similar to the previous command, but slightly less used as we generally want to know the intersection point of lines (rather than arbitrary paths).<br />
|-<br />
| rightanglemark<br />
| Marks a given [[angle]] as [[right angle|right]]. Used, obviously, in diagrams containing [[right angle|right angles]]; there are many of these.<br />
| anglemark<br />
| Marks a given [[angle]] with a given value. Used surprisingly little, since directly marking [[angle|angles]] isn't generally that important, but angle chase solutions will make heavy use of it.<br />
|-<br />
| linewidth<br />
| Sets the (visual -- [[line|lines]] have no real [[width]]!) [[width]] of a [[line]]. Also little used because defaultpen is more general.<br />
| currentpicture<br />
| A reference to the current picture. Used as an auxiliary command in other commands. This is the default value, so it is used only in very complicated drawings (or as a formality/copied and pasted sections).<br />
|}<br />
<br />
Note that simply searching "asy" will generally turn up [[Asymptote (Vector Graphics Language)|Asymptote]] drawings or discussions of such; especially when combined with a username or date range, simply remembering a post had any [[Asymptote (Vector Graphics Language)|Asymptote]] in it whatsoever is usually a good way to find it. As [[Asymptote (Vector Graphics Language)|Asymptote]] becomes more and more popular, the previous statement will become less true ([[LaTeX]], for example, is in a huge number of posts these days), but for now the numbers are small enough that you can sift through them pretty quickly.</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=Searching_the_community&diff=70692Searching the community2015-06-08T05:25:45Z<p>BOGTRO: /* Searching for LaTeX */</p>
<hr />
<div>This article is an introduction to <b>searching</b> the [http://artofproblemsolving.com/community AoPS forums]. All searching takes place from one of three pages: the [http://artofproblemsolving.com/community main webpage], any of the specific forums, or from the [http://artofproblemsolving.com/community/search dedicated webpage]. <br />
=Searching methods=<br />
==Searching from the community==<br />
[[Image:search.png|thumb|right|300px|Searching from the community page]]<br />
<br />
The first of these two options is shown in the image to the right. It is primarily useful for quickly searching, especially when the search is of a general nature and without a specific post in mind. The method is simple: simply type your query into the "Search Community" field, click the magnifying glass (or press the Enter key), and posts containing terms matching your query will be shown to you. The parts of the posts that match your query will be <span style="background:yellow"> highlighted in yellow</span>. For example, when searching for problems involving a [[circle]], one would simply type "[[circle]]" into the indicated field, getting a result similar to the following image:<br />
<br />
[[Image:searchresult.png|thumb|right|300px|Result of searching "[[circle]]"]]<br />
<br />
Clicking on any of these results will open the full topic in which the post was made, starting from the post you clicked on. For example, if the post you clicked on was the fourth post in its topic, you would originally see that post and could scroll up (or down) to see the rest of the topic.<br />
<br />
If these are not the results you were looking for, you can click the "Edit search settings" link in the top right corner to adjust your search parameters. <br />
<br />
==Searching from a forum==<br />
<br />
It is possible to initiate a search from a specific forum, using the toolbar on its header. This will limit the search results to posts in that forum. <br />
<br />
[[Image:searchforum.png|thumb|right|500px|The header of a forum]]<br />
<br />
To search from a forum, click the magnifying glass on its header (see image to the right). This will redirect you to the main search webpage, with the forum information already filled in. <br />
<br />
==Searching from the main webpage==<br />
<br />
[[Image:search2.png|thumbnail|left|300px|Searching from the [http://artofproblemsolving.com/community/search webpage]]]<br />
<br />
This page can be reached in three ways: by clicking on the "Advanced search" button under the quick-search option shown above, through the Community drop-down menu, or directly through the link http://artofproblemsolving.com/community/search. Compared to the other options, the [http://artofproblemsolving.com/community/search webpage] gives you significantly more ways to customize your search. There are five different fields to be filled in, but any of them can be left blank. For example, to search for all posts by [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk] made within the last year, the "search term" and "Posted In forum" fields should be left blank, but the other fields should be filled out with the appropriate information. It is even possible to leave every field blank, in which case the search results will mimic the [[global feed]]. The five fields are:<br />
<br />
{| class="wikitable"<br />
|+ Search fields<br />
|-<br />
! Field<br />
! Function<br />
|-<br />
| Search term<br />
| Fairly self-explanatory: enter the term(s) that you are searching for. Note that titles, tags, posts, and sources are all simultaneously searched. To search these separately, click the indicated option. It is possible to search different places for different terms simultaneously; for example, to search for [[AMC]] problems using [[Simon's Favorite Factoring Trick]], search for posts containing "[[SFFT]]" in topics with source containing "[[AMC]]". The indicated option will also allow you the choice of restricting your search to opening posts. This field is blank by default, indicating that all posts are searched regardless of content.<br />
<br />
Searching for multiple terms will return posts matching at least one of those terms, prioritizing posts "closer" to the query as a whole. See the following section for ways to further customize these queries.<br />
|-<br />
| Posted By User<br />
| Enter the name(s) of user(s) to restrict your search to. The search results will only contain posts posted by the user(s) you entered. Note that the posters of the original <i>topics</i> may be different from the users you enter here. You can also search by user ID instead of username, if you happen to know the ID of the user you are searching for (you can find this in their profile URL, which is of the form artofproblemsolving.com/community/user/<user ID>). Users entered must be valid users and will be authenticated prior to searching. This field is blank by default, indicating that posts by all users are searched.<br />
|-<br />
| Posted In Forum<br />
| Enter the name(s) of forum(s) to restrict your search to. The search results will only contain posts posted in the forum(s) you entered. If you reached this webpage through clicking on the magnifying glass in one of the forums, this field will be pre-populated with that forum. Forums entered must be valid forums and will be authenticated prior to searching. This field is blank by default, indicating that all forums are searched.<br />
<br />
Note: On the previous website, forums were associated with a unique ID that could be used in searching, similar to user ID numbers, but this is no longer the case; type in the name of the forum instead.<br />
|-<br />
| Dates<br />
| Select the timeframe in which posts you're searching for must have been made. The options are "Any" (default), "During the last 24 hours", "During the last week", "During the last month", "During the last year", or any manually entered date range.<br />
|-<br />
| Sorting<br />
| Select whether to sort results by "Relevance" (default), "Newest first", or "Oldest first". If "relevance" is selected, the posts will be sorted according to a scoring algorithm that approximates how well a post correlates to the search query. The other two options, "Newest first" and "Oldest first", are self-explanatory.<br />
|}<br />
<br />
For example, to search for the aforementioned posts made by [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk] within the last year, the "Search term" field should be blank, the "Posted by User" field should contain [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk], the "Posted in Forum" field should be blank, the "Dates" field should be set to "During the last year", and the "Sorting" field can be set according to how the searcher wishes the results to be presented. To search for topics that [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk] has started within the last year, the steps are the same, except that the "search only the first post of each topic" should be selected. See the images below.<br />
<br />
[[Image:rrusczykposts.png|thumb||530px|Posts by rrusczyk in the last year]]<br />
[[Image:rrusczykposts2.png|thumb|left|420px|Topics started by rrusczyk in the last year]]<br />
<br />
=Getting the most out of search=<br />
==Searching for a specific post==<br />
One of the most common uses of search is to find a specific post that you remember some details about, but cannot find. For example, you might recall having once read a particularly well-written solution, a very nice question, or an important announcement, but you can't remember quite where you saw it before. How frustrating!<br />
<br />
Obviously, the more details you remember about the post, the more likely you are to find it. If you remember that, for example, the post was written sometime in the summer of 2013, you can set the date range from (for example) May to September of that year. If you remember the author, that narrows down the possibilities significantly, but even remembering that it was one of several authors is a good way to whittle the possibilities down. Finally, remembering the forum that it was posted in would be excellent, but even if you only vaguely remember the post, you can make some educated guesses. For example, if the post was about a new and exciting technique for the [[USAMO]], it was probably posted in either the [http://artofproblemsolving.com/community/c5_contests_amp_programs Contests & Programs] forum or the [http://artofproblemsolving.com/community/c6_high_school_olympiads High School Olympiads] forum. If the post was a collection of [[MATHCOUNTS]] strategies, it's almost certainly in [http://artofproblemsolving.com/community/c3_middle_school_math Middle School Math]. <br />
<br />
==General searching tips==<br />
<br />
Of course, the above strategies are helpful, but still leave a lot of posts to sift through - unless you remember some of the language used in the post. You might remember, for example, a particularly memorable phrase in the post, or perhaps they used a math problem as reference that you remember a bit about. In these cases,<br />
<ul><br />
<li>Include, in your search query, unusual or uncommon words. For example, searching for just the word "[[circumcenter]]", along with the tips in the previous section, narrows down the possibilities significantly</li><br />
<li>Avoid common words such as "a", "the", "of", and so on, even if you remember a word-for-word phrase from the post containing these words. You'll get bogged down in posts matching those words - which there are a lot of!</li><br />
<li>Avoid searching words that are contained within another common word, as they will get matched to words you certainly didn't intend. For example, search queries containing the word "in" might return results for "logg<b>in</b>g", "<b>In</b>equality", and so on. The word "a" is particularly guilty of this, as it often returns words containing the letter "a".</li><br />
<li>Be sure to avoid searching for words that are special modifiers - see the below section. In particular, avoid searches containing the words "and" and "not". Similarly, do not include quotes ("), asterisks (*), question marks (?), plus signs (+), minus signs (-), or parentheses as these all represent special commands.<br />
</ul><br />
<br />
For example, if you remember a post contained the phrase "the three [[perpendicular bisector|perpendicular bisectors]] of a [[triangle]] intersect at the [[circumcenter]]", your search query should be something similar to "[[perpendicular bisector|perpendicular bisectors]] intersect [[circumcenter]]", as these are all specific words that limit the number of posts returned (unlike words like "of", "a", "the", and "at"). <br />
<br />
==Customizing search queries==<br />
<br />
We've already mentioned that posts are matched to the search query using a scoring algorithm, which approximates how "close" a post is to the given query. However, especially when searching for multiple terms, this algorithm often weights certain factors in different ways than the user intended. As such, there are several ways to customize your search queries.<br />
<br />
{| class="wikitable"<br />
|+ Customizing search queries<br />
|-<br />
| Operator<br />
| Example<br />
| Result<br />
|-<br />
| <i>(no adjustment)</i> <br />
| incenter circumcenter<br />
| Returns posts containing the word "[[incenter]]" and/or the word "[[circumcenter]]", with higher weight given to posts containing both.<br />
|-<br />
| +<br />
| +incenter circumcenter<br />
| Returned posts <b>must</b> contain the word "[[incenter]]", but may or may not contain "[[circumcenter]]". Again, higher weight is given to posts containing both words.<br />
|-<br />
| -<br />
| -incenter circumcenter excenter<br />
| Returned posts <b>must not</b> contain the word "[[incenter]]". Returned posts will contain the word "[[circumcenter]]" and/or the word "[[excenter]]", with higher weight given to posts containing both.<br />
|-<br />
| AND<br />
| incenter AND circumcenter<br />
| Returned posts <b>must</b> contain <i>both</i> "[[incenter]]" and "[[circumcenter]]". This is equivalent to the query "+incenter +circumcenter".<br />
|-<br />
| NOT<br />
| incenter NOT circumcenter<br />
| Returned posts will contain "[[incenter]]", but will <b>not</b> contain "[[circumcenter]]". Equivalent to the "-" and "!" operators.<br />
|-<br />
| "" (quotes)<br />
| "incenter circumcenter"<br />
| Returns posts containing the phrase "incenter circumcenter". Punctuation is usually ignored in results, so posts containing "incenter, circumcenter" or "incenter-circumcenter" will also be returned.<br />
|-<br />
| ? and *<br />
| te?t, inc*, in*e<br />
| Wildcard symbols. The ? symbol allows any character to replace it, so posts containing the words "test" or "text" will match the query "te?t". The * symbol allows any number of characters to replace it, so posts containing the words "[[incenter]]", "[[incircle]]", "[[inclusive]]", etc. will match the query "inc*". The * symbol can also be used in the middle of a word, so posts containing the words "interface", "[[incircle]]", "intermediate", "[[infinite]]", etc. will all match the query "in*e". <br />
|-<br />
| () (parentheses)<br />
| incenter AND (circumcenter OR excenter)<br />
| Grouping symbols to allow one boolean command (e.g. AND, NOT, +, -, !) to modify multiple elements. The example returns posts that contain both "[[incenter]]" and at least one of "[[circumcenter]]" or "[[excenter]]". Equivalent to the query "(incenter AND circumcenter) OR (incenter AND excenter)" (as usual, boolean logic applies to search strings).<br />
|-<br />
| \ <br />
| \AND<br />
| An "escape" character that allows you to search for reserved keywords and symbols. For example, the above query will return posts containing the word "and". Without the escape character, the search engine would parse the query "AND" as a command linking two nonexistent terms, and would thus throw an error. Similarly, the search term "[[incenter]] \AND [[circumcenter]]" would include results containing the word "[[incenter]]" and the word "and", but not the word "[[circumcenter]]".<br />
<br />
Note: in order to search for terms containing backslashes, such as LaTeX commands, the somewhat non-intuitive \\ is necessary (the first backslash "escapes" the second one). <br />
|}<br />
<br />
Note that, when using search modifiers, the <span style="background:yellow"> yellow background</span> indicating words that match your query will not generally be entirely accurate; for example, searching for "[[incenter]] AND [[circumcenter]]" will return posts containing both words as expected, but the word "and" will also be highlighted. Don't get confused by this - the search engine is still searching according to your query (and is not searching for the word "and"), the highlighting is simply slightly misleading.<br />
<br />
=Searching for LaTeX and Asympotote=<br />
<br />
Searching for [[LaTeX]] or [[Asymptote]] can be complicated, as they are their own languages, but this can actually be a big advantage! Predicting what code they've used is usually quite easy, and since the keywords are generally quite unique, searching for them will often narrow results down to posts using [[LaTeX]]/[[Asymptote]] themselves. Below are some common commands that [[LaTeX]]/[[Asymptote]] users often use, to help you search for them.<br />
<br />
==Searching for LaTeX==<br />
[[LaTeX]] is a programming language for rendering mathematical statements, and is very popular on [[AoPS]] (and other mathematical sources). [[LaTeX]] commands are enclosed in dollar signs for rendering, but you should not generally include those while searching. If you are searching for "full" commands (e.g. \frac{1}{2}), it is highly recommended that you enclose the entire command with quotation marks (e.g. "\\frac{1}{2}"; recall double backslash is needed), as otherwise it may parse as three different search terms (\frac, 1, and 2).<br />
<br />
{| class="wikitable"<br />
|+ Common LaTeX commands<br />
| Command<br />
| Use<br />
| Example<br />
| Rendered<br />
|-<br />
| \frac<br />
| Creates fractions<br />
| \frac{1}{2}<br />
| <math>\frac{1}{2}</math><br />
|-<br />
| \sqrt<br />
| Creates square (or, more generally, <math>n</math>th) roots<br />
| \sqrt{3}, \sqrt[3]{3}<br />
| <math>\sqrt{3}</math>, <math>\sqrt[3]{3}</math><br />
|-<br />
| \leq, \neq, \geq<br />
| Less than or equal to, not equal to, greater than or equal to (respectively)<br />
| a \leq b, a \neq b, a \geq b<br />
| <math>a \leq b, a \neq b, a \geq b</math><br />
|-<br />
| \alpha<br />
| Renders greek letters (most often alpha, beta, epsilon, pi, theta, phi, and omega)<br />
| \alpha+\beta=\pi-\epsilon<br />
| <math>\alpha+\beta=\pi-\epsilon</math><br />
|-<br />
|\rightarrow, \implies, \iff<br />
| Used for implication, algorithms, etc.<br />
| a>b \implies a^2>b^2, a>b \iff a-b>0, A\rightarrow A+1<br />
| <math>a>b \implies a^2>b^2, a>b \iff a-b>0, A\rightarrow A+1</math><br />
|-<br />
|\sum, \prod, \int<br />
|Used for summation, product, and integration symbols<br />
|\sum_1^5 x=15, \prod_1^5x=120, \int_1^5x=12<br />
|<math>\sum_1^5 x=15, \prod_1^5x=120, \int_1^5x=12</math><br />
|}<br />
<br />
See [[LaTeX:Symbols]] for a more comprehensive list of LaTeX commands, and use the [http://artofproblemsolving.com/texer/ TeXeR] to test how commands look when rendered.<br />
