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The figure shows a square of side $y$ units divided into a square of side $x$ units and four congruent rectangles. What is the perimeter, in units, of one of the four congruent rectangles? Express your answer in terms of $y$.

0 bytes (0 words) - 22:13, 4 March 2020

Page text matches

Pythagorean Theorem
...f geometry problems can be solved by building right triangles and applying the Pythagorean Theorem. ...Geometric inequality#Pythagorean_Inequality | Pythagorean Inequality]] and the [[Law of Cosines]].

5 KB (886 words) - 21:12, 22 January 2024
2016 AMC 10A Problems/Problem 7
...0, 100, x, 40, 50, 200, 90</math> are all equal to <math>x</math>. What is the value of <math>x</math>? Since <math>x</math> is the mean,

2 KB (268 words) - 18:19, 27 September 2023
2016 AMC 10A Problems/Problem 10
...<math>1</math> foot wide on all four sides. What is the length in feet of the inner rectangle? Let the length of the inner rectangle be <math>x</math>.

2 KB (337 words) - 14:56, 25 June 2023
2016 AMC 10A Problems/Problem 11
Find the area of the shaded region. ...h>, <math>2</math>, and <math>\frac{5}{4}</math>, which add to the area of the shaded region, which is <math>\boxed{6\frac{1}{2}}</math>.

8 KB (1,016 words) - 00:17, 31 December 2023
2016 AMC 10A Problems/Problem 13
...moved two seats to the right, Ceci had moved one seat to the left, and Dee and Edie had switched seats, leaving an end seat for Ada. In which seat had Ada ...cupied and the positioning would not work. So, Edie and Dee are in seats 4 and 5. This means that Bea was originally in seat 1. Ceci must have been in sea

2 KB (402 words) - 14:54, 25 June 2023
List of mathematics competitions
...l links to more helpful pages about mathematics competitions. This is not the place to list individual competitions. ...an mathematics competitions are categorized in two, one for public schools and other for particular schools.

4 KB (406 words) - 11:20, 26 February 2021
Alabama mathematics competitions
...nd there are a number of quality contests around the state for both middle and high school students. ...298 middle school math forums] where students can discuss contest problems and mathematics.

3 KB (411 words) - 21:32, 8 December 2014
MathILy (serious mathematics infused with levity)
...r undergraduate math students. The math content covered is undergraduate- and graduate-level. ...3, with MathILy at Bryn Mawr College and MathILy-Er at Arcadia University. The program fee will be \$5300.

5 KB (706 words) - 23:49, 29 January 2024
Mathematics, science, and technology scholarships
This page is for listing of '''Mathematics, science, and technology scholarships''' that are not subject specific. Links to scholar == Mathematics, science, and technology scholarships ==

7 KB (851 words) - 10:54, 29 January 2022
Proton Energy Scholarship
...of science and technology. They must also be planning further education in the field. ...th>\textdollar</math>100,000, though only one had been originally promised the scholarship.

894 bytes (123 words) - 15:48, 13 June 2022
MATHCOUNTS
...of Teachers of Mathematics], and others including Art of Problem Solving, the focus of MATHCOUNTS is on mathematical problem solving. Students are eligib ...]], [[geometry]], [[number theory]], [[probability]], and [[statistics]]. The focus of MATHCOUNTS curriculum is in developing [[mathematical problem solv

10 KB (1,497 words) - 11:42, 10 March 2024
ASIA TEAM Problems/Problem 1
...er of <math>2n-1</math> is one more than the order of <math>2n</math>, and the answer is <math>\frac{1000}{2}=\boxed{500}</math>.

227 bytes (40 words) - 05:42, 16 February 2024
ICTM Math Contest
...ade School (Grades 3, 4, 5, 6, 7, 8 + Algebra 1) and High School (Regional and State Finals). ...schools at each grade level will receive certificates and be recognized in the ICTM Bulletin.

8 KB (1,182 words) - 14:26, 3 April 2024
Resources for mathematics competitions
...Many also have links to books, websites, and other resources relevant to the topic. == Quick Start Video Introduction to the AMC ==

24 KB (3,269 words) - 00:43, 24 April 2024
Math books
...re recommended by [[Art of Problem Solving]] administrators and members of the [http://aops.com/community AoPS Community]. Levels of reading and math ability are loosely defined as follows:

24 KB (3,177 words) - 12:53, 20 February 2024
Physics
...is considered to be the most fundamental of all the sciences, and is also the oldest. ...e 19th century is called Classical Physics. Physics after the 19th century is know as Modern Physics.