<br />
==Searching for Asymptote==<br />
[[Asymptote (Vector Graphics Language)|Asymptote]] is a programming language for creating diagrams. Unlike [[LaTeX]], dollar signs are not necessary, and [[Asymptote (Vector Graphics Language)|Asymptote]] code is enclosed in [asy] tags. [[Asymptote (Vector Graphics Language)|Asymptote]] commands take the form of most modern programming languages; lines are generally of the form <i>command(param1, param2, ...)</i> (this is different from TeX, where each parameter is enclosed in separate brackets). <br />
<br />
"Unfortunately" (for our purposes), most [[Asymptote (Vector Graphics Language)|Asymptote]] commands are simply the word-for-word descriptors of their function; for example, the command that returns the [[midpoint]] of a path is simply "[[midpoint]]", and the command that returns the [[circumcenter]] of a triangle is "[[circumcenter]]". This is further complicated by the usage of [[variable|variables]], the names of which are entirely up to the posters (unlike TeX, in which [[variable|variables]] are generally not used). Below are commonly used [[Asymptote (Vector Graphics Language)|Asymptote]] commands that are not actual words, so they are less likely to be confused with other posts during searching.<br />
<br />
{| class="wikitable"<br />
|+ Common [[Asymptote (Vector Graphics Language)|Asymptote]] commands<br />
| Command<br />
| Purpose<br />
| Command<br />
| Purpose<br />
|-<br />
| defaultpen<br />
| Adjusts the default settings for the pen. Very likely for this command to be in an [[Asymptote (Vector Graphics Language)|Asymptote]] drawing.<br />
| orthographic<br />
| Adjust the "camera position" in [[dimension|3-D]] drawings. Very likely for this command to be in a [[dimension|3-D]] [[Asymptote (Vector Graphics Language)|Asymptote]] drawing.<br />
|-<br />
| filldraw<br />
| Colors a given shape in some manner. Useful for shading in parts of diagrams; used reasonably foten.<br />
| unitsize<br />
| Sets the default size of a "unit" to a specified value. Default is very small. Not used particularly often because defaultpen is more general.<br />
|-<br />
| intersectionpoint<br />
| Determines the [[intersection]] (if there is exactly one) of two [[path|paths]]. Very useful command, and thus in many drawings.<br />
| intersectionpoints<br />
| Determine all the intersections of two [[path|paths]]. Obviously very similar to the previous command, but slightly less used as we generally want to know the intersection point of lines (rather than arbitrary paths).<br />
|-<br />
| rightanglemark<br />
| Marks a given [[angle]] as [[right angle|right]]. Used, obviously, in diagrams containing [[right angle|right angles]]; there are many of these.<br />
| anglemark<br />
| Marks a given [[angle]] with a given value. Used surprisingly little, since directly marking [[angle|angles]] isn't generally that important, but angle chase solutions will make heavy use of it.<br />
|-<br />
| linewidth<br />
| Sets the (visual -- [[line|lines]] have no real [[width]]!) [[width]] of a [[line]]. Also little used because defaultpen is more general.<br />
| currentpicture<br />
| A reference to the current picture. Used as an auxiliary command in other commands. This is the default value, so it is used only in very complicated drawings (or as a formality/copied and pasted sections).<br />
|}<br />
<br />
Note that simply searching "asy" will generally turn up [[Asymptote (Vector Graphics Language)|Asymptote]] drawings or discussions of such; especially when combined with a username or date range, simply remembering a post had any [[Asymptote (Vector Graphics Language)|Asymptote]] in it whatsoever is usually a good way to find it. As [[Asymptote (Vector Graphics Language)|Asymptote]] becomes more and more popular, the previous statement will become less true ([[LaTeX]], for example, is in a huge number of posts these days), but for now the numbers are small enough that you can sift through them pretty quickly.</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=Searching_the_community&diff=70691Searching the community2015-06-08T05:24:52Z<p>BOGTRO: </p>
<hr />
<div>This article is an introduction to <b>searching</b> the [http://artofproblemsolving.com/community AoPS forums]. All searching takes place from one of three pages: the [http://artofproblemsolving.com/community main webpage], any of the specific forums, or from the [http://artofproblemsolving.com/community/search dedicated webpage]. <br />
=Searching methods=<br />
==Searching from the community==<br />
[[Image:search.png|thumb|right|300px|Searching from the community page]]<br />
<br />
The first of these two options is shown in the image to the right. It is primarily useful for quickly searching, especially when the search is of a general nature and without a specific post in mind. The method is simple: simply type your query into the "Search Community" field, click the magnifying glass (or press the Enter key), and posts containing terms matching your query will be shown to you. The parts of the posts that match your query will be <span style="background:yellow"> highlighted in yellow</span>. For example, when searching for problems involving a [[circle]], one would simply type "[[circle]]" into the indicated field, getting a result similar to the following image:<br />
<br />
[[Image:searchresult.png|thumb|right|300px|Result of searching "[[circle]]"]]<br />
<br />
Clicking on any of these results will open the full topic in which the post was made, starting from the post you clicked on. For example, if the post you clicked on was the fourth post in its topic, you would originally see that post and could scroll up (or down) to see the rest of the topic.<br />
<br />
If these are not the results you were looking for, you can click the "Edit search settings" link in the top right corner to adjust your search parameters. <br />
<br />
==Searching from a forum==<br />
<br />
It is possible to initiate a search from a specific forum, using the toolbar on its header. This will limit the search results to posts in that forum. <br />
<br />
[[Image:searchforum.png|thumb|right|500px|The header of a forum]]<br />
<br />
To search from a forum, click the magnifying glass on its header (see image to the right). This will redirect you to the main search webpage, with the forum information already filled in. <br />
<br />
==Searching from the main webpage==<br />
<br />
[[Image:search2.png|thumbnail|left|300px|Searching from the [http://artofproblemsolving.com/community/search webpage]]]<br />
<br />
This page can be reached in three ways: by clicking on the "Advanced search" button under the quick-search option shown above, through the Community drop-down menu, or directly through the link http://artofproblemsolving.com/community/search. Compared to the other options, the [http://artofproblemsolving.com/community/search webpage] gives you significantly more ways to customize your search. There are five different fields to be filled in, but any of them can be left blank. For example, to search for all posts by [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk] made within the last year, the "search term" and "Posted In forum" fields should be left blank, but the other fields should be filled out with the appropriate information. It is even possible to leave every field blank, in which case the search results will mimic the [[global feed]]. The five fields are:<br />
<br />
{| class="wikitable"<br />
|+ Search fields<br />
|-<br />
! Field<br />
! Function<br />
|-<br />
| Search term<br />
| Fairly self-explanatory: enter the term(s) that you are searching for. Note that titles, tags, posts, and sources are all simultaneously searched. To search these separately, click the indicated option. It is possible to search different places for different terms simultaneously; for example, to search for [[AMC]] problems using [[Simon's Favorite Factoring Trick]], search for posts containing "[[SFFT]]" in topics with source containing "[[AMC]]". The indicated option will also allow you the choice of restricting your search to opening posts. This field is blank by default, indicating that all posts are searched regardless of content.<br />
<br />
Searching for multiple terms will return posts matching at least one of those terms, prioritizing posts "closer" to the query as a whole. See the following section for ways to further customize these queries.<br />
|-<br />
| Posted By User<br />
| Enter the name(s) of user(s) to restrict your search to. The search results will only contain posts posted by the user(s) you entered. Note that the posters of the original <i>topics</i> may be different from the users you enter here. You can also search by user ID instead of username, if you happen to know the ID of the user you are searching for (you can find this in their profile URL, which is of the form artofproblemsolving.com/community/user/<user ID>). Users entered must be valid users and will be authenticated prior to searching. This field is blank by default, indicating that posts by all users are searched.<br />
|-<br />
| Posted In Forum<br />
| Enter the name(s) of forum(s) to restrict your search to. The search results will only contain posts posted in the forum(s) you entered. If you reached this webpage through clicking on the magnifying glass in one of the forums, this field will be pre-populated with that forum. Forums entered must be valid forums and will be authenticated prior to searching. This field is blank by default, indicating that all forums are searched.<br />
<br />
Note: On the previous website, forums were associated with a unique ID that could be used in searching, similar to user ID numbers, but this is no longer the case; type in the name of the forum instead.<br />
|-<br />
| Dates<br />
| Select the timeframe in which posts you're searching for must have been made. The options are "Any" (default), "During the last 24 hours", "During the last week", "During the last month", "During the last year", or any manually entered date range.<br />
|-<br />
| Sorting<br />
| Select whether to sort results by "Relevance" (default), "Newest first", or "Oldest first". If "relevance" is selected, the posts will be sorted according to a scoring algorithm that approximates how well a post correlates to the search query. The other two options, "Newest first" and "Oldest first", are self-explanatory.<br />
|}<br />
<br />
For example, to search for the aforementioned posts made by [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk] within the last year, the "Search term" field should be blank, the "Posted by User" field should contain [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk], the "Posted in Forum" field should be blank, the "Dates" field should be set to "During the last year", and the "Sorting" field can be set according to how the searcher wishes the results to be presented. To search for topics that [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk] has started within the last year, the steps are the same, except that the "search only the first post of each topic" should be selected. See the images below.<br />
<br />
[[Image:rrusczykposts.png|thumb||530px|Posts by rrusczyk in the last year]]<br />
[[Image:rrusczykposts2.png|thumb|left|420px|Topics started by rrusczyk in the last year]]<br />
<br />
=Getting the most out of search=<br />
==Searching for a specific post==<br />
One of the most common uses of search is to find a specific post that you remember some details about, but cannot find. For example, you might recall having once read a particularly well-written solution, a very nice question, or an important announcement, but you can't remember quite where you saw it before. How frustrating!<br />
<br />
Obviously, the more details you remember about the post, the more likely you are to find it. If you remember that, for example, the post was written sometime in the summer of 2013, you can set the date range from (for example) May to September of that year. If you remember the author, that narrows down the possibilities significantly, but even remembering that it was one of several authors is a good way to whittle the possibilities down. Finally, remembering the forum that it was posted in would be excellent, but even if you only vaguely remember the post, you can make some educated guesses. For example, if the post was about a new and exciting technique for the [[USAMO]], it was probably posted in either the [http://artofproblemsolving.com/community/c5_contests_amp_programs Contests & Programs] forum or the [http://artofproblemsolving.com/community/c6_high_school_olympiads High School Olympiads] forum. If the post was a collection of [[MATHCOUNTS]] strategies, it's almost certainly in [http://artofproblemsolving.com/community/c3_middle_school_math Middle School Math]. <br />
<br />
==General searching tips==<br />
<br />
Of course, the above strategies are helpful, but still leave a lot of posts to sift through - unless you remember some of the language used in the post. You might remember, for example, a particularly memorable phrase in the post, or perhaps they used a math problem as reference that you remember a bit about. In these cases,<br />
<ul><br />
<li>Include, in your search query, unusual or uncommon words. For example, searching for just the word "[[circumcenter]]", along with the tips in the previous section, narrows down the possibilities significantly</li><br />
<li>Avoid common words such as "a", "the", "of", and so on, even if you remember a word-for-word phrase from the post containing these words. You'll get bogged down in posts matching those words - which there are a lot of!</li><br />
<li>Avoid searching words that are contained within another common word, as they will get matched to words you certainly didn't intend. For example, search queries containing the word "in" might return results for "logg<b>in</b>g", "<b>In</b>equality", and so on. The word "a" is particularly guilty of this, as it often returns words containing the letter "a".</li><br />
<li>Be sure to avoid searching for words that are special modifiers - see the below section. In particular, avoid searches containing the words "and" and "not". Similarly, do not include quotes ("), asterisks (*), question marks (?), plus signs (+), minus signs (-), or parentheses as these all represent special commands.<br />
</ul><br />
<br />
For example, if you remember a post contained the phrase "the three [[perpendicular bisector|perpendicular bisectors]] of a [[triangle]] intersect at the [[circumcenter]]", your search query should be something similar to "[[perpendicular bisector|perpendicular bisectors]] intersect [[circumcenter]]", as these are all specific words that limit the number of posts returned (unlike words like "of", "a", "the", and "at"). <br />
<br />
==Customizing search queries==<br />
<br />
We've already mentioned that posts are matched to the search query using a scoring algorithm, which approximates how "close" a post is to the given query. However, especially when searching for multiple terms, this algorithm often weights certain factors in different ways than the user intended. As such, there are several ways to customize your search queries.<br />
<br />
{| class="wikitable"<br />
|+ Customizing search queries<br />
|-<br />
| Operator<br />
| Example<br />
| Result<br />
|-<br />
| <i>(no adjustment)</i> <br />
| incenter circumcenter<br />
| Returns posts containing the word "[[incenter]]" and/or the word "[[circumcenter]]", with higher weight given to posts containing both.<br />
|-<br />
| +<br />
| +incenter circumcenter<br />
| Returned posts <b>must</b> contain the word "[[incenter]]", but may or may not contain "[[circumcenter]]". Again, higher weight is given to posts containing both words.<br />
|-<br />
| -<br />
| -incenter circumcenter excenter<br />
| Returned posts <b>must not</b> contain the word "[[incenter]]". Returned posts will contain the word "[[circumcenter]]" and/or the word "[[excenter]]", with higher weight given to posts containing both.<br />
|-<br />
| AND<br />
| incenter AND circumcenter<br />
| Returned posts <b>must</b> contain <i>both</i> "[[incenter]]" and "[[circumcenter]]". This is equivalent to the query "+incenter +circumcenter".<br />
|-<br />
| NOT<br />
| incenter NOT circumcenter<br />
| Returned posts will contain "[[incenter]]", but will <b>not</b> contain "[[circumcenter]]". Equivalent to the "-" and "!" operators.<br />
|-<br />
| "" (quotes)<br />
| "incenter circumcenter"<br />
| Returns posts containing the phrase "incenter circumcenter". Punctuation is usually ignored in results, so posts containing "incenter, circumcenter" or "incenter-circumcenter" will also be returned.<br />
|-<br />
| ? and *<br />
| te?t, inc*, in*e<br />
| Wildcard symbols. The ? symbol allows any character to replace it, so posts containing the words "test" or "text" will match the query "te?t". The * symbol allows any number of characters to replace it, so posts containing the words "[[incenter]]", "[[incircle]]", "[[inclusive]]", etc. will match the query "inc*". The * symbol can also be used in the middle of a word, so posts containing the words "interface", "[[incircle]]", "intermediate", "[[infinite]]", etc. will all match the query "in*e". <br />
|-<br />
| () (parentheses)<br />
| incenter AND (circumcenter OR excenter)<br />
| Grouping symbols to allow one boolean command (e.g. AND, NOT, +, -, !) to modify multiple elements. The example returns posts that contain both "[[incenter]]" and at least one of "[[circumcenter]]" or "[[excenter]]". Equivalent to the query "(incenter AND circumcenter) OR (incenter AND excenter)" (as usual, boolean logic applies to search strings).<br />
|-<br />
| \ <br />
| \AND<br />
| An "escape" character that allows you to search for reserved keywords and symbols. For example, the above query will return posts containing the word "and". Without the escape character, the search engine would parse the query "AND" as a command linking two nonexistent terms, and would thus throw an error. Similarly, the search term "[[incenter]] \AND [[circumcenter]]" would include results containing the word "[[incenter]]" and the word "and", but not the word "[[circumcenter]]".<br />
<br />
Note: in order to search for terms containing backslashes, such as LaTeX commands, the somewhat non-intuitive \\ is necessary (the first backslash "escapes" the second one). <br />
|}<br />
<br />
Note that, when using search modifiers, the <span style="background:yellow"> yellow background</span> indicating words that match your query will not generally be entirely accurate; for example, searching for "[[incenter]] AND [[circumcenter]]" will return posts containing both words as expected, but the word "and" will also be highlighted. Don't get confused by this - the search engine is still searching according to your query (and is not searching for the word "and"), the highlighting is simply slightly misleading.<br />
<br />
=Searching for LaTeX and Asympotote=<br />
<br />
Searching for [[LaTeX]] or [[Asymptote]] can be complicated, as they are their own languages, but this can actually be a big advantage! Predicting what code they've used is usually quite easy, and since the keywords are generally quite unique, searching for them will often narrow results down to posts using [[LaTeX]]/[[Asymptote]] themselves. Below are some common commands that [[LaTeX]]/[[Asymptote]] users often use, to help you search for them.<br />
<br />
==Searching for LaTeX==<br />
[[LaTeX]] is a programming language for rendering mathematical statements, and is very popular on [[AoPS]] (and other mathematical sources). [[LaTeX]] commands are enclosed in dollar signs for rendering, but you should not generally include those while searching. If you are searching for "full" commands (e.g. \frac{1}{2}), it is highly recommended that you enclose the entire command with quotation marks (e.g. "\frac{1}{2}"), as otherwise it may parse as three different search terms (\frac, 1, and 2).<br />
<br />
{| class="wikitable"<br />
|+ Common LaTeX commands<br />
| Command<br />
| Use<br />
| Example<br />
| Rendered<br />
|-<br />
| \frac<br />
| Creates fractions<br />
| \frac{1}{2}<br />
| <math>\frac{1}{2}</math><br />
|-<br />
| \sqrt<br />
| Creates square (or, more generally, <math>n</math>th) roots<br />
| \sqrt{3}, \sqrt[3]{3}<br />
| <math>\sqrt{3}</math>, <math>\sqrt[3]{3}</math><br />
|-<br />
| \leq, \neq, \geq<br />
| Less than or equal to, not equal to, greater than or equal to (respectively)<br />
| a \leq b, a \neq b, a \geq b<br />
| <math>a \leq b, a \neq b, a \geq b</math><br />
|-<br />
| \alpha<br />
| Renders greek letters (most often alpha, beta, epsilon, pi, theta, phi, and omega)<br />
| \alpha+\beta=\pi-\epsilon<br />
| <math>\alpha+\beta=\pi-\epsilon</math><br />
|-<br />
|\rightarrow, \implies, \iff<br />
| Used for implication, algorithms, etc.<br />
| a>b \implies a^2>b^2, a>b \iff a-b>0, A\rightarrow A+1<br />
| <math>a>b \implies a^2>b^2, a>b \iff a-b>0, A\rightarrow A+1</math><br />
|-<br />
|\sum, \prod, \int<br />
|Used for summation, product, and integration symbols<br />
|\sum_1^5 x=15, \prod_1^5x=120, \int_1^5x=12<br />
|<math>\sum_1^5 x=15, \prod_1^5x=120, \int_1^5x=12</math><br />
|}<br />
<br />
See [[LaTeX:Symbols]] for a more comprehensive list of LaTeX commands, and use the [http://artofproblemsolving.com/texer/ TeXeR] to test how commands look when rendered.<br />
<br />
==Searching for Asymptote==<br />
[[Asymptote (Vector Graphics Language)|Asymptote]] is a programming language for creating diagrams. Unlike [[LaTeX]], dollar signs are not necessary, and [[Asymptote (Vector Graphics Language)|Asymptote]] code is enclosed in [asy] tags. [[Asymptote (Vector Graphics Language)|Asymptote]] commands take the form of most modern programming languages; lines are generally of the form <i>command(param1, param2, ...)</i> (this is different from TeX, where each parameter is enclosed in separate brackets). <br />
<br />
"Unfortunately" (for our purposes), most [[Asymptote (Vector Graphics Language)|Asymptote]] commands are simply the word-for-word descriptors of their function; for example, the command that returns the [[midpoint]] of a path is simply "[[midpoint]]", and the command that returns the [[circumcenter]] of a triangle is "[[circumcenter]]". This is further complicated by the usage of [[variable|variables]], the names of which are entirely up to the posters (unlike TeX, in which [[variable|variables]] are generally not used). Below are commonly used [[Asymptote (Vector Graphics Language)|Asymptote]] commands that are not actual words, so they are less likely to be confused with other posts during searching.<br />
<br />
{| class="wikitable"<br />
|+ Common [[Asymptote (Vector Graphics Language)|Asymptote]] commands<br />
| Command<br />
| Purpose<br />
| Command<br />
| Purpose<br />
|-<br />
| defaultpen<br />
| Adjusts the default settings for the pen. Very likely for this command to be in an [[Asymptote (Vector Graphics Language)|Asymptote]] drawing.<br />
| orthographic<br />
| Adjust the "camera position" in [[dimension|3-D]] drawings. Very likely for this command to be in a [[dimension|3-D]] [[Asymptote (Vector Graphics Language)|Asymptote]] drawing.<br />
|-<br />
| filldraw<br />
| Colors a given shape in some manner. Useful for shading in parts of diagrams; used reasonably foten.<br />
| unitsize<br />
| Sets the default size of a "unit" to a specified value. Default is very small. Not used particularly often because defaultpen is more general.<br />
|-<br />
| intersectionpoint<br />
| Determines the [[intersection]] (if there is exactly one) of two [[path|paths]]. Very useful command, and thus in many drawings.<br />
| intersectionpoints<br />
| Determine all the intersections of two [[path|paths]]. Obviously very similar to the previous command, but slightly less used as we generally want to know the intersection point of lines (rather than arbitrary paths).<br />
|-<br />
| rightanglemark<br />
| Marks a given [[angle]] as [[right angle|right]]. Used, obviously, in diagrams containing [[right angle|right angles]]; there are many of these.<br />
| anglemark<br />
| Marks a given [[angle]] with a given value. Used surprisingly little, since directly marking [[angle|angles]] isn't generally that important, but angle chase solutions will make heavy use of it.<br />
|-<br />
| linewidth<br />
| Sets the (visual -- [[line|lines]] have no real [[width]]!) [[width]] of a [[line]]. Also little used because defaultpen is more general.<br />
| currentpicture<br />
| A reference to the current picture. Used as an auxiliary command in other commands. This is the default value, so it is used only in very complicated drawings (or as a formality/copied and pasted sections).<br />
|}<br />
<br />
Note that simply searching "asy" will generally turn up [[Asymptote (Vector Graphics Language)|Asymptote]] drawings or discussions of such; especially when combined with a username or date range, simply remembering a post had any [[Asymptote (Vector Graphics Language)|Asymptote]] in it whatsoever is usually a good way to find it. As [[Asymptote (Vector Graphics Language)|Asymptote]] becomes more and more popular, the previous statement will become less true ([[LaTeX]], for example, is in a huge number of posts these days), but for now the numbers are small enough that you can sift through them pretty quickly.</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=Searching_the_community&diff=70690Searching the community2015-06-08T05:21:53Z<p>BOGTRO: </p>
<hr />
<div>This article is an introduction to <b>searching</b> the [http://artofproblemsolving.com/community AoPS forums]. All searching takes place from one of three pages: the [http://artofproblemsolving.com/community main webpage], any of the specific forums, or from the [http://artofproblemsolving.com/community/search dedicated webpage]. <br />
=Searching methods=<br />
==Searching from the community==<br />
[[Image:search.png|thumb|right|300px|Searching from the community page]]<br />
<br />
The first of these two options is shown in the image to the right. It is primarily useful for quickly searching, especially when the search is of a general nature and without a specific post in mind. The method is simple: simply type your query into the "Search Community" field, click the magnifying glass (or press the Enter key), and posts containing terms matching your query will be shown to you. The parts of the posts that match your query will be <span style="background:yellow"> highlighted in yellow</span>. For example, when searching for problems involving a [[circle]], one would simply type "[[circle]]" into the indicated field, getting a result similar to the following image:<br />
<br />
[[Image:searchresult.png|thumb|right|300px|Result of searching "[[circle]]"]]<br />
<br />
Clicking on any of these results will open the full topic in which the post was made, starting from the post you clicked on. For example, if the post you clicked on was the fourth post in its topic, you would originally see that post and could scroll up (or down) to see the rest of the topic.<br />
<br />
If these are not the results you were looking for, you can click the "Edit search settings" link in the top right corner to adjust your search parameters. <br />
<br />
==Searching from a forum==<br />
<br />
It is possible to initiate a search from a specific forum, using the toolbar on its header. This will limit the search results to posts in that forum. <br />
<br />
[[Image:searchforum.png|thumb|right|500px|The header of a forum]]<br />
<br />
To search from a forum, click the magnifying glass on its header (see image to the right). This will redirect you to the main search webpage, with the forum information already filled in. <br />
<br />
==Searching from the main webpage==<br />
<br />
[[Image:search2.png|thumbnail|left|300px|Searching from the [http://artofproblemsolving.com/community/search webpage]]]<br />
<br />
This page can be reached in three ways: by clicking on the "Advanced search" button under the quick-search option shown above, through the Community drop-down menu, or directly through the link http://artofproblemsolving.com/community/search. Compared to the other options, the [http://artofproblemsolving.com/community/search webpage] gives you significantly more ways to customize your search. There are five different fields to be filled in, but any of them can be left blank. For example, to search for all posts by [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk] made within the last year, the "search term" and "Posted In forum" fields should be left blank, but the other fields should be filled out with the appropriate information. It is even possible to leave every field blank, in which case the search results will mimic the [[global feed]]. The five fields are:<br />
<br />
{| class="wikitable"<br />
|+ Search fields<br />
|-<br />
! Field<br />
! Function<br />
|-<br />
| Search term<br />
| Fairly self-explanatory: enter the term(s) that you are searching for. Note that titles, tags, posts, and sources are all simultaneously searched. To search these separately, click the indicated option. It is possible to search different places for different terms simultaneously; for example, to search for [[AMC]] problems using [[Simon's Favorite Factoring Trick]], search for posts containing "[[SFFT]]" in topics with source containing "[[AMC]]". The indicated option will also allow you the choice of restricting your search to opening posts. This field is blank by default, indicating that all posts are searched regardless of content.<br />
<br />
Searching for multiple terms will return posts matching at least one of those terms, prioritizing posts "closer" to the query as a whole. See the following section for ways to further customize these queries.<br />
|-<br />
| Posted By User<br />
| Enter the name(s) of user(s) to restrict your search to. The search results will only contain posts posted by the user(s) you entered. Note that the posters of the original <i>topics</i> may be different from the users you enter here. You can also search by user ID instead of username, if you happen to know the ID of the user you are searching for (you can find this in their profile URL, which is of the form artofproblemsolving.com/community/user/<user ID>). Users entered must be valid users and will be authenticated prior to searching. This field is blank by default, indicating that posts by all users are searched.<br />
|-<br />
| Posted In Forum<br />
| Enter the name(s) of forum(s) to restrict your search to. The search results will only contain posts posted in the forum(s) you entered. If you reached this webpage through clicking on the magnifying glass in one of the forums, this field will be pre-populated with that forum. Forums entered must be valid forums and will be authenticated prior to searching. This field is blank by default, indicating that all forums are searched.<br />
<br />
Note: On the previous website, forums were associated with a unique ID that could be used in searching, similar to user ID numbers, but this is no longer the case; type in the name of the forum instead.<br />
|-<br />
| Dates<br />
| Select the timeframe in which posts you're searching for must have been made. The options are "Any" (default), "During the last 24 hours", "During the last week", "During the last month", "During the last year", or any manually entered date range.<br />
|-<br />
| Sorting<br />
| Select whether to sort results by "Relevance" (default), "Newest first", or "Oldest first". If "relevance" is selected, the posts will be sorted according to a scoring algorithm that approximates how well a post correlates to the search query. The other two options, "Newest first" and "Oldest first", are self-explanatory.<br />
|}<br />
<br />
For example, to search for the aforementioned posts made by [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk] within the last year, the "Search term" field should be blank, the "Posted by User" field should contain [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk], the "Posted in Forum" field should be blank, the "Dates" field should be set to "During the last year", and the "Sorting" field can be set according to how the searcher wishes the results to be presented. To search for topics that [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk] has started within the last year, the steps are the same, except that the "search only the first post of each topic" should be selected. See the images below.<br />
<br />
[[Image:rrusczykposts.png|thumb||530px|Posts by rrusczyk in the last year]]<br />
[[Image:rrusczykposts2.png|thumb|left|420px|Topics started by rrusczyk in the last year]]<br />
<br />
=Getting the most out of search=<br />
==Searching for a specific post==<br />
One of the most common uses of search is to find a specific post that you remember some details about, but cannot find. For example, you might recall having once read a particularly well-written solution, a very nice question, or an important announcement, but you can't remember quite where you saw it before. How frustrating!<br />
<br />
Obviously, the more details you remember about the post, the more likely you are to find it. If you remember that, for example, the post was written sometime in the summer of 2013, you can set the date range from (for example) May to September of that year. If you remember the author, that narrows down the possibilities significantly, but even remembering that it was one of several authors is a good way to whittle the possibilities down. Finally, remembering the forum that it was posted in would be excellent, but even if you only vaguely remember the post, you can make some educated guesses. For example, if the post was about a new and exciting technique for the [[USAMO]], it was probably posted in either the [http://artofproblemsolving.com/community/c5_contests_amp_programs Contests & Programs] forum or the [http://artofproblemsolving.com/community/c6_high_school_olympiads High School Olympiads] forum. If the post was a collection of [[MATHCOUNTS]] strategies, it's almost certainly in [http://artofproblemsolving.com/community/c3_middle_school_math Middle School Math]. <br />
<br />
==General searching tips==<br />
<br />
Of course, the above strategies are helpful, but still leave a lot of posts to sift through - unless you remember some of the language used in the post. You might remember, for example, a particularly memorable phrase in the post, or perhaps they used a math problem as reference that you remember a bit about. In these cases,<br />
<ul><br />
<li>Include, in your search query, unusual or uncommon words. For example, searching for just the word "[[circumcenter]]", along with the tips in the previous section, narrows down the possibilities significantly</li><br />
<li>Avoid common words such as "a", "the", "of", and so on, even if you remember a word-for-word phrase from the post containing these words. You'll get bogged down in posts matching those words - which there are a lot of!</li><br />
<li>Avoid searching words that are contained within another common word, as they will get matched to words you certainly didn't intend. For example, search queries containing the word "in" might return results for "logg<b>in</b>g", "<b>In</b>equality", and so on. The word "a" is particularly guilty of this, as it often returns words containing the letter "a".</li><br />
<li>Be sure to avoid searching for words that are special modifiers - see the below section. In particular, avoid searches containing the words "and" and "not". Similarly, do not include quotes ("), asterisks (*), question marks (?), plus signs (+), minus signs (-), or parentheses as these all represent special commands.<br />
</ul><br />
<br />
For example, if you remember a post contained the phrase "the three [[perpendicular bisector|perpendicular bisectors]] of a [[triangle]] intersect at the [[circumcenter]]", your search query should be something similar to "[[perpendicular bisector|perpendicular bisectors]] intersect [[circumcenter]]", as these are all specific words that limit the number of posts returned (unlike words like "of", "a", "the", and "at"). <br />
<br />
==Customizing search queries==<br />
<br />
We've already mentioned that posts are matched to the search query using a scoring algorithm, which approximates how "close" a post is to the given query. However, especially when searching for multiple terms, this algorithm often weights certain factors in different ways than the user intended. As such, there are several ways to customize your search queries.<br />
<br />
{| class="wikitable"<br />
|+ Customizing search queries<br />
|-<br />
| Operator<br />
| Example<br />
| Result<br />
|-<br />
| <i>(no adjustment)</i> <br />
| incenter circumcenter<br />
| Returns posts containing the word "[[incenter]]" and/or the word "[[circumcenter]]", with higher weight given to posts containing both.<br />
|-<br />
| +<br />
| +incenter circumcenter<br />
| Returned posts <b>must</b> contain the word "[[incenter]]", but may or may not contain "[[circumcenter]]". Again, higher weight is given to posts containing both words.<br />
|-<br />
| -<br />
| -incenter circumcenter excenter<br />
| Returned posts <b>must not</b> contain the word "[[incenter]]". Returned posts will contain the word "[[circumcenter]]" and/or the word "[[excenter]]", with higher weight given to posts containing both.<br />
|-<br />
| AND<br />
| incenter AND circumcenter<br />
| Returned posts <b>must</b> contain <i>both</i> "[[incenter]]" and "[[circumcenter]]". This is equivalent to the query "+incenter +circumcenter".<br />
|-<br />
| NOT<br />
| incenter NOT circumcenter<br />
| Returned posts will contain "[[incenter]]", but will <b>not</b> contain "[[circumcenter]]". Equivalent to the "-" and "!" operators.<br />
|-<br />
| "" (quotes)<br />
| "incenter circumcenter"<br />
| Returns posts containing the phrase "incenter circumcenter". Punctuation is usually ignored in results, so posts containing "incenter, circumcenter" or "incenter-circumcenter" will also be returned.<br />