9 KB (1,355 words) - 07:29, 29 September 2021
Mathematics
...mportant to people in most modern technical discplines such as engineering and economics. ...2\,3\,4\,5\,6\,7\,8\,9\,0</math>|right|The ten [[digit]]s making up the base ten number system.}}

6 KB (902 words) - 12:53, 3 September 2019
AMC historical results
 ...he '''AMC historical results''' page. This page should include results for the [[AIME]] as well. For [[USAMO]] results, see [[USAMO historical results]].

17 KB (1,921 words) - 13:00, 28 April 2024
Inequality
...] methods. While most of the subject of inequalities is often left out of the ordinary educational track, they are common in [[mathematics Olympiads]]. Inequalities are arguably a branch of [[elementary algebra]], and relate slightly to [[number theory]]. They deal with [[relations]] of [[var

12 KB (1,798 words) - 16:20, 14 March 2023
United States of America Mathematical Talent Search
...ics competition]] in which students are challenged to write full solutions and mathematical proofs to exploratory math problems. ...the [[Art of Problem Solving Foundation]] with support and sponsorship by the [[National Security Agency]] (NSA).

4 KB (613 words) - 13:08, 18 July 2023
Academic scholarships
...ve guides to '''academic scholarships'''. Get started by clicking through the links below by subject area. ...a category rather than a list, please create a new page for that category and list it here.

3 KB (337 words) - 03:35, 7 September 2020
AMC 10
...on the path towards choosing the team that represents the United States at the [[International Mathematics Olympiad]] (IMO). High scoring AMC 10 and AMC 12 students are invited to take the [[American Invitational Mathematics Examination]] (AIME).

4 KB (574 words) - 15:28, 22 February 2024
1955 AHSME Problems/Problem 38
...numbers <math>29, 23, 21</math>, and <math>17</math> are obtained. One of the original integers is: ...ath> to be the four numbers. In order to satisfy the following conditions, the system of equation should be constructed. (It doesn't matter which variable

1 KB (200 words) - 23:35, 28 August 2020
American Invitational Mathematics Examination
...on the path toward choosing the team that represents the United States at the [[International Mathematics Olympiad]] (IMO). While most AIME participants ...America Junior Mathematics Olympiad (USAJMO) for qualification from taking the AMC 10.

8 KB (1,057 words) - 12:02, 25 February 2024
American Mathematics Competitions
...bbreviation for American Math Contest, used to refer to the AMC 8, AMC 10, and AMC 12. * [[AMC 8]] — for students grades 8 and under.

5 KB (696 words) - 03:47, 24 December 2019
United States of America Mathematical Olympiad
...on the path toward choosing the team that represents the United States at the [[International Mathematics Olympiad]] (IMO). ...). [[Art of Problem Solving]] (AoPS) is a proud sponsor of the AMC and of the recent expansion of USAMO participants from around 250 to around 500.

6 KB (869 words) - 12:52, 20 February 2024
American Regions Mathematics League
The '''American Regions Math League''' (ARML) is a [[mathematical problem solvi ...details. If your area does not already have a team, ask ARML how to start one.

2 KB (267 words) - 17:06, 7 March 2020
Joining an ARML team
Team selection for the [[American Regions Mathematics League]] varies from team to team. ...ge Xinke's AoPS account "hurdler", if you are interested in trying out for the Alabama team.

21 KB (3,500 words) - 18:41, 23 April 2024
Proof writing
...a proof, they intend a different meaning to how the word is understood by the wider population. Students who spend time studying maths can develop proof- ...good proof are precision, accuracy, and clarity. A single word can change the intended meaning of a proof, so it is best to be as precise as possible.

3 KB (502 words) - 18:16, 18 January 2016
Community Service Scholarships
...rship programs in other countries. Just make that reorganization as clear and as clean as possible. ...[[Mathew Crawford]] using the email crawford@artofproblemsolving.com with the scholarship listing you wish to contribute.

3 KB (350 words) - 01:18, 19 June 2016
California MathCounts
...nts]] team is made up of the top four students during the written round of the state competition. ...won eight national championships (1986, 1992, 2000, 2002, 2003, 2010, 2011 and 2014), more than any other team.

644 bytes (87 words) - 02:05, 25 March 2015
Mu Alpha Theta
...itions]] and each year a national Mu Alpha Theta convention is held during the summer that includes a large competition. == The Competition ==

4 KB (632 words) - 17:09, 11 October 2020
Wilson's Theorem
...ath> if and only if <math>p</math> is prime. It was stated by John Wilson. The French mathematician Lagrange proved it in 1771. ...entary one that rests close to basic principles of [[modular arithmetic]], and an elegant method that relies on more powerful [[algebra]]ic tools.

4 KB (639 words) - 01:53, 2 February 2023
Trivial Inequality
...uare of any real number is nonnegative. Its name comes from its simplicity and straightforwardness. ...>x<0</math>, then <math>x^2 = (-x)(-x) > 0,</math> again by the closure of the set of positive numbers under multiplication.

3 KB (560 words) - 22:51, 13 January 2024
Heron's Formula
...formula | formula]] for finding the [[area]] of a [[triangle]] given only the three side lengths. ...s <math>{a}, {b}, {c}</math>, the area <math>{A}</math> can be found using the following formula:

4 KB (675 words) - 00:05, 22 January 2024
Polynomial
...s and multiplied by [[coefficient]]s from a predetermined [[set]] (usually the set of integers; [[rational]], [[real]] or [[complex]] numbers; but in [[ab * <math>4x^2 + 6x - 9</math>, in the variable <math>x</math>

6 KB (1,100 words) - 01:44, 17 January 2024
Simon's Favorite Factoring Trick
==The General Statement== ...s the product of the variables, <math>66x</math> and <math>-88y</math> are the variables in linear terms.

7 KB (1,107 words) - 07:35, 26 March 2024
Factoring
...r]] or [[polynomial]]) as a product of different terms. This often allows one to find information about an expression that was not otherwise obvious. ==Differences and Sums of Powers==

3 KB (532 words) - 22:00, 13 January 2024
Proof by contradiction
...ue usually works well on problems where not a lot of information is known, and thus we can create some using proof by contradiction. ===Proof that the square root of 2 is irrational===

2 KB (374 words) - 14:01, 21 August 2022
Mathematical problem solving
...thinking. Mathematical [[problem solving]] involves using all the tools at one's disposal to attack a problem in a new way. ...eresting example of this kind of thinking is the calculation of the sum of the [[series]] <math>\frac11 + \frac14 + \frac19 + \cdots + \frac{1}{n^2} + \cd

2 KB (314 words) - 06:45, 1 May 2014
Pigeonhole Principle
...if <math>n+1</math> or more pigeons are placed into <math>n</math> holes, one hole must contain two or more pigeons. This seemingly trivial statement may ...> boxes and <math>n>k</math>, then at least one box must contain more than one ball.

11 KB (1,985 words) - 21:03, 5 August 2023
Quadratic equation
...one of three main strategies: [[factoring]], [[completing the square]] and the [[quadratic formula]]. The purpose of factoring is to turn a general quadratic into a product of [[bin

2 KB (264 words) - 12:04, 15 July 2021
1965 AHSME Problems/Problem 40
...<math>x</math> such that <math>P = x^4 + 6x^3 + 11x^2 + 3x + 31</math> is the square of an integer. Then <math>n</math> is: ...ginning of <math>P</math>, we notice <math>x^4+6x^3</math>, which gives us the idea to use <math>(x^2+3x)^2=x^4+6x^3+9x^2</math>.

3 KB (571 words) - 00:42, 22 October 2021
Minnesota MathCounts
...held every year at the Crowne Plaza Minneapolis West Hotel in Plymouth on the second weekend of March (Friday-Saturday). == Past Winners and Schools ==

995 bytes (131 words) - 18:02, 12 March 2023
Combinatorics
...ive]] formula for the [[Fibonacci numbers]], and so too methods of solving the [[Rubiks cube]]. Mathematicians who spend their careers studying combinator ...mathematics, notably in [[theoretical computer science]], [[statistics]], and various fields of science.