|-<br />
| ? and *<br />
| te?t, inc*, in*e<br />
| Wildcard symbols. The ? symbol allows any character to replace it, so posts containing the words "test" or "text" will match the query "te?t". The * symbol allows any number of characters to replace it, so posts containing the words "[[incenter]]", "[[incircle]]", "[[inclusive]]", etc. will match the query "inc*". The * symbol can also be used in the middle of a word, so posts containing the words "interface", "[[incircle]]", "intermediate", "[[infinite]]", etc. will all match the query "in*e". <br />
|-<br />
| () (parentheses)<br />
| incenter AND (circumcenter OR excenter)<br />
| Grouping symbols to allow one boolean command (e.g. AND, NOT, +, -, !) to modify multiple elements. The example returns posts that contain both "[[incenter]]" and at least one of "[[circumcenter]]" or "[[excenter]]". Equivalent to the query "(incenter AND circumcenter) OR (incenter AND excenter)" (as usual, boolean logic applies to search strings).<br />
|-<br />
| \ <br />
| \AND<br />
| An "escape" character that allows you to search for reserved keywords and symbols. For example, the above query will return posts containing the word "and". Without the escape character, the search engine would parse the query "AND" as a command linking two nonexistent terms, and would thus throw an error. Similarly, the search term "[[incenter]] \AND [[circumcenter]]" would include results containing the word "[[incenter]]" and the word "and", but not the word "[[circumcenter]]".<br />
<br />
Note: in order to search for terms containing backslashes, such as LaTeX commands, the somewhat non-intuitive \\ is necessary (the first backslash "escapes" the second one). <br />
|}<br />
<br />
Note that, when using search modifiers, the <span style="background:yellow"> yellow background</span> indicating words that match your query will not generally be entirely accurate; for example, searching for "[[incenter]] AND [[circumcenter]]" will return posts containing both words as expected, but the word "and" will also be highlighted. Don't get confused by this - the search engine is still searching according to your query (and is not searching for the word "and"), the highlighting is simply slightly misleading.<br />
<br />
=Searching for LaTeX and Asympotote=<br />
<br />
Searching for [[LaTeX]] or [[Asymptote]] can be complicated, as they are their own languages, but this can actually be a big advantage! Predicting what code they've used is usually quite easy, and since the keywords are generally quite unique, searching for them will often narrow results down to posts using [[LaTeX]]/[[Asymptote]] themselves. Below are some common commands that [[LaTeX]]/[[Asymptote]] users often use, to help you search for them.<br />
<br />
==Searching for LaTeX==<br />
[[LaTeX]] is a programming language for rendering mathematical statements, and is very popular on [[AoPS]] (and other mathematical sources). [[LaTeX]] commands are enclosed in dollar signs for rendering, but you should not generally include those while searching. If you are searching for "full" commands (e.g. \frac{1}{2}), it is highly recommended that you enclose the entire command with quotation marks (e.g. "\frac{1}{2}"), as otherwise it may parse as three different search terms (\frac, 1, and 2).<br />
<br />
{| class="wikitable"<br />
|+ Common LaTeX commands<br />
| Command<br />
| Use<br />
| Example<br />
| Rendered<br />
|-<br />
| \frac<br />
| Creates fractions<br />
| \frac{1}{2}<br />
| <math>\frac{1}{2}</math><br />
|-<br />
| \sqrt<br />
| Creates square (or, more generally, <math>n</math>th) roots<br />
| \sqrt{3}, \sqrt[3]{3}<br />
| <math>\sqrt{3}</math>, <math>\sqrt[3]{3}</math><br />
|-<br />
| \leq, \neq, \geq<br />
| Less than or equal to, not equal to, greater than or equal to (respectively)<br />
| a \leq b, a \neq b, a \geq b<br />
| <math>a \leq b, a \neq b, a \geq b</math><br />
|-<br />
| \alpha<br />
| Renders greek letters (most often alpha, beta, epsilon, pi, theta, phi, and omega)<br />
| \alpha+\beta=\pi-\epsilon<br />
| <math>\alpha+\beta=\pi-\epsilon</math><br />
|-<br />
|\rightarrow, \implies, \iff<br />
| Used for implication, algorithms, etc.<br />
| a>b \implies a^2>b^2, a>b \iff a-b>0, A\rightarrow A+1<br />
| <math>a>b \implies a^2>b^2, a>b \iff a-b>0, A\rightarrow A+1</math><br />
|-<br />
|\sum, \prod, \int<br />
|Used for summation, product, and integration symbols<br />
|\sum_1^5 x=15, \prod_1^5x=120, \int_1^5x=12<br />
|<math>\sum_1^5 x=15, \prod_1^5x=120, \int_1^5x=12</math><br />
|}<br />
<br />
See [[LaTeX:Symbols]] for a more comprehensive list of LaTeX commands, and use the [[http://artofproblemsolving.com/texer/ TeXeR]] to test how commands look when rendered.<br />
<br />
==Searching for Asymptote==<br />
[[Asymptote (Vector Graphics Language)|Asymptote]] is a programming language for creating diagrams. Unlike [[LaTeX]], dollar signs are not necessary, and [[Asymptote (Vector Graphics Language)|Asymptote]] code is enclosed in [asy] tags. [[Asymptote (Vector Graphics Language)|Asymptote]] commands take the form of most modern programming languages; lines are generally of the form <i>command(param1, param2, ...)</i> (this is different from TeX, where each parameter is enclosed in separate brackets). <br />
<br />
"Unfortunately" (for our purposes), most [[Asymptote (Vector Graphics Language)|Asymptote]] commands are simply the word-for-word descriptors of their function; for example, the command that returns the [[midpoint]] of a path is simply "[[midpoint]]", and the command that returns the [[circumcenter]] of a triangle is "[[circumcenter]]". This is further complicated by the usage of [[variable|variables]], the names of which are entirely up to the posters (unlike TeX, in which [[variable|variables]] are generally not used). Below are commonly used [[Asymptote (Vector Graphics Language)|Asymptote]] commands that are not actual words, so they are less likely to be confused with other posts during searching.<br />
<br />
{| class="wikitable"<br />
|+ Common [[Asymptote (Vector Graphics Language)|Asymptote]] commands<br />
| Command<br />
| Purpose<br />
| Command<br />
| Purpose<br />
|-<br />
| defaultpen<br />
| Adjusts the default settings for the pen. Very likely for this command to be in an [[Asymptote (Vector Graphics Language)|Asymptote]] drawing.<br />
| orthographic<br />
| Adjust the "camera position" in [[dimension|3-D]] drawings. Very likely for this command to be in a [[dimension|3-D]] [[Asymptote (Vector Graphics Language)|Asymptote]] drawing.<br />
|-<br />
| filldraw<br />
| Colors a given shape in some manner. Useful for shading in parts of diagrams; used reasonably foten.<br />
| unitsize<br />
| Sets the default size of a "unit" to a specified value. Default is very small. Not used particularly often because defaultpen is more general.<br />
|-<br />
| intersectionpoint<br />
| Determines the [[intersection]] (if there is exactly one) of two [[path|paths]]. Very useful command, and thus in many drawings.<br />
| intersectionpoints<br />
| Determine all the intersections of two [[path|paths]]. Obviously very similar to the previous command, but slightly less used as we generally want to know the intersection point of lines (rather than arbitrary paths).<br />
|-<br />
| rightanglemark<br />
| Marks a given [[angle]] as [[right angle|right]]. Used, obviously, in diagrams containing [[right angle|right angles]]; there are many of these.<br />
| anglemark<br />
| Marks a given [[angle]] with a given value. Used surprisingly little, since directly marking [[angle|angles]] isn't generally that important, but angle chase solutions will make heavy use of it.<br />
|-<br />
| linewidth<br />
| Sets the (visual -- [[line|lines]] have no real [[width]]!) [[width]] of a [[line]]. Also little used because defaultpen is more general.<br />
| currentpicture<br />
| A reference to the current picture. Used as an auxiliary command in other commands. This is the default value, so it is used only in very complicated drawings (or as a formality/copied and pasted sections).<br />
|}<br />
<br />
Note that simply searching "asy" will generally turn up [[Asymptote (Vector Graphics Language)|Asymptote]] drawings or discussions of such; especially when combined with a username or date range, simply remembering a post had any [[Asymptote (Vector Graphics Language)|Asymptote]] in it whatsoever is usually a good way to find it. As [[Asymptote (Vector Graphics Language)|Asymptote]] becomes more and more popular, the previous statement will become less true ([[LaTeX]], for example, is in a huge number of posts these days), but for now the numbers are small enough that you can sift through them pretty quickly.</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=Search_(disambiguation)&diff=70689Search (disambiguation)2015-06-08T05:17:18Z<p>BOGTRO: Created page with "<b>Search</b> could refer to: * Help:Searching - an explanation of how to search the AoPSWiki * Searching the community - a tutorial on how to effectively search ..."</p>
<hr />
<div><b>Search</b> could refer to:<br />
<br />
* [[Help:Searching]] - an explanation of how to search the [[AoPSWiki]]<br />
* [[Searching the community]] - a tutorial on how to effectively search the [http://artofproblemsolving.com/community AoPS Community]<br />
<br />
{{disambig}}</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=Search&diff=70688Search2015-06-08T05:14:31Z<p>BOGTRO: Redirected page to Search (disambiguation)</p>
<hr />
<div>#redirect [[Search (disambiguation)]]</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=Search&diff=70687Search2015-06-08T05:12:55Z<p>BOGTRO: Redirected page to Searching the community</p>
<hr />
<div>#redirect [[Searching the community]]</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=How_to_use_search_in_the_community&diff=70686How to use search in the community2015-06-08T05:12:01Z<p>BOGTRO: Redirected page to Searching the community</p>
<hr />
<div>#redirect [[Searching the community]]</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=How_to_use_search_in_the_community&diff=70685How to use search in the community2015-06-08T05:11:31Z<p>BOGTRO: Redirected page to Searching the Community</p>
<hr />
<div>#redirect [[Searching the Community]]</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=Searching_the_community&diff=70684Searching the community2015-06-08T05:08:57Z<p>BOGTRO: Created page with "This article is an introduction to <b>searching</b> the [http://artofproblemsolving.com/community AoPS forums]. All searching takes place from one of three pages: the [http://..."</p>
<hr />
<div>This article is an introduction to <b>searching</b> the [http://artofproblemsolving.com/community AoPS forums]. All searching takes place from one of three pages: the [http://artofproblemsolving.com/community main webpage], any of the specific forums, or from the [http://artofproblemsolving.com/community/search dedicated webpage]. <br />
=Searching methods=<br />
==Searching from the community==<br />
[[Image:search.png|thumb|right|300px|Searching from the community page]]<br />
<br />
The first of these two options is shown in the image to the right. It is primarily useful for quickly searching, especially when the search is of a general nature and without a specific post in mind. The method is simple: simply type your query into the "Search Community" field, click the magnifying glass (or press the Enter key), and posts containing terms matching your query will be shown to you. The parts of the posts that match your query will be <span style="background:yellow"> highlighted in yellow</span>. For example, when searching for problems involving a [[circle]], one would simply type "[[circle]]" into the indicated field, getting a result similar to the following image:<br />
<br />
[[Image:searchresult.png|thumb|right|300px|Result of searching "[[circle]]"]]<br />
<br />
Clicking on any of these results will open the full topic in which the post was made, starting from the post you clicked on. For example, if the post you clicked on was the fourth post in its topic, you would originally see that post and could scroll up (or down) to see the rest of the topic.<br />
<br />
If these are not the results you were looking for, you can click the "Edit search settings" link in the top right corner to adjust your search parameters. <br />
<br />
==Searching from a forum==<br />
<br />
It is possible to initiate a search from a specific forum, using the toolbar on its header. This will limit the search results to posts in that forum. <br />
<br />
[[Image:searchforum.png|thumb|right|500px|The header of a forum]]<br />
<br />
To search from a forum, click the magnifying glass on its header (see image to the right). This will redirect you to the main search webpage, with the forum information already filled in. <br />
<br />
==Searching from the main webpage==<br />
<br />
[[Image:search2.png|thumbnail|left|300px|Searching from the [http://artofproblemsolving.com/community/search webpage]]]<br />
<br />
Compared to the other options, the [http://artofproblemsolving.com/community/search webpage] gives you significantly more ways to customize your search. There are five different fields to be filled in, but any of them can be left blank. For example, to search for all posts by [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk] made within the last year, the "search term" and "Posted In forum" fields should be left blank, but the other fields should be filled out with the appropriate information. It is even possible to leave every field blank, in which case the search results will mimic the [[global feed]]. The five fields are:<br />
<br />
{| class="wikitable"<br />
|+ Search fields<br />
|-<br />
! Field<br />
! Function<br />
|-<br />
| Search term<br />
| Fairly self-explanatory: enter the term(s) that you are searching for. Note that titles, tags, posts, and sources are all simultaneously searched. To search these separately, click the indicated option. It is possible to search different places for different terms simultaneously; for example, to search for [[AMC]] problems using [[Simon's Favorite Factoring Trick]], search for posts containing "[[SFFT]]" in topics with source containing "[[AMC]]". The indicated option will also allow you the choice of restricting your search to opening posts. This field is blank by default, indicating that all posts are searched regardless of content.<br />
<br />
Searching for multiple terms will return posts matching at least one of those terms, prioritizing posts "closer" to the query as a whole. See the following section for ways to further customize these queries.<br />
|-<br />
| Posted By User<br />
| Enter the name(s) of user(s) to restrict your search to. The search results will only contain posts posted by the user(s) you entered. Note that the posters of the original <i>topics</i> may be different from the users you enter here. You can also search by user ID instead of username, if you happen to know the ID of the user you are searching for (you can find this in their profile URL, which is of the form artofproblemsolving.com/community/user/<user ID>). Users entered must be valid users and will be authenticated prior to searching. This field is blank by default, indicating that posts by all users are searched.<br />
|-<br />
| Posted In Forum<br />
| Enter the name(s) of forum(s) to restrict your search to. The search results will only contain posts posted in the forum(s) you entered. If you reached this webpage through clicking on the magnifying glass in one of the forums, this field will be pre-populated with that forum. Forums entered must be valid forums and will be authenticated prior to searching. This field is blank by default, indicating that all forums are searched.<br />
<br />
Note: On the previous website, forums were associated with a unique ID that could be used in searching, similar to user ID numbers, but this is no longer the case; type in the name of the forum instead.<br />
|-<br />
| Dates<br />
| Select the timeframe in which posts you're searching for must have been made. The options are "Any" (default), "During the last 24 hours", "During the last week", "During the last month", "During the last year", or any manually entered date range.<br />
|-<br />
| Sorting<br />
| Select whether to sort results by "Relevance" (default), "Newest first", or "Oldest first". If "relevance" is selected, the posts will be sorted according to a scoring algorithm that approximates how well a post correlates to the search query. The other two options, "Newest first" and "Oldest first", are self-explanatory.<br />
|}<br />
<br />
For example, to search for the aforementioned posts made by [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk] within the last year, the "Search term" field should be blank, the "Posted by User" field should contain [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk], the "Posted in Forum" field should be blank, the "Dates" field should be set to "During the last year", and the "Sorting" field can be set according to how the searcher wishes the results to be presented. To search for topics that [http://artofproblemsolving.com/community/user/rrusczyk rrusczyk] has started within the last year, the steps are the same, except that the "search only the first post of each topic" should be selected. See the images below.<br />
<br />
[[Image:rrusczykposts.png|thumb||530px|Posts by rrusczyk in the last year]]<br />
[[Image:rrusczykposts2.png|thumb|left|420px|Topics started by rrusczyk in the last year]]<br />
<br />
=Getting the most out of search=<br />
==Searching for a specific post==<br />
One of the most common uses of search is to find a specific post that you remember some details about, but cannot find. For example, you might recall having once read a particularly well-written solution, a very nice question, or an important announcement, but you can't remember quite where you saw it before. How frustrating!<br />
<br />
Obviously, the more details you remember about the post, the more likely you are to find it. If you remember that, for example, the post was written sometime in the summer of 2013, you can set the date range from (for example) May to September of that year. If you remember the author, that narrows down the possibilities significantly, but even remembering that it was one of several authors is a good way to whittle the possibilities down. Finally, remembering the forum that it was posted in would be excellent, but even if you only vaguely remember the post, you can make some educated guesses. For example, if the post was about a new and exciting technique for the [[USAMO]], it was probably posted in either the [http://artofproblemsolving.com/community/c5_contests_amp_programs Contests & Programs] forum or the [http://artofproblemsolving.com/community/c6_high_school_olympiads High School Olympiads] forum. If the post was a collection of [[MATHCOUNTS]] strategies, it's almost certainly in [http://artofproblemsolving.com/community/c3_middle_school_math Middle School Math]. <br />
<br />
==General searching tips==<br />
<br />
Of course, the above strategies are helpful, but still leave a lot of posts to sift through - unless you remember some of the language used in the post. You might remember, for example, a particularly memorable phrase in the post, or perhaps they used a math problem as reference that you remember a bit about. In these cases,<br />
<ul><br />
<li>Include, in your search query, unusual or uncommon words. For example, searching for just the word "[[circumcenter]]", along with the tips in the previous section, narrows down the possibilities significantly</li><br />
<li>Avoid common words such as "a", "the", "of", and so on, even if you remember a word-for-word phrase from the post containing these words. You'll get bogged down in posts matching those words - which there are a lot of!</li><br />
<li>Avoid searching words that are contained within another common word, as they will get matched to words you certainly didn't intend. For example, search queries containing the word "in" might return results for "logg<b>in</b>g", "<b>In</b>equality", and so on. The word "a" is particularly guilty of this, as it often returns words containing the letter "a".</li><br />
<li>Be sure to avoid searching for words that are special modifiers - see the below section. In particular, avoid searches containing the words "and" and "not". Similarly, do not include quotes ("), asterisks (*), question marks (?), plus signs (+), minus signs (-), or parentheses as these all represent special commands.<br />
</ul><br />
<br />
For example, if you remember a post contained the phrase "the three [[perpendicular bisector|perpendicular bisectors]] of a [[triangle]] intersect at the [[circumcenter]]", your search query should be something similar to "[[perpendicular bisector|perpendicular bisectors]] intersect [[circumcenter]]", as these are all specific words that limit the number of posts returned (unlike words like "of", "a", "the", and "at"). <br />
<br />
==Customizing search queries==<br />
<br />
We've already mentioned that posts are matched to the search query using a scoring algorithm, which approximates how "close" a post is to the given query. However, especially when searching for multiple terms, this algorithm often weights certain factors in different ways than the user intended. As such, there are several ways to customize your search queries.<br />
<br />
{| class="wikitable"<br />
|+ Customizing search queries<br />
|-<br />
| Operator<br />
| Example<br />
| Result<br />
|-<br />
| <i>(no adjustment)</i> <br />
| incenter circumcenter<br />
| Returns posts containing the word "[[incenter]]" and/or the word "[[circumcenter]]", with higher weight given to posts containing both.<br />
|-<br />
| +<br />
| +incenter circumcenter<br />
| Returned posts <b>must</b> contain the word "[[incenter]]", but may or may not contain "[[circumcenter]]". Again, higher weight is given to posts containing both words.<br />
|-<br />
| -<br />
| -incenter circumcenter excenter<br />
| Returned posts <b>must not</b> contain the word "[[incenter]]". Returned posts will contain the word "[[circumcenter]]" and/or the word "[[excenter]]", with higher weight given to posts containing both.<br />
|-<br />
| AND<br />
| incenter AND circumcenter<br />
| Returned posts <b>must</b> contain <i>both</i> "[[incenter]]" and "[[circumcenter]]". This is equivalent to the query "+incenter +circumcenter".<br />
|-<br />
| NOT<br />
| incenter NOT circumcenter<br />
| Returned posts will contain "[[incenter]]", but will <b>not</b> contain "[[circumcenter]]". Equivalent to the "-" and "!" operators.<br />
|-<br />
| "" (quotes)<br />
| "incenter circumcenter"<br />
| Returns posts containing the phrase "incenter circumcenter". Punctuation is usually ignored in results, so posts containing "incenter, circumcenter" or "incenter-circumcenter" will also be returned.<br />
|-<br />
| ? and *<br />
| te?t, inc*, in*e<br />
| Wildcard symbols. The ? symbol allows any character to replace it, so posts containing the words "test" or "text" will match the query "te?t". The * symbol allows any number of characters to replace it, so posts containing the words "[[incenter]]", "[[incircle]]", "[[inclusive]]", etc. will match the query "inc*". The * symbol can also be used in the middle of a word, so posts containing the words "interface", "[[incircle]]", "intermediate", "[[infinite]]", etc. will all match the query "in*e". <br />
|-<br />
| () (parentheses)<br />
| incenter AND (circumcenter OR excenter)<br />
| Grouping symbols to allow one boolean command (e.g. AND, NOT, +, -, !) to modify multiple elements. The example returns posts that contain both "[[incenter]]" and at least one of "[[circumcenter]]" or "[[excenter]]". Equivalent to the query "(incenter AND circumcenter) OR (incenter AND excenter)" (as usual, boolean logic applies to search strings).<br />
|-<br />
| \ <br />
| \AND<br />
| An "escape" character that allows you to search for reserved keywords and symbols. For example, the above query will return posts containing the word "and". Without the escape character, the search engine would parse the query "AND" as a command linking two nonexistent terms, and would thus throw an error. Similarly, the search term "[[incenter]] \AND [[circumcenter]]" would include results containing the word "[[incenter]]" and the word "and", but not the word "[[circumcenter]]".<br />
<br />
Note: in order to search for terms containing backslashes, such as LaTeX commands, the somewhat non-intuitive \\ is necessary (the first backslash "escapes" the second one). <br />
|}<br />
<br />
Note that, when using search modifiers, the <span style="background:yellow"> yellow background</span> indicating words that match your query will not generally be entirely accurate; for example, searching for "[[incenter]] AND [[circumcenter]]" will return posts containing both words as expected, but the word "and" will also be highlighted. Don't get confused by this - the search engine is still searching according to your query (and is not searching for the word "and"), the highlighting is simply slightly misleading.<br />
<br />
=Searching for LaTeX and Asympotote=<br />
<br />
Searching for [[LaTeX]] or [[Asymptote]] can be complicated, as they are their own languages, but this can actually be a big advantage! Predicting what code they've used is usually quite easy, and since the keywords are generally quite unique, searching for them will often narrow results down to posts using [[LaTeX]]/[[Asymptote]] themselves. Below are some common commands that [[LaTeX]]/[[Asymptote]] users often use, to help you search for them.<br />
<br />
==Searching for LaTeX==<br />
[[LaTeX]] is a programming language for rendering mathematical statements, and is very popular on [[AoPS]] (and other mathematical sources). [[LaTeX]] commands are enclosed in dollar signs for rendering, but you should not generally include those while searching. If you are searching for "full" commands (e.g. \frac{1}{2}), it is highly recommended that you enclose the entire command with quotation marks (e.g. "\frac{1}{2}"), as otherwise it may parse as three different search terms (\frac, 1, and 2).<br />
<br />
{| class="wikitable"<br />
|+ Common LaTeX commands<br />
| Command<br />
| Use<br />
| Example<br />
| Rendered<br />
|-<br />
| \frac<br />
| Creates fractions<br />
| \frac{1}{2}<br />
| <math>\frac{1}{2}</math><br />
|-<br />
| \sqrt<br />
| Creates square (or, more generally, <math>n</math>th) roots<br />
| \sqrt{3}, \sqrt[3]{3}<br />
| <math>\sqrt{3}</math>, <math>\sqrt[3]{3}</math><br />
|-<br />
| \leq, \neq, \geq<br />
| Less than or equal to, not equal to, greater than or equal to (respectively)<br />
| a \leq b, a \neq b, a \geq b<br />
| <math>a \leq b, a \neq b, a \geq b</math><br />
|-<br />
| \alpha<br />
| Renders greek letters (most often alpha, beta, epsilon, pi, theta, phi, and omega)<br />
| \alpha+\beta=\pi-\epsilon<br />
| <math>\alpha+\beta=\pi-\epsilon</math><br />
|-<br />
|\rightarrow, \implies, \iff<br />
| Used for implication, algorithms, etc.<br />
| a>b \implies a^2>b^2, a>b \iff a-b>0, A\rightarrow A+1<br />
| <math>a>b \implies a^2>b^2, a>b \iff a-b>0, A\rightarrow A+1</math><br />
|-<br />
|\sum, \prod, \int<br />
|Used for summation, product, and integration symbols<br />
|\sum_1^5 x=15, \prod_1^5x=120, \int_1^5x=12<br />
|<math>\sum_1^5 x=15, \prod_1^5x=120, \int_1^5x=12</math><br />
|}<br />
<br />
See [[LaTeX:Symbols]] for a more comprehensive list of LaTeX commands, and use the [[http://artofproblemsolving.com/texer/ TeXeR]] to test how commands look when rendered.<br />
<br />
==Searching for Asymptote==<br />
[[Asymptote (Vector Graphics Language)|Asymptote]] is a programming language for creating diagrams. Unlike [[LaTeX]], dollar signs are not necessary, and [[Asymptote (Vector Graphics Language)|Asymptote]] code is enclosed in [asy] tags. [[Asymptote (Vector Graphics Language)|Asymptote]] commands take the form of most modern programming languages; lines are generally of the form <i>command(param1, param2, ...)</i> (this is different from TeX, where each parameter is enclosed in separate brackets). <br />
<br />
"Unfortunately" (for our purposes), most [[Asymptote (Vector Graphics Language)|Asymptote]] commands are simply the word-for-word descriptors of their function; for example, the command that returns the [[midpoint]] of a path is simply "[[midpoint]]", and the command that returns the [[circumcenter]] of a triangle is "[[circumcenter]]". This is further complicated by the usage of [[variable|variables]], the names of which are entirely up to the posters (unlike TeX, in which [[variable|variables]] are generally not used). Below are commonly used [[Asymptote (Vector Graphics Language)|Asymptote]] commands that are not actual words, so they are less likely to be confused with other posts during searching.<br />
<br />
{| class="wikitable"<br />
|+ Common [[Asymptote (Vector Graphics Language)|Asymptote]] commands<br />
| Command<br />
| Purpose<br />
| Command<br />
| Purpose<br />
|-<br />
| defaultpen<br />
| Adjusts the default settings for the pen. Very likely for this command to be in an [[Asymptote (Vector Graphics Language)|Asymptote]] drawing.<br />
| orthographic<br />
| Adjust the "camera position" in [[dimension|3-D]] drawings. Very likely for this command to be in a [[dimension|3-D]] [[Asymptote (Vector Graphics Language)|Asymptote]] drawing.<br />
|-<br />
| filldraw<br />
| Colors a given shape in some manner. Useful for shading in parts of diagrams; used reasonably foten.<br />
| unitsize<br />
| Sets the default size of a "unit" to a specified value. Default is very small. Not used particularly often because defaultpen is more general.<br />
|-<br />
| intersectionpoint<br />
| Determines the [[intersection]] (if there is exactly one) of two [[path|paths]]. Very useful command, and thus in many drawings.<br />
| intersectionpoints<br />
| Determine all the intersections of two [[path|paths]]. Obviously very similar to the previous command, but slightly less used as we generally want to know the intersection point of lines (rather than arbitrary paths).<br />
|-<br />
| rightanglemark<br />
| Marks a given [[angle]] as [[right angle|right]]. Used, obviously, in diagrams containing [[right angle|right angles]]; there are many of these.<br />
| anglemark<br />
| Marks a given [[angle]] with a given value. Used surprisingly little, since directly marking [[angle|angles]] isn't generally that important, but angle chase solutions will make heavy use of it.<br />
|-<br />
| linewidth<br />
| Sets the (visual -- [[line|lines]] have no real [[width]]!) [[width]] of a [[line]]. Also little used because defaultpen is more general.<br />
| currentpicture<br />
| A reference to the current picture. Used as an auxiliary command in other commands. This is the default value, so it is used only in very complicated drawings (or as a formality/copied and pasted sections).<br />
|}<br />
<br />
Note that simply searching "asy" will generally turn up [[Asymptote (Vector Graphics Language)|Asymptote]] drawings or discussions of such; especially when combined with a username or date range, simply remembering a post had any [[Asymptote (Vector Graphics Language)|Asymptote]] in it whatsoever is usually a good way to find it. As [[Asymptote (Vector Graphics Language)|Asymptote]] becomes more and more popular, the previous statement will become less true ([[LaTeX]], for example, is in a huge number of posts these days), but for now the numbers are small enough that you can sift through them pretty quickly.</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=File:Rrusczykposts2.png&diff=70682File:Rrusczykposts2.png2015-06-08T01:08:10Z<p>BOGTRO: BOGTRO uploaded a new version of &quot;File:Rrusczykposts2.png&quot;</p>
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<div></div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=File:Rrusczykposts.png&diff=70680File:Rrusczykposts.png2015-06-08T01:07:06Z<p>BOGTRO: </p>
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<div></div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=File:Searchforum.png&diff=70679File:Searchforum.png2015-06-08T00:19:57Z<p>BOGTRO: </p>
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<div></div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=File:Search2.png&diff=70676File:Search2.png2015-06-07T23:57:12Z<p>BOGTRO: </p>
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<div></div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=File:Search.png&diff=70675File:Search.png2015-06-07T23:50:44Z<p>BOGTRO: </p>
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<div></div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=AoPS_Wiki:FAQ&diff=58519AoPS Wiki:FAQ2014-01-02T19:11:56Z<p>BOGTRO: /* I rated a post but the post rating does not appear on the post. Why? */</p>
<hr />
<div>{{shortcut|[[A:FAQ]]}}<br />
<br />
This is a community created list of Frequently Asked Questions about Art of Problem Solving. If you have a request to edit or add a question on this page, please make it [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=416&t=414129 here].<br />
<br />
== General==<br />
<br />
<br />
==== Can I change my user name? ====<br />
<br />
:As indicated during the time of your registration, you are unable to change your username. <br />
::[[File:Registration.jpg]]<br />
<br />
====What software does Art of Problem Solving use to run the website?====<br />
<br />
:* Forums: phpBB3<br />
:* Blog: User Blog Mod for phpBB3<br />
:* Search: Sphinx<br />
:* Wiki: MediaWiki<br />
:* Asymptote, Latex, and Geogebra are generated through their respective binary packages<br />
:* Videos: YouTube<br />
<br />
Note that as AoPS does not develop the above software, they are not responsible for the proper functioning of said software. Bug reports and feature requests should be sent to the appropriate developers of the above software.<br />
<br />
== Forums ==<br />
<br />
==== What do the stars under my username next to a forum post represent? ====<br />
<br />
:On the Art of Problem Solving website, under your username, you will find stars, as well as the name of one of the Millenium Problems. The number of stars you have, as well as the name of the Millenium Problem, depends on your post count. Here is the table that determines your "rank."<br />
<br />
:*0 - 19 New Member (Zero Stars)<br />
:*20 - 49 P Versus NP (Half Star)<br />
:*50 - 99 Hodge Conjecture (One Star)<br />
:*100 - 249 Poincare Conjecture (Two Stars)<br />
:*250 - 499 Riemann Hypothesis (Two and Half stars) <br />
:*500 - 999 Yang Mills Theory (Three Stars)<br />
:*1000 - 2499 Navier-Stokes Equation (Four Stars)<br />
:*2500 - <math>\infty</math> Birch & Swinnerton Dyer. (Five Stars)<br />
:*Administrators have six stars.<br />
<br />
==== I got the message "You can not post at this time" when trying to post, why? ====<br />
<br />
:New users are not allowed to post messages with URLs and various other things. Once you have five posts you can post normally.<br />
<br />
====I got the message "Too many messages." when trying to send a private message, why?====<br />
:To prevent PM spam abuse, users with less than five forum posts are limited to four private messages within a forty-eight hour period.<br />
<br />
==== If I make more posts, it means I'm a better user, right? ====<br />
<br />
:Absolutely not. Post quality is far more important than post quantity. Users making a lot of senseless posts are often considered worse users, or spammers.<br />
<br />
==== I have made some posts but my post count did not increase. Why? ====<br />
<br />
:When you post in some of the forums, such as the Test Forum, Mafia Forum, and the Fun Factory, it does not count towards your post count.<br />
<br />
==== When can I rate posts? ====<br />
<br />
:You will be able to rate posts after posting 10 messages.<br />
<br />
==== Who can see my post rating? ====<br />
<br />
:Only you, moderators, and administrators.<br />
<br />
==== I rated a post but the post rating does not appear on the post. Why?====<br />
:One or two ratings is not enough to determine a post's overall rating. Therefore, a post has to receive a preset number of ratings before the overall rating of the post appears. Ratings will continue to affect the user's overall post rating even if they are not yet displayed on the post.<br />
<br />
==== How does AoPS select moderators? ====<br />
<br />
:When a new moderator is needed in the forums, AoPS administrators first check if any current moderators could serve as a moderator of the forum which needs a moderator. Should none be found, AoPS administrators and/or other moderators scour the forum looking for productive users. They may also ask for suggestions from other moderators or trusted users on the site. Once they have pinpointed a possible candidate based on their long term usage of the site, productive posts in the forum, and having no recent behavioral issues, that user is asked if he or she would like to moderate the forum. <br />
<br />
:Less active forums often have no moderator. Inappropriate posts should be reported by users and administrators will take appropriate action.<br />
<br />
:AoPS receives MANY requests to be a moderator. As they receive so many, it is possible that you won't get a response should you request to be one. Also, AoPS very rarely makes someone a mod for asking to be one, so '''please do not ask'''.<br />
<br />
==== I believe a post needs corrective action. What should I do? ====<br />
<br />
:If you believe a post needs moderative action, you may report it by clicking the "!" icon on the bottom-right corner of that post. If it's a minor mistake, you may want to PM the offending user instead and explain how they can make their post better. Usually, you shouldn't publicly post such things on a thread itself, which is called "backseat moderation" and is considered rude.<br />
<br />
==== How long of a non-commented thread is considered reviving? ====<br />
<br />
:If any post is still on-topic and isn't spammy or anything, it isn't considered reviving. The definition of reviving in the Games forum is 1 month. However, everyone has a different period of time that they consider reviving. In general, apply common sense.<br />
<br />
==== Someone is marking all my posts as spam, what should I do? ====<br />
<br />
:It happens to everyone. There's really not much you can do.<br />
<br />
==== Are posts marked spam more often than good? ====<br />
<br />
:No. The most common rating is 6 cubes. We understand that many posts are rated 1 when they shouldn't be. We also know that many posts are rated a 6 when they shouldn't be. It pretty much all averages out in the end. The best way to safeguard yourself is not to complain about it! In fact, most other members cannot see your rating. If you want to make a mark here, let your post quality do the talking.<br />
<br />
==== How do I post images? ====<br />
:There are limited attachment options for posts. Attachments have an overall size limit, and will be deleted as they get old. Attachments also may be deleted during any server move or software upgrade or change. You may instead wish to host images on another site and embed them in to your post using the [img] tags. The general format is [img]{url to image}[/img], excluding the braces. There are a number of image hosting sites, including:<br />
:* [http://imgur.com/ Imgur]<br />
:* [http://photobucket.com Photobucket]<br />
::*In thumbnail view<br />
:::*Hover over image and click the text box labeled IMG code. It will automatically copy to your clipboard<br />
:::*Paste to your message<br />
::*In image view<br />
:::*Look for the '''Links''' box which should appear at the right side of your screen<br />
:::*Click the box labeled IMG Code<br />
:::*Copy the text<br />
:::*Paste to your message<br />
:* [http://imageshack.com ImageShack]<br />
:* [http://minus.com minus.com]<br />
::*Go to image you wish to embed<br />
::*Click the share tab<br />
::*Copy the contents of the Forum Code text<br />
::*Paste to your message<br />
:* [http://bayfiles.com bayfiles.com]<br />
:* [http://picasaweb.google.com Picasa]<br />
:** This will vary by browser and OS, but the process is similar. The provided directions are for Firefox on Windows<br />
:** Go to the image you want to embed<br />
:** Right click on the image<br />
:** Select Copy Image Location<br />
:** Paste into your message, surrounding the pasted text with [img] and [/img] tags<br />
:* [http://www.flickr.com Flickr]<br />
<br />
See also:<br />
[http://www.artofproblemsolving.com/Wiki/index.php/Direct_Image_Link Direct Image Link]<br />
<br />
== Blogs ==<br />
==== How come I can't create a blog? ====<br />
One needs to have at least 5 posts in order to make a blog.<br />
<br />
== Contests ==<br />
==== Where can I find past contest questions and solutions? ====<br />
:In the [http://www.artofproblemsolving.com/Forum/resources.php Contests] section.<br />
<br />
==== How do I get problems onto the contest page? ====<br />
<br />
:Make a topic for each question in the appropriate forum, copy/paste the urls to the National Olympiad. Your problems may eventually be submitted into the Contest page.<br />
<br />
==== Who can I ask to add posts to the contests section? ====<br />
:Any one of the members in the the [http://www.artofproblemsolving.com/Forum/memberlist.php?mode=group&g=417 RManagers] group.<br />
<br />
==== What are the guidelines for posting problems to be added to the contests section? ====<br />
:Refer to the [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=144&t=195579 guidelines in this post].<br />
<br />
==== Why is the wiki missing many contest questions? ====<br />
:Generally, it is because users have not yet posted them onto the wiki (translation difficulties, not having access to the actual problems, lack of interest, etc). If you have a copy, please post the problems in the Community Section! In some cases, however, problems may be missing due to copyright claims from maths organizations. See, for example, [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1391106#p1391106 this post].<br />
<br />
==== What if I find an error on a problem? ====<br />
Please post an accurate description of the problem in [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=133&t=426693 this thread]<br />
<br />
== LaTeX, Asymptote, GeoGebra ==<br />
==== What is LaTeX, and how do I use it? ====<br />
<br />
:<math>\LaTeX</math> is a typesetting markup language that is useful to produce properly formatted mathematical and scientific expressions.<br />
<br />
==== How can I download LaTeX to use on the forums? ====<br />
<br />
:There are no downloads necessary; the forums and the wiki render LaTeX commands between dollar signs. <br />
<br />
==== How can I download LaTeX for personal use? ====<br />
:You can download TeXstudio [http://texstudio.sourceforge.net here] or TeXnicCenter [http://www.texniccenter.org here]<br />
<br />
==== Where can I find a list of LaTeX commands? ====<br />
:See [[LaTeX:Symbols|here]].<br />
<br />
==== Where can I test LaTeX commands? ====<br />
<br />
:[[A:SAND|Sandbox]] or [http://www.artofproblemsolving.com/Resources/texer.php TeXeR]. <br />
<br />
==== Where can I find examples of Asymptote diagrams and code? ====<br />
<br />
:Search this wiki for the <tt><nowiki><asy></nowiki></tt> tag or the Forums for the <tt><nowiki>[asy]</nowiki></tt> tag. See also [[Asymptote:_Useful_commands_and_their_Output|these examples]] and [[Proofs without words|this article]] (click on the images to obtain the code).<br />
<br />
==== How can I draw 3D diagrams? ====<br />
<br />
:See [[Asymptote: 3D graphics]].<br />
<br />
==== What is the cse5 package? ==== <br />
<br />
:See [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=519&t=149650 here]. The package contains a set of shorthand commands that implement the behavior of usual commands, for example <tt>D()</tt> for <tt>draw()</tt> and <tt>dot()</tt>, and so forth.<br />
<br />
==== What is the olympiad package? ====<br />
<br />
:See [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=519&t=165767 here]. The package contains a set of commands useful for drawing diagrams related to [[:Category:Olympiad Geometry Problems|olympiad geometry problems]].<br />
<br />
==== Can I convert diagrams from GeoGebra to other formats? ====<br />
:It is possible to export GeoGebra to [[Asymptote (Vector Graphics Language)|Asymptote]] (see [[User:Azjps/geogebra|here]]), PsTricks, and PGF/TikZ; and GeoGebra animations into .gif or video files. <br />
<br />
== AoPSWiki ==<br />
==== Is there a guide for wiki syntax? ====<br />
<br />
:See [http://en.wikipedia.org/wiki/Help:Wiki_markup wiki markup], [[AoPSWiki:Tutorial]], and [[Help:Contents]].<br />
<br />
==== What do I do if I see a mistake in the wiki? ====<br />
<br />
:Edit the page and correct the error! You can edit most pages on the wiki. Click the "edit" button on the right sidebar to edit a page.<br />
<br />
==== Why can't I edit the wiki? ====<br />
<br />
You must be a registered user to edit. To be registered, make sure you give a correct email, and activate your account.<br />
<br />
== Miscellaneous ==<br />
==== Is it possible to join the AoPS Staff? ====<br />
<br />
:Yes. Mr. Rusczyk will sometimes hire a small army of college students to work as interns. You must be at least in your second semester of your senior year and be legal to work in the U.S. (at least 16).<br />
<br />
==== What is the minimum age to be an assistant in an Art of Problem Solving class? ====<br />
<br />
:You must have graduated from high school, or at least be in the second term of your senior year.<br />
<br />
==What do some of the acronyms such as "OP" stand for?==<br />
*'''AFK'''- Away from keyboard<br />
*'''AoPS'''- Art of Problem Solving, the website you're on right now!<br />
*'''AIME'''- American Invitational Mathematics Examination<br />
*'''AMC'''- American Math Competititions<br />
*'''ATM'''- At the Moment<br />
*'''brb'''- Be right Back<br />
*'''BTW'''- By the way<br />
*'''CEMC''' - Centre for Mathematics and Computing<br />
*'''EBWOP'''- Editing by way of post<br />
*'''FTW'''- For the Win, a game on AoPS<br />
*'''gj'''- Good Job<br />
*'''GLHF'''-Good Luck Have Fun<br />
*'''gtg''' - Got to go<br />
*'''ID(R)K'''-I Don't (Really) Know<br />
*'''iff'''-If and only if<br />
*'''IIRC'''- If I recall correctly<br />
*'''IMO'''- In my opinion (or International Math Olympiad, depending on context)<br />
*'''lol'''- Laugh Out Loud<br />
*'''MC'''- Mathcounts, a popular math contest for Middle School students.<br />
*'''MOP'''- Mathematical Olympiad (Summer) Program<br />
*'''OBC'''- Online by computer<br />
*'''OMG'''- Oh My Gosh.<br />
*'''OP'''- Original Poster/Original Post/Original Problem, or Overpowered/Overpowering<br />
*'''QED'''- Quod erat demonstrandum, Latin for Which was to be proven<br />
*'''QS&A'''- Questions, Suggestions, and Announcements Forum<br />
*'''rotfl''' - Rolling on the floor laughing<br />
*'''sa''' - sa<br />
*'''smh''' - Shaking my head<br />
*'''USA(J)MO'''- USA (Junior) Mathematical Olympiad<br />
*'''V/LA'''- Vacation or Long Absence<br />
*'''WLOG'''- Without loss of generality<br />
*'''wrt'''- With respect to<br />
*'''wtg''' - Way to go<br />
*'''tytia'''- Thank you, that is all<br />
*'''xD'''- Bursting Laugh<br />
<br />
== FTW! ==<br />
<br />
==== How do you access FTW? ====<br />
You can access FTW by clicking FTW! on the green bar at the top of the page.<br />
<br />
<br />
==== Did FTW miscount my number of games?====<br />
<br />
No! However, the (Overall) rating statistics do not count games with less than 6 problems or less than 15 seconds.<br />
<br />
For example, if you have played 30 games, but not all of them were 6 problems or higher, then you will still be muted.<br />
<br />
== School ==<br />
<br />
==== What if I want to drop out of a class? ====<br />
:For any course with more than 2 classes, students can drop the course any time before the third class begins and receive a full refund. No drops are allowed after the third class has started. To drop the class, go to the My Classes section by clicking the My Classes link at the top-right of the website. Then find the area on the right side of the page that lets you drop the class. A refund will be processed within 10 business days.<br />
<br />
==== What if I miss a class? ====<br />
:There are classroom transcripts available under My Classes, available at the top right of the web site. You can view these transcripts in order to review any missed material. You can also ask questions on the class message board.<br />
<br />
==== Is there audio or video in class? ====<br />
There is no audio or video in the class. The classes are completely text based, in an interactive chat room environment, which allows students to ask questions at any time during the class. In addition to audio and video limiting interactivity, the technology isn't quite there yet for all students to be able to adequately receive streaming audio and video. <br />
<br />
====I feel like joining! What are my class choices? ====<br />
:[http://www.artofproblemsolving.com/School/classlist.php Class List] [http://www.artofproblemsolving.com/School/index.php?page=school.instructors Instructors List]</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=User:BOGTRO&diff=47634User:BOGTRO2012-07-14T03:55:10Z<p>BOGTRO: </p>
<hr />
<div>I have thought of a most marvelous wiki page, but this margin is too small to contain it.</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=User:BOGTRO&diff=47633User:BOGTRO2012-07-14T03:53:32Z<p>BOGTRO: </p>
<hr />
<div>I have thought of a truly magnificent wiki page, but this margin is too small to contain it.</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=1998_AHSME_Problems/Problem_29&diff=393341998 AHSME Problems/Problem 292011-06-06T19:53:08Z<p>BOGTRO: Created page with "== Problem 29 == A point <math>(x,y)</math> in the plane is called a lattice point if both <math>x</math> and <math>y</math> are integers. The area of the largest square that con..."</p>
<hr />
<div>== Problem 29 ==<br />
A point <math>(x,y)</math> in the plane is called a lattice point if both <math>x</math> and <math>y</math> are integers. The area of the largest square that contains exactly three lattice points in its interior is closest to<br />
<br />
<math> \mathrm{(A) \ } 4.0 \qquad \mathrm{(B) \ } 4.2 \qquad \mathrm{(C) \ } 4.5 \qquad \mathrm{(D) \ } 5.0 \qquad \mathrm{(E) \ } 5.6</math><br />
<br />
[[1998 AHSME Problems/Problem 29|Solution]]</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=1998_AHSME_Problems/Problem_2&diff=393331998 AHSME Problems/Problem 22011-06-06T19:51:24Z<p>BOGTRO: Created page with "== Problem 2 == Letters <math>A,B,C,</math> and <math>D</math> represent four different digits selected from <math>0,1,2,\ldots ,9.</math> If <math>(A+B)/(C+D)</math> is an integ..."</p>
<hr />
<div>== Problem 2 ==<br />
Letters <math>A,B,C,</math> and <math>D</math> represent four different digits selected from <math>0,1,2,\ldots ,9.</math> If <math>(A+B)/(C+D)</math> is an integer that is as large as possible, what is the value of <math>A+B</math>?<br />
<br />
<math> \mathrm{(A) \ }13 \qquad \mathrm{(B) \ }14 \qquad \mathrm{(C) \ } 15\qquad \mathrm{(D) \ }16 \qquad \mathrm{(E) \ } 17 </math><br />
<br />
[[1998 AHSME Problems/Problem 2|Solution]]</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=1998_AHSME_Problems/Problem_16&diff=393321998 AHSME Problems/Problem 162011-06-06T19:51:09Z<p>BOGTRO: Created page with "== Problem 16 == The figure shown is the union of a circle and two semicircles of diameters <math>a</math> and <math>b</math>, all of whose centers are collinear. The ratio of th..."</p>
<hr />
<div>== Problem 16 ==<br />
The figure shown is the union of a circle and two semicircles of diameters <math>a</math> and <math>b</math>, all of whose centers are collinear. The ratio of the area, of the shaded region to that of the unshaded region is<br />
<br />
[[Image:Problem 16.png|center|###px]]<br />
<br />
<math> \mathrm{(A) \ } \sqrt{\frac ab} \qquad \mathrm{(B) \ }\frac ab \qquad \mathrm{(C) \ } \frac{a^2}{b^2} \qquad \mathrm{(D) \ }\frac{a+b}{2b} \qquad \mathrm{(E) \ } \frac{a^2 + 2ab}{b^2 + 2ab}</math><br />
<br />
[[1998 AHSME Problems/Problem 16|Solution]]</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=1998_AHSME_Problems/Problem_15&diff=393311998 AHSME Problems/Problem 152011-06-06T19:50:53Z<p>BOGTRO: Created page with "== Problem 15 == A regular hexagon and an equilateral triangle have equal areas. What is the ratio of the length of a side of the triangle to the length of a side of the hexagon?..."</p>
<hr />
<div>== Problem 15 ==<br />
A regular hexagon and an equilateral triangle have equal areas. What is the ratio of the length of a side of the triangle to the length of a side of the hexagon?<br />
<br />
<math> \mathrm{(A) \ }\sqrt{3} \qquad \mathrm{(B) \ }2 \qquad \mathrm{(C) \ }\sqrt{6} \qquad \mathrm{(D) \ }3 \qquad \mathrm{(E) \ }6 </math><br />
<br />
[[1998 AHSME Problems/Problem 15|Solution]]</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=1998_AHSME_Problems/Problem_14&diff=393301998 AHSME Problems/Problem 142011-06-06T19:50:36Z<p>BOGTRO: Created page with "== Problem 14 == A parabola has vertex of <math>(4,-5)</math> and has two <math>x-</math>intercepts, one positive, and one negative. If this parabola is the graph of <math>y = ax..."</p>
<hr />
<div>== Problem 14 ==<br />
A parabola has vertex of <math>(4,-5)</math> and has two <math>x-</math>intercepts, one positive, and one negative. If this parabola is the graph of <math>y = ax^2 + bx + c,</math> which of <math>a,b,</math> and <math>c</math> must be positive?<br />
<br />
<math> \mathrm{(A) \ } \text{only}\ a \qquad \mathrm{(B) \ } \text{only}\ b \qquad \mathrm{(C) \ } \text{only}\ c \qquad \mathrm{(D) \ } a\ \text{and}\ b\ \text{only} \qquad \mathrm{(E) \ } \text{none}</math><br />
<br />
[[1998 AHSME Problems/Problem 14|Solution]]</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=1998_AHSME_Problems/Problem_10&diff=393261998 AHSME Problems/Problem 102011-06-06T19:38:06Z<p>BOGTRO: Created page with "== Problem 10 == A large square is divided into a small square surrounded by four congruent rectangles as shown. The perimter of each of the congruent rectangles is <math>14</mat..."</p>
<hr />
<div>== Problem 10 ==<br />
A large square is divided into a small square surrounded by four congruent rectangles as shown. The perimter of each of the congruent rectangles is <math>14</math>. What is the area of the large square?<br />
<br />
<center><asy>pathpen = black+linewidth(0.7);<br />
D((0,0)--(7,0)--(7,7)--(0,7)--cycle); D((1,0)--(1,6)); D((0,6)--(6,6)); D((1,1)--(7,1)); D((6,7)--(6,1));<br />
</asy></center><br />
<br />
<math> \mathrm{(A) \ }49 \qquad \mathrm{(B) \ }64 \qquad \mathrm{(C) \ }100 \qquad \mathrm{(D) \ }121 \qquad \mathrm{(E) \ }196 </math><br />
<br />
[[1998 AHSME Problems/Problem 10|Solution]]</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=1998_AHSME_Problems/Problem_1&diff=393251998 AHSME Problems/Problem 12011-06-06T19:37:31Z<p>BOGTRO: Created page with "== Problem 1 == Each of the sides of five congruent rectangles is labeled with an integer. In rectangle A, <math>w = 4, x = 1, y = 6, z = 9</math>. In rectangle B, <math>w = 1, x..."</p>
<hr />
<div>== Problem 1 ==<br />
Each of the sides of five congruent rectangles is labeled with an integer. In rectangle A, <math>w = 4, x = 1, y = 6, z = 9</math>. In rectangle B, <math>w = 1, x = 0, y = 3, z = 6</math>. In rectangle C, <math>w = 3, x = 8, y = 5, z = 2</math>. In rectangle D, <math>w = 7, x = 5, y = 4, z = 8</math>. In rectangle E, <math>w = 9, x = 2, y = 7, z = 0</math>. These five rectangles are placed, without rotating or reflecting, in position as below. Which of the rectangle is the top leftmost one?<br />
<br />
<center><asy><br />
draw((0,5)--(0,7)--(3,7)--(3,5)--cycle);<br />
draw((0,4)--(9,4)--(9,2)--(6,2)--(6,0)--(0,0)--cycle);<br />
draw((3,0)--(3,4));draw((6,2)--(6,4));draw((0,2)--(6,2));<br />
label("$w$",(0,6),(-1,0));label("$x$",(1.5,7),(0,1));label("$y$",(3,6),(1,0));label("$z$",(1.5,5),(0,-1));<br />
</asy></center><br />
<br />
<math> \mathrm{(A)\ } A \qquad \mathrm{(B) \ }B \qquad \mathrm{(C) \ } C \qquad \mathrm{(D) \ } D \qquad \mathrm{(E) \ }E </math><br />
<br />
[[1998 AHSME Problems/Problem 1|Solution]]</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=1998_AHSME_Problems/Problem_9&diff=393191998 AHSME Problems/Problem 92011-06-06T19:30:54Z<p>BOGTRO: Created page with "== Problem 9 == A speaker talked for sixty minutes to a full auditorium. Twenty percent of the audience heard the entire talk and ten percent slept through the entire talk. Half ..."</p>
<hr />
<div>== Problem 9 ==<br />
A speaker talked for sixty minutes to a full auditorium. Twenty percent of the audience heard the entire talk and ten percent slept through the entire talk. Half of the remainder heard one third of the talk and the other half heard two thirds of the talk. What was the average number of minutes of the talk heard by members of the audience?<br />
<br />
<math> \mathrm{(A) \ } 24 \qquad \mathrm{(B) \ } 27\qquad \mathrm{(C) \ }30 \qquad \mathrm{(D) \ }33 \qquad \mathrm{(E) \ }36 </math><br />
<br />
[[1998 AHSME Problems/Problem 9|Solution]]</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=1998_AHSME_Problems/Problem_7&diff=393181998 AHSME Problems/Problem 72011-06-06T19:30:31Z<p>BOGTRO: Created page with "== Problem 7 == If <math>N > 1</math>, then <math>\sqrt[3]{N\sqrt[3]{N\sqrt[3]{N}}} =</math> <math> \mathrm{(A) \ } N^{\frac 1{27}} \qquad \mathrm{(B) \ } N^{\frac 1{9}} \qquad ..."</p>
<hr />
<div>== Problem 7 ==<br />
If <math>N > 1</math>, then <math>\sqrt[3]{N\sqrt[3]{N\sqrt[3]{N}}} =</math><br />
<br />
<math> \mathrm{(A) \ } N^{\frac 1{27}} \qquad \mathrm{(B) \ } N^{\frac 1{9}} \qquad \mathrm{(C) \ } N^{\frac 1{3}} \qquad \mathrm{(D) \ } N^{\frac {13}{27}} \qquad \mathrm{(E) \ } N</math><br />
<br />
[[1998 AHSME Problems/Problem 7|Solution]]</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=1998_AHSME_Problems/Problem_6&diff=393161998 AHSME Problems/Problem 62011-06-06T19:25:18Z<p>BOGTRO: Created page with "== Problem 6 == If <math>1998</math> is written as a product of two positive integers whose difference is as small as possible, then the difference is <math> \mathrm{(A) \ }8 \..."</p>
<hr />
<div>== Problem 6 ==<br />
If <math>1998</math> is written as a product of two positive integers whose difference is as small as possible, then the difference is <br />
<br />
<math> \mathrm{(A) \ }8 \qquad \mathrm{(B) \ }15 \qquad \mathrm{(C) \ }17 \qquad \mathrm{(D) \ }47 \qquad \mathrm{(E) \ } 93</math><br />
<br />
[[1998 AHSME Problems/Problem 6|Solution]]</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=1998_AHSME_Problems/Problem_3&diff=393151998 AHSME Problems/Problem 32011-06-06T19:25:02Z<p>BOGTRO: Created page with "== Problem 3 == If <math>\texttt{a,b,}</math> and <math>\texttt{c}</math> are digits for which <center><math>\begin{tabular}{r}&\ \texttt{7 a 2}\\ &- \texttt{4 8 b} \\ \hline ..."</p>
<hr />
<div>== Problem 3 ==<br />
If <math>\texttt{a,b,}</math> and <math>\texttt{c}</math> are digits for which<br />
<br />
<center><math>\begin{tabular}{r}&\ \texttt{7 a 2}\\ &- \texttt{4 8 b} \\ <br />
\hline <br />
&\ \texttt{c 7 3} \end{tabular}</math></center><br />
<br />
then <math>\texttt{a+b+c =}</math><br />
<br />
<math> \mathrm{(A) \ }14 \qquad \mathrm{(B) \ }15 \qquad \mathrm{(C) \ }16 \qquad \mathrm{(D) \ }17 \qquad \mathrm{(E) \ }18 </math><br />
<br />
[[1998 AHSME Problems/Problem 3|Solution]]</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=2011_AMC_10B_Problems/Problem_25&diff=393142011 AMC 10B Problems/Problem 252011-06-06T19:22:15Z<p>BOGTRO: Created page with "== Problem 25 == Let <math>T_1</math> be a triangle with sides <math>2011, 2012,</math> and <math>2013</math>. For <math>n \ge 1</math>, if <math>T_n = \triangle ABC</math> and ..."</p>
<hr />
<div>== Problem 25 ==<br />
<br />
Let <math>T_1</math> be a triangle with sides <math>2011, 2012,</math> and <math>2013</math>. For <math>n \ge 1</math>, if <math>T_n = \triangle ABC</math> and <math>D, E,</math> and <math>F</math> are the points of tangency of the incircle of <math>\triangle ABC</math> to the sides <math>AB, BC</math> and <math>AC,</math> respectively, then <math>T_{n+1}</math> is a triangle with side lengths <math>AD, BE,</math> and <math>CF,</math> if it exists. What is the perimeter of the last triangle in the sequence <math>( T_n )</math>?<br />
<br />
<math> \textbf{(A)}\ \frac{1509}{8} \qquad\textbf{(B)}\ \frac{1509}{32} \qquad\textbf{(C)}\ \frac{1509}{64} \qquad\textbf{(D)}\ \frac{1509}{128} \qquad\textbf{(E)}\ \frac{1509}{256}</math><br />
<br />
[[2011 AMC 10B Problems/Problem 25|Solution]]</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=2011_AMC_10B_Problems/Problem_24&diff=393022011 AMC 10B Problems/Problem 242011-06-06T19:16:15Z<p>BOGTRO: Created page with "== Problem 24 == A lattice point in an <math>xy</math>-coordinate system in any point <math>(x, y)</math> where both <math>x</math> and <math>y</math> are integers. The graph of..."</p>
<hr />
<div>== Problem 24 ==<br />
<br />
A lattice point in an <math>xy</math>-coordinate system in any point <math>(x, y)</math> where both <math>x</math> and <math>y</math> are integers. The graph of <math>y = mx +2</math> passes through no lattice point with <math>0 < x \le 100</math> for all <math>m</math> such that <math>1/2 < m < a</math>. What is the maximum possible value of <math>a</math>?<br />
<br />
<math> \textbf{(A)}\ \frac{51}{101} \qquad\textbf{(B)}\ \frac{50}{99} \qquad\textbf{(C)}\ \frac{51}{100} \qquad\textbf{(D)}\ \frac{52}{101} \qquad\textbf{(E)}\ \frac{13}{25}</math><br />
<br />
[[2011 AMC 10B Problems/Problem 24|Solution]]</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=AoPS_Wiki_talk:Problem_of_the_Day/June_7,_2011&diff=39295AoPS Wiki talk:Problem of the Day/June 7, 20112011-06-06T18:58:14Z<p>BOGTRO: /* Solution */</p>
<hr />
<div>==Problem==<br />
{{:AoPSWiki:Problem of the Day/June 7, 2011}}<br />
==Solution==<br />
<math>\sqrt{x+2}=x-18 \implies</math><br />
<math>x+2=(x-18)^2=x^2-36x+324 \implies</math><br />
<math>x^2-37x+322=0 \implies</math><br />
<math>(x-23)(x-14)=0</math>.<br />
<br />
Clearly <math>x=14</math> is extraneous, so our answer is <math>x=\boxed{23}</math>.</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=2010_AMC_12B_Problems/Problem_20&diff=388792010 AMC 12B Problems/Problem 202011-06-01T01:27:52Z<p>BOGTRO: /* Solution */</p>
<hr />
<div>== Problem==<br />
A geometric sequence <math>(a_n)</math> has <math>a_1=\sin x</math>, <math>a_2=\cos x</math>, and <math>a_3= \tan x</math> for some real number <math>x</math>. For what value of <math>n</math> does <math>a_n=1+\cos x</math>?<br />
<br />
<br />
<math>\textbf{(A)}\ 4 \qquad \textbf{(B)}\ 5 \qquad \textbf{(C)}\ 6 \qquad \textbf{(D)}\ 7 \qquad \textbf{(E)}\ 8</math><br />
<br />
== Solution ==<br />
By defintion, we have <math>\cos^2x=\sin x \tan x</math>. Since <math>\tan x=\frac{\sin x}{\cos x}</math>, we can rewrite this as <math>\cos^3x=\sin^2x</math>. <br />
<br />
The common ratio of the sequence is <math>\frac{\cos x}{\sin x}</math>, so we can write<br />
<br />
<math>a_1= \sin x</math><br />
<math>a_2= \cos x</math><br />
<math>a_3= \frac{\cos^2x}{\sin x}</math><br />
<math>a_4=\frac{\cos^3x}{\sin^2x}=1</math><br />
<math>a_5=\frac{\cos x}{\sin x}</math><br />
<math>a_6=\frac{\cos^2x}{\sin^2x}</math><br />
<math>a_7=\frac{\cos^3x}{\sin^3x}=\frac{1}{\sin x}</math><br />
<math>a_8=\frac{\cos x}{\sin x^2}=\frac{1}{\cos^2 x}</math><br />
<math>a_9=\frac{\cos x}{\sin x}</math><br />
<br />
<br />
We can conclude that the sequence from <math>a_4</math> to <math>a_8</math> repeats. <br />
<br />
Since <math>\cos^3x=\sin^2x=1-\cos^2x</math>, we have <math>\cos^3x+\cos^2x=1 \implies \cos^2x(\cos x+1)=1 \implies \cos x+1=\frac{1}{\cos^2 x}</math>, which is <math>a_8</math> making our answer <math>8 \Rightarrow \boxed{E}</math>.<br />
<br />
--Please fix formatting--<br />
<br />
== See also ==<br />
{{AMC12 box|year=2010|num-b=19|num-a=21|ab=B}}</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=2010_AMC_12B_Problems/Problem_20&diff=388392010 AMC 12B Problems/Problem 202011-05-31T19:59:23Z<p>BOGTRO: /* Solution */</p>
<hr />
<div>== Problem==<br />
A geometric sequence <math>(a_n)</math> has <math>a_1=\sin x</math>, <math>a_2=\cos x</math>, and <math>a_3= \tan x</math> for some real number <math>x</math>. For what value of <math>n</math> does <math>a_n=1+\cos x</math>?<br />
<br />
<br />
<math>\textbf{(A)}\ 4 \qquad \textbf{(B)}\ 5 \qquad \textbf{(C)}\ 6 \qquad \textbf{(D)}\ 7 \qquad \textbf{(E)}\ 8</math><br />
<br />
== Solution ==<br />
By defintion, we have <math>\cos^2x=\sin x \tan x</math>. Since <math>\tan x=\frac{\sin x}{\cos x}</math>, we can rewrite this as <math>\cos^3x=\sin^2x</math>. <br />
<br />
The common ratio of the sequence is <math>\frac{\cos x}{\sin x}</math>, so we can write<br />
<br />
<math>a_1= \sin x</math><br />
<math>a_2= \cos x</math><br />
<math>a_3= \frac{\cos^2x}{\sin x}</math><br />
<math>a_4=\frac{\cos^3x}{\sin^2x}=1</math><br />
<math>a_5=\frac{\cos x}{\sin x}</math><br />
<math>a_6=\frac{\cos^2x}{\sin^2x}</math><br />
<math>a_7=\frac{\cos^3x}{\sin^3x}=\frac{1}{\sin x}</math><br />
<math>a_8=\frac{\cos x}{\sin x^2}=\frac{1}{\cos^2 x}</math><br />
<math>a_9=\frac{\cos x}{\sin x}</math><br />
<br />
<br />
We can conclude that the sequence from <math>a_4</math> to <math>a_8</math> repeats. <br />
<br />
Since <math>\cos^3x=\sin^2x=1-\cos^2x</math>, we have <math>\cos^3x+\cos^2x=1 \implies \cos^2x(\cos x+1)=1 \implies \cos x+1=\frac{1}{\cos^2 x}</math>, which is <math>a_8</math> making our answer <math>8 \Rightarrow \boxed{E}</math>.<br />
<br />
<Fix formatting please><br />
<br />
== See also ==<br />
{{AMC12 box|year=2010|num-b=19|num-a=21|ab=B}}</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=2010_AMC_12B_Problems/Problem_20&diff=388372010 AMC 12B Problems/Problem 202011-05-31T19:25:50Z<p>BOGTRO: /* Solution */</p>
<hr />
<div>{{solution}}<br />
== Problem 20 ==<br />
A geometric sequence <math>(a_n)</math> has <math>a_1=\sin x</math>, <math>a_2=\cos x</math>, and <math>a_3= \tan x</math> for some real number <math>x</math>. For what value of <math>n</math> does <math>a_n=1+\cos x</math>?<br />
<br />
<br />
<math>\textbf{(A)}\ 4 \qquad \textbf{(B)}\ 5 \qquad \textbf{(C)}\ 6 \qquad \textbf{(D)}\ 7 \qquad \textbf{(E)}\ 8</math><br />
<br />
== Solution ==<br />
By defintion, we have <math>\cos^2x=\sin x \tan x</math>. Since <math>\tan x=\frac{\sin x}{\cos x}</math>, we can rewrite this as <math>\cos^3x=\sin^2x</math>. <br />
<br />
The common ratio of the sequence is <math>\frac{\cos x}{\sin x}</math>, so we can write<br />
<br />
<math>a_1= \sin x</math><br />
<math>a_2= \cos x</math><br />
<math>a_3= \frac{\cos^2x}{\sin x}</math><br />
<math>a_4=\frac{\cos^3x}{\sin^2x}=1</math><br />
<math>a_5=\frac{\cos x}{\sin x}</math><br />
<math>a_6=\frac{\cos^2x}{\sin^2x}</math><br />
<math>a_7=\frac{\cos^3x}{\sin^3x}=\frac{1}{\sin x}</math><br />
<math>a_8=\frac{\cos x}{\sin x^2}=\frac{1}{\cos^2 x}</math><br />
<math>a_9=\frac{\cos x}{\sin x}</math><br />
<br />
<br />
We can conclude that the sequence from <math>a_4</math> to <math>a_8</math> repeats. <br />
<br />
Since <math>\cos^3x=\sin^2x=1-\cos^2x</math>, we have <math>\cos^3x+\cos^2x=1 \implies \cos^2x(\cos x+1)=1 \implies \cos x+1=\frac{1}{\cos^2 x}</math>, which is <math>a_8</math> making our answer <math>\boxed{8}</math>, or E.<br />
<br />
== See also ==<br />
{{AMC12 box|year=2010|num-b=19|num-a=21|ab=B}}</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=User:BOGTRO&diff=38758User:BOGTRO2011-05-28T22:08:03Z<p>BOGTRO: </p>
<hr />
<div>There once was a guy. <br />
<br />
His name was BOGTRO. <br />
<br />
He was bad at math. <br />
<br />
Then he thought he got good at math. <br />
<br />
Of course, he was being silly. <br />
<br />
So now he is still bad at math.</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=MATHCOUNTS&diff=38356MATHCOUNTS2011-05-07T02:15:09Z<p>BOGTRO: /* Past Winners */</p>
<hr />
<div>'''MATHCOUNTS''' is a large national [[mathematics competition]] and [[mathematics coaching]] program that has served millions of middle school students since 1984. Sponsored by the [[CNA Foundation]], [[National Society of Professional Engineers]], the [[National Council of Teachers of Mathematics]], and others, the focus of MATHCOUNTS is on [[mathematical problem solving]]. Students are eligible for up to three years, but cannot compete beyond their eighth grade year.<br />
<br />
== MATHCOUNTS Curriculum ==<br />
MATHCOUNTS curriculum includes [[arithmetic]], [[algebra]], [[counting]], [[geometry]], [[number theory]], [[probability]], and [[statistics]]. The focus of MATHCOUNTS curriculum is in developing [[mathematical problem solving]] skills.<br />
<br />
Before 1990, MATHCOUNTS chose particular areas of mathematics to highlight each year before changing the focus of the competition more broadly to problem solving.<br />
<br />
==Past Winners==<br />
* 1984: Michael Edwards, Texas<br />
* 1985: Timothy Kokesh, Oklahoma<br />
* 1986: Brian David Ewald, Florida<br />
* 1987: Russell Mann, Tennessee<br />
* 1988: Andrew Schultz, Illinois<br />
* 1989: Albert Kurz, Pennsylvania<br />
* 1990: Brian Jenkins, Arkansas<br />
* 1991: Jonathan L. Weinstein, Massachusetts<br />
* 1992: Andrei C. Gnepp, Ohio<br />
* 1993: Carleton Bosley, Kansas<br />
* 1994: William O. Engel, Illinois<br />
* 1995: Richard Reifsnyder, Kentucky<br />
* 1996: Alexander Schwartz, Pennsylvania<br />
* 1997: Zhihao Liu, Wisconsin<br />
* 1998: Ricky Liu, Massachusetts<br />
* 1999: Po-Ru Loh, Wisconsin<br />
* 2000: Ruozhou Jia, Illinois<br />
* 2001: Ryan Ko, New Jersey<br />
* 2002: Albert Ni, Illinois<br />
* 2003: Adam Hesterberg, Washington<br />
* 2004: Gregory Gauthier, Illinois<br />
* 2005: Neal Wu, Louisiana (Neal is a user on AoPS under the username [[User:nebula42|nebula42]])<br />
* 2006: Daesun Yim, New Jersey (Daesun is a user on AoPS under the usernames [[User:Treething|Treething]] and [[User:Lazarus|Lazarus]])<br />
* 2007: Kevin Chen, Texas (Kevin is a user on AoPS under the username [[User:binonunquineist|binonunquineist]])<br />
* 2008: Darryl Wu, Washington (youngest winner ever, at 11, as well as the first 6th grader to ever even make the National Countdown Round)<br />
* 2009: Bobby Shen, Texas (Bobby is a user on AoPS under the username [[User:stevenmeow|stevenmeow]])<br />
* 2010: Mark Sellke, Indiana<br />
* 2011: Scott Wu, Louisiana (Scott is a user on AoPS under the username [[User: Ttocs45|Ttocs45]], and is a brother of previous winner Neal Wu)<br />
<br />
== MATHCOUNTS Competition Structure ==<br />
<br />
=== Sprint Round ===<br />
<br />
30 problems in 40 minutes. This round is generally made up questions ranging from relatively easy to relatively difficult. Some of the difficult problems are only difficult because calculators are not allowed in this round.<br />
<br />
=== Target Round ===<br />
8 problems given 2 at a time. Each set of two problems is given six minutes. Students may not go back to previous rounds (or forwards to future rounds) even if they finish before time is called. Students may use calculators.<br />
<br />
=== Team Round ===<br />
<br />
10 problems in 20 minutes for a team of 4 students. These problems typically include some of the most difficult problems of the competition. Use of a calculator is allowed (and required for some questions).<br />
<br />
=== Countdown Round ===<br />
High scoring individuals compete head-to-head until a champion is crowned. People compete from off a screen taking 45 seconds or less to finish the problem. The Countdown round is run differently in various different chapter, state, and national competitions. In the national competitions, it is the round that determines the champion.<br />
<br />
<br />
=== Ciphering Round ===<br />
In some states, (most notably Florida) there is an optional ciphering round. Very similar to countdown (in both difficulty and layout), a team sends up a representative to go against all representatives from the other teams. A problem is shown on a screen and students work fast to answer the problem. The students give their answer and after 45 seconds the answer is shown and the answers are checked to see if they are right. The fastest correct answer gets five points, the next fastest gets 4, etc. There are 4 questions per individual and teams send up 4 people. A perfect score is then 80. Often times the questions take clever reading skills. For example, one question was "How much dirt is in a 3 ft by 3 ft by 4 ft hole?" The answer was 0 because there is no dirt in a hole.<br />
<br />
====Chapter and State Competitions====<br />
<br />
In the chapter and state competitions, the countdown round is not mandatory. However, if it is deemed official by the chapter or state, the following format must be used:<br />
<br />
*The 10th place written finisher competes against the 9th place written finisher. A problem is displayed, and both competitors have 45 seconds to answer the question, and the first competitor to correctly answer the question receives one point. The person who gets the most correct out of three questions (not necessarily two out of three) is the winner.<br />
<br />
*The winner of the first round goes up against the 8th place finisher.<br />
<br />
*The winner of the second round goes up against the 7th place finisher.<br />
<br />
This process is continued until the countdown round reaches the top four written competitors. Starting then, the first person to get three question correct wins (as opposed to the best-out-of-three rule).<br />
<br />
If the countdown round is unofficial, any format may be used. Single-elimination bracket-style tournaments are common.<br />
<br />
====National Competition====<br />
<br />
At the national competition, there are some structural changes to the countdown round. The top 12 (not the top 10) written finishers make it to the countdown round, and the format is changed from a ladder competition to a single elimination tournament where the top four written competitors get a bye. This setup makes it far more likely for a 12th place finisher to become champion, and it makes it less likely for a first place written finisher to become champion, equalizing the field. But even then, a 12th place written competitor will have less of a chance to become champion than the top 4, because the top 4 get a bye. Until the semi-finals, the scoring is best out of five advances.<br />
<br />
At the first round and the second round, the first person to correctly answer three questions wins. However, at the semifinals, the rules slightly change&mdash;the first person to correctly answer four questions wins.<br />
<br />
=== Masters Round ===<br />
Top students give in-depth explanations to challenging problems. This round is optional at the state level competition and is mandatory at the national competition. At nationals the top two on the written and countdown participate.<br />
<br />
=== Scoring and Ranking ===<br />
An individual's score is their total number of correct sprint round answers plus 2 times their total number of correct target round answers. This total is out of a maximum of <math>30 + 2(8) = 46</math> points.<br />
<br />
A team's score is the average of the individual scores of its four members plus 2 points for every correct team round answer, making a team's maximum possible score 66 points. Therefore, it is possible to win with a relatively low team score and a phenomenal individual score, as the team score is only roughly 30% of the total team score.<br />
<br />
== MATHCOUNTS Competition Levels ==<br />
=== School Competition ===<br />
Students vie for the chance to make their school teams. Problems at this level are generally the easiest and most basic in curriculum.<br />
<br />
=== Chapter Competition ===<br />
Chapter competitions serve as a selection filter for state competitions. A few states don't need to host chapter competitions due to a small population size.<br />
<br />
=== State Competition ===<br />
The top 4 students in each state form the state team for the national competition. The coach of the top school team at the state level is invited to coach the state team at the national competition. Interestingly, the coach of a state team is not necessarily the coach of any of the state's team members.<br />
<br />
=== National Competition ===<br />
==== Nation Competition Sites ====<br />
For many years, the National MATHCOUNTS competition was held in Washington, D.C. More recently, the competition has changed venues often.<br />
<br />
* The 2011 competition will be held in Washington, D.C.<br />
* The 2009 and 2010 competitions was held in Orlando, Florida.<br />
* The 2008 competition was held in Denver, Colorado.<br />
* The 2007 competition was held in Fort Worth, Texas.<br />
* The 2006 competition was held in Arlington, Virginia.<br />
* The 2005 competition was held in Detroit, Michigan.<br />
* The 2004 competition was held in Washington, D.C.<br />
* The 2002 and 2003 competitions were held in Chicago, Illinois.<br />
<br />
==== Rewards ====<br />
<br />
Every competitor at the national competition receives a graphing calculator that varies by year - for example, in 2006 it was a TI-84 Plus Silver Edition with the MATHCOUNTS logo on the back. In 2007, MATHCOUNTS took the logo off. In 2008 and 2009, they gave TI-<math>n</math>spires to everyone. They also give out a laptop and an 8000 dollar scholarship to the winner.<br />
<br />
== MATHCOUNTS Resources ==<br />
=== MATHCOUNTS Books ===<br />
* [http://www.artofproblemsolving.com/Books/AoPS_B_CP_MC.php MATHCOUNTS books] at the [http://www.artofproblemsolving.com/Books/AoPS_B_About.php AoPS Bookstore]<br />
* [[Art of Problem Solving]]'s [http://www.artofproblemsolving.com/Books/AoPS_B_Rec_Middle.php Introductory subject textbooks] are ideal for students preparing for MATHCOUNTS.<br />
<br />
=== MATHCOUNTS Classes ===<br />
* [[Art of Problem Solving]] hosts [http://www.artofproblemsolving.com/Classes/AoPS_C_ClassesP.php#mc MATHCOUNTS preparation classes].<br />
* [[Art of Problem Solving]] hosts many free MATHCOUNTS [[Math Jams]]. [http://www.artofproblemsolving.com/Community/AoPS_Y_Math_Jams.php Math Jam Schedule]. [http://www.artofproblemsolving.com/Community/AoPS_Y_MJ_Transcripts.php Math Jam Transcript Archive].<br />
<br />
=== MATHCOUNTS Online ===<br />
* [http://www.mathcounts.org MATHCOUNTS Homepage]<br />
* [[Art of Problem Solving]] hosts a large [http://www.artofproblemsolving.com/Forum/index.php?f=132 MATHCOUNTS Forum] as well as a private [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=23209 MATHCOUNTS Coaches Forum].<br />
* [http://mathcounts.saab.org/ Elias Saab's MATHCOUNTS Preparation Homepage]<br />
* [http://www.unidata.ucar.edu/staff/russ/mathcounts/diaz.html The MATHCOUNTS Bible According to Mr. Diaz]<br />
*[http://www.artofproblemsolving.com/Resources/AoPS_R_A_MATHCOUNTS.php/ Building a Successful MATHCOUNTS Program] by [[Jeff Boyd]], who coached the 2005, 2007, and 2008 National Champion [[Texas MathCounts]] team.<br />
<br />
== What comes after MATHCOUNTS? ==<br />
<br />
Give the following competitions a try and take a look at the [[List of United States high school mathematics competitions]].<br />
* [[American Mathematics Competitions]]<br />
* [[American Regions Math League]]<br />
* [[Mandelbrot Competition]]<br />
* [[Mu Alpha Theta]]<br />
<br />
[[Category:Mathematics competitions]]<br />
<br />
== See also ==<br />
* [[List of national MATHCOUNTS teams]]<br />
* [[MATHCOUNTS historical results]]<br />
* [[Mathematics competition resources]]<br />
* [[Math contest books]]<br />
* [[Math books]]<br />
* [[List of United States middle school mathematics competitions]]<br />
* [[List of United States high school mathematics competitions]]<br />
* [http://www.mathcounts.org/webarticles/anmviewer.asp?a=921&z=71 2006 MATHCOUNTS Countdown Video]</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=MATHCOUNTS&diff=38355MATHCOUNTS2011-05-07T02:14:53Z<p>BOGTRO: /* Past Winners */</p>
<hr />
<div>'''MATHCOUNTS''' is a large national [[mathematics competition]] and [[mathematics coaching]] program that has served millions of middle school students since 1984. Sponsored by the [[CNA Foundation]], [[National Society of Professional Engineers]], the [[National Council of Teachers of Mathematics]], and others, the focus of MATHCOUNTS is on [[mathematical problem solving]]. Students are eligible for up to three years, but cannot compete beyond their eighth grade year.<br />
<br />
== MATHCOUNTS Curriculum ==<br />
MATHCOUNTS curriculum includes [[arithmetic]], [[algebra]], [[counting]], [[geometry]], [[number theory]], [[probability]], and [[statistics]]. The focus of MATHCOUNTS curriculum is in developing [[mathematical problem solving]] skills.<br />
<br />
Before 1990, MATHCOUNTS chose particular areas of mathematics to highlight each year before changing the focus of the competition more broadly to problem solving.<br />
<br />
==Past Winners==<br />
* 1984: Michael Edwards, Texas<br />
* 1985: Timothy Kokesh, Oklahoma<br />
* 1986: Brian David Ewald, Florida<br />
* 1987: Russell Mann, Tennessee<br />
* 1988: Andrew Schultz, Illinois<br />
* 1989: Albert Kurz, Pennsylvania<br />
* 1990: Brian Jenkins, Arkansas<br />
* 1991: Jonathan L. Weinstein, Massachusetts<br />
* 1992: Andrei C. Gnepp, Ohio<br />
* 1993: Carleton Bosley, Kansas<br />
* 1994: William O. Engel, Illinois<br />
* 1995: Richard Reifsnyder, Kentucky<br />
* 1996: Alexander Schwartz, Pennsylvania<br />
* 1997: Zhihao Liu, Wisconsin<br />
* 1998: Ricky Liu, Massachusetts<br />
* 1999: Po-Ru Loh, Wisconsin<br />
* 2000: Ruozhou Jia, Illinois<br />
* 2001: Ryan Ko, New Jersey<br />
* 2002: Albert Ni, Illinois<br />
* 2003: Adam Hesterberg, Washington<br />
* 2004: Gregory Gauthier, Illinois<br />
* 2005: Neal Wu, Louisiana (Neal is a user on AoPS under the username [[User:nebula42|nebula42]])<br />
* 2006: Daesun Yim, New Jersey (Daesun is a user on AoPS under the usernames [[User:Treething|Treething]] and [[User:Lazarus|Lazarus]])<br />
* 2007: Kevin Chen, Texas (Kevin is a user on AoPS under the username [[User:binonunquineist|binonunquineist]])<br />
* 2008: Darryl Wu, Washington (youngest winner ever, at 11, as well as the first 6th grader to ever even make the National Countdown Round)<br />
* 2009: Bobby Shen, Texas (Bobby is a user on AoPS under the username [[User:stevenmeow|stevenmeow]])<br />
* 2010: Mark Sellke, Indiana<br />
* 2011: Scott Wu, Louisiana (Scott is a user on AoPS under the username [[User: Ttocs45|Ttocs45]])<br />
<br />
== MATHCOUNTS Competition Structure ==<br />
<br />
=== Sprint Round ===<br />
<br />
30 problems in 40 minutes. This round is generally made up questions ranging from relatively easy to relatively difficult. Some of the difficult problems are only difficult because calculators are not allowed in this round.<br />
<br />
=== Target Round ===<br />
8 problems given 2 at a time. Each set of two problems is given six minutes. Students may not go back to previous rounds (or forwards to future rounds) even if they finish before time is called. Students may use calculators.<br />
<br />
=== Team Round ===<br />
<br />
10 problems in 20 minutes for a team of 4 students. These problems typically include some of the most difficult problems of the competition. Use of a calculator is allowed (and required for some questions).<br />
<br />
=== Countdown Round ===<br />
High scoring individuals compete head-to-head until a champion is crowned. People compete from off a screen taking 45 seconds or less to finish the problem. The Countdown round is run differently in various different chapter, state, and national competitions. In the national competitions, it is the round that determines the champion.<br />
<br />
<br />
=== Ciphering Round ===<br />
In some states, (most notably Florida) there is an optional ciphering round. Very similar to countdown (in both difficulty and layout), a team sends up a representative to go against all representatives from the other teams. A problem is shown on a screen and students work fast to answer the problem. The students give their answer and after 45 seconds the answer is shown and the answers are checked to see if they are right. The fastest correct answer gets five points, the next fastest gets 4, etc. There are 4 questions per individual and teams send up 4 people. A perfect score is then 80. Often times the questions take clever reading skills. For example, one question was "How much dirt is in a 3 ft by 3 ft by 4 ft hole?" The answer was 0 because there is no dirt in a hole.<br />
<br />
====Chapter and State Competitions====<br />
<br />
In the chapter and state competitions, the countdown round is not mandatory. However, if it is deemed official by the chapter or state, the following format must be used:<br />
<br />
*The 10th place written finisher competes against the 9th place written finisher. A problem is displayed, and both competitors have 45 seconds to answer the question, and the first competitor to correctly answer the question receives one point. The person who gets the most correct out of three questions (not necessarily two out of three) is the winner.<br />
<br />
*The winner of the first round goes up against the 8th place finisher.<br />
<br />
*The winner of the second round goes up against the 7th place finisher.<br />
<br />
This process is continued until the countdown round reaches the top four written competitors. Starting then, the first person to get three question correct wins (as opposed to the best-out-of-three rule).<br />
<br />
If the countdown round is unofficial, any format may be used. Single-elimination bracket-style tournaments are common.<br />
<br />
====National Competition====<br />
<br />
At the national competition, there are some structural changes to the countdown round. The top 12 (not the top 10) written finishers make it to the countdown round, and the format is changed from a ladder competition to a single elimination tournament where the top four written competitors get a bye. This setup makes it far more likely for a 12th place finisher to become champion, and it makes it less likely for a first place written finisher to become champion, equalizing the field. But even then, a 12th place written competitor will have less of a chance to become champion than the top 4, because the top 4 get a bye. Until the semi-finals, the scoring is best out of five advances.<br />
<br />
At the first round and the second round, the first person to correctly answer three questions wins. However, at the semifinals, the rules slightly change&mdash;the first person to correctly answer four questions wins.<br />
<br />
=== Masters Round ===<br />
Top students give in-depth explanations to challenging problems. This round is optional at the state level competition and is mandatory at the national competition. At nationals the top two on the written and countdown participate.<br />
<br />
=== Scoring and Ranking ===<br />
An individual's score is their total number of correct sprint round answers plus 2 times their total number of correct target round answers. This total is out of a maximum of <math>30 + 2(8) = 46</math> points.<br />
<br />
A team's score is the average of the individual scores of its four members plus 2 points for every correct team round answer, making a team's maximum possible score 66 points. Therefore, it is possible to win with a relatively low team score and a phenomenal individual score, as the team score is only roughly 30% of the total team score.<br />
<br />
== MATHCOUNTS Competition Levels ==<br />
=== School Competition ===<br />
Students vie for the chance to make their school teams. Problems at this level are generally the easiest and most basic in curriculum.<br />
<br />
=== Chapter Competition ===<br />
Chapter competitions serve as a selection filter for state competitions. A few states don't need to host chapter competitions due to a small population size.<br />
<br />
=== State Competition ===<br />
The top 4 students in each state form the state team for the national competition. The coach of the top school team at the state level is invited to coach the state team at the national competition. Interestingly, the coach of a state team is not necessarily the coach of any of the state's team members.<br />
<br />
=== National Competition ===<br />
==== Nation Competition Sites ====<br />
For many years, the National MATHCOUNTS competition was held in Washington, D.C. More recently, the competition has changed venues often.<br />
<br />
* The 2011 competition will be held in Washington, D.C.<br />
* The 2009 and 2010 competitions was held in Orlando, Florida.<br />
* The 2008 competition was held in Denver, Colorado.<br />
* The 2007 competition was held in Fort Worth, Texas.<br />
* The 2006 competition was held in Arlington, Virginia.<br />
* The 2005 competition was held in Detroit, Michigan.<br />
* The 2004 competition was held in Washington, D.C.<br />
* The 2002 and 2003 competitions were held in Chicago, Illinois.<br />
<br />
==== Rewards ====<br />
<br />
Every competitor at the national competition receives a graphing calculator that varies by year - for example, in 2006 it was a TI-84 Plus Silver Edition with the MATHCOUNTS logo on the back. In 2007, MATHCOUNTS took the logo off. In 2008 and 2009, they gave TI-<math>n</math>spires to everyone. They also give out a laptop and an 8000 dollar scholarship to the winner.<br />
<br />
== MATHCOUNTS Resources ==<br />
=== MATHCOUNTS Books ===<br />
* [http://www.artofproblemsolving.com/Books/AoPS_B_CP_MC.php MATHCOUNTS books] at the [http://www.artofproblemsolving.com/Books/AoPS_B_About.php AoPS Bookstore]<br />
* [[Art of Problem Solving]]'s [http://www.artofproblemsolving.com/Books/AoPS_B_Rec_Middle.php Introductory subject textbooks] are ideal for students preparing for MATHCOUNTS.<br />
<br />
=== MATHCOUNTS Classes ===<br />
* [[Art of Problem Solving]] hosts [http://www.artofproblemsolving.com/Classes/AoPS_C_ClassesP.php#mc MATHCOUNTS preparation classes].<br />
* [[Art of Problem Solving]] hosts many free MATHCOUNTS [[Math Jams]]. [http://www.artofproblemsolving.com/Community/AoPS_Y_Math_Jams.php Math Jam Schedule]. [http://www.artofproblemsolving.com/Community/AoPS_Y_MJ_Transcripts.php Math Jam Transcript Archive].<br />
<br />
=== MATHCOUNTS Online ===<br />
* [http://www.mathcounts.org MATHCOUNTS Homepage]<br />
* [[Art of Problem Solving]] hosts a large [http://www.artofproblemsolving.com/Forum/index.php?f=132 MATHCOUNTS Forum] as well as a private [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=23209 MATHCOUNTS Coaches Forum].<br />
* [http://mathcounts.saab.org/ Elias Saab's MATHCOUNTS Preparation Homepage]<br />
* [http://www.unidata.ucar.edu/staff/russ/mathcounts/diaz.html The MATHCOUNTS Bible According to Mr. Diaz]<br />
*[http://www.artofproblemsolving.com/Resources/AoPS_R_A_MATHCOUNTS.php/ Building a Successful MATHCOUNTS Program] by [[Jeff Boyd]], who coached the 2005, 2007, and 2008 National Champion [[Texas MathCounts]] team.<br />
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== What comes after MATHCOUNTS? ==<br />
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Give the following competitions a try and take a look at the [[List of United States high school mathematics competitions]].<br />
* [[American Mathematics Competitions]]<br />
* [[American Regions Math League]]<br />
* [[Mandelbrot Competition]]<br />
* [[Mu Alpha Theta]]<br />
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[[Category:Mathematics competitions]]<br />
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== See also ==<br />
* [[List of national MATHCOUNTS teams]]<br />
* [[MATHCOUNTS historical results]]<br />
* [[Mathematics competition resources]]<br />
* [[Math contest books]]<br />
* [[Math books]]<br />
* [[List of United States middle school mathematics competitions]]<br />
* [[List of United States high school mathematics competitions]]<br />
* [http://www.mathcounts.org/webarticles/anmviewer.asp?a=921&z=71 2006 MATHCOUNTS Countdown Video]</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=User:BOGTRO&diff=38311User:BOGTRO2011-05-02T20:37:21Z<p>BOGTRO: </p>
<hr />
<div>My name is BOGTRO.<br />
<br />
I am BOGTRO.<br />
<br />
To other people: stop making my user page and putting random stuff on it please.<br />
<br />
I am too lazy to make a page.<br />
<br />
I will make a page when I win MATHCOUNTS.<br />
<br />
TYTIA.</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=Overcounting&diff=38304Overcounting2011-05-01T23:42:45Z<p>BOGTRO: </p>
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<div>'''Overcounting''' is the process of counting more than what you need and then systematically subtracting the parts which do not belong. <br />
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The [[Principle of Inclusion-Exclusion]] (PIE) is a systematic method of repeated overcounting that is a tool in solving many [[combinatorics]] problems.<br />
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An example of a classic problem is as follows:<br />
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"How many numbers less than or equal to 100 are divisible by either 2 or 3?"<br />
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Solution: Clearly, there are 50 numbers less than 100 that are divisible by 2, and 33 that are divisible by 3. However, we note that we overcount several numbers, such as 12, which is divisible by both 2 and 3. To correct for this overcounting, we must subtract out the numbers that are divisible by both 2 and 3, as we have counted them twice. A number that is divisible by both 2 and 3 must be divisible by 6, and there are 16 such numbers. Thus, there are <math>50+33-16=\boxed{67}</math> numbers that are divisible by either 2 or 3. <br />
(Note that it is not a coincidence that 67 is close to 2 thirds of 100! We can approach this problem in a constructive way, building the set based on the remainders when divided by 3, but that is a different subject). <br />
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Another basic example is combinations. In these, we correct for overcounting with division, by dividing out what we overcount (as opposed to above where we subtracted it out). <br />
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Here is MATHCOUNTS 2008 National Target #1: Try to solve this.<br />
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"How many numbers less than or equal to 100 are divisible by 2 or 3 but not 4?".<br />
== Examples ==<br />
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* [[2004 AIME I Problems/Problem 3|AIME 2004I/3]]<br />
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{{stub}}<br />
[[Category:Definition]]<br />
[[Category:Combinatorics]]</div>BOGTROhttps://artofproblemsolving.com/wiki/index.php?title=User:BOGTRO&diff=38299User:BOGTRO2011-05-01T20:36:20Z<p>BOGTRO: </p>
<hr />
<div>My name is BOGTRO.<br />
<br />
I am BOGTRO.<br />
<br />
To other people: stop making my user page and putting random stuff on it please.</div>BOGTRO