1 KB (208 words) - 02:12, 4 October 2020
Principle of Inclusion-Exclusion
...the size of each set, and the size of all possible [[intersection]]s among the sets. ...t and undercount, in the end making sure every element is counted once and only once. In particular, memorizing a formula for PIE is a bad idea for problem

9 KB (1,703 words) - 07:25, 24 March 2024
Combination
...objects are chosen is irrelevant. We are generally concerned with finding the number of combinations of size <math>r</math> from an original set of size ...pe! It serves as a great introductory video to combinations, permutations, and counting problems in general! [https://bit.ly/CombinationsAndPermutations P

4 KB (615 words) - 11:43, 21 May 2021
Cauchy-Schwarz Inequality
...s. In high-school competitions, its applications are limited to elementary and linear algebra. ...auchy-Schwarz forms the foundation for inequality problems in intermediate and olympiad competitions. It is particularly crucial in proof-based contests.

13 KB (2,048 words) - 15:28, 22 February 2024
Factorial
...mportant function in [[combinatorics]] and [[analysis]], used to determine the number of ways to arrange objects. ...{i=1}^n i</math>. Alternatively, a [[recursion|recursive definition]] for the factorial is <math>n!=n \cdot (n-1)!</math>.

10 KB (809 words) - 16:40, 17 March 2024
Discriminant
...ive, the equation has two [[nonreal]] roots; and if the discriminant is 0, the equation has a real [[double root]]. ...(x)=a_nx^n+a_{n-1}x^{n-1}+...+a_0</math> of degree <math>n</math> with all the coefficients being real. But for polynomials of degree 4 or higher it can b

4 KB (734 words) - 19:19, 10 October 2023
Menelaus' theorem
'''Menelaus' theorem''' deals with the [[collinearity]] of points on each of the three sides (extended when necessary) of a [[triangle]]. ...<math>AC</math>, and <math>R</math> on the intersection of <math>PQ</math> and <math>AB</math>, then

5 KB (804 words) - 03:01, 12 June 2023
ARML historical results
This is a list of historical results from the [[American Regions Mathematics League]]. * 2022: Luke Robitaille ([[Texas ARML]]) and Chris Qiu ([[Lehigh Valley ARML]])

19 KB (2,632 words) - 14:31, 12 June 2022
Fermat's Little Theorem
...ld study more at the introductory level if they have a hard time following the rest of this article). This theorem is credited to [[Pierre de Fermat]]. If <math>{a}</math> is an [[integer]], <math>{p}</math> is a [[prime number]] and <math>{a}</math> is not [[divisibility|divisible]] by <math>{p}</math>, the

16 KB (2,675 words) - 10:57, 7 March 2024
Euler's Totient Theorem
...are relatively prime to <math>n</math>. If <math>{a}</math> is an integer and <math>m</math> is a positive integer [[relatively prime]] to <math>a</math> ...h> is prime. For this reason it is also known as Euler's generalization or the Fermat-Euler theorem.

3 KB (542 words) - 17:45, 21 March 2023
Geometric inequality
...y on Intermediate level geometry problems. It also provides the basis for the definition of a [[metric space]] in [[analysis]]. ...ality extends this to [[obtuse triangle| obtuse]] and [[acute triangle]]s. The inequality says:

7 KB (1,296 words) - 14:22, 22 October 2023
Algebra
...name and usually denoted by a letter or symbol. Many contest problems test one's fluency with [[algebraic manipulation]]. ...and high school algebra. [[Group]]s, [[ring]]s, [[field]]s, [[module]]s, and [[vector space]]s are common objects of study in higher algebra.

3 KB (369 words) - 21:18, 18 June 2021
Number theory/Advanced
...gebraic number theory include the [[Birch and Swinnerton-Dyer Conjecture]] and [[Fermat's Last Theorem]]. ...ies of prime numbers. The most famous problem in analytic number theory is the [[Riemann Hypothesis]].

5 KB (849 words) - 16:14, 18 May 2021
1959 IMO Problems/Problem 2
...<math>A=\sqrt{2}</math>, (b) <math>A=1</math>, (c) <math>A=2</math>, where only non-negative real numbers are admitted for square roots? The square roots imply that <math>x\ge \frac{1}{2}</math>.

3 KB (466 words) - 12:04, 12 April 2024
Euler's totient function
...)</math> applied to a [[positive integer]] <math>n</math> is defined to be the number of positive integers less than or equal to <math>n</math> that are [ ...e_2} \cdots {p}_m^{e_m}</math>, one can compute <math>\phi(n)</math> using the formula <cmath>\phi(n)= n\left(1-\frac{1}{p_1} \right) \left(1-\frac{1}{p_2

5 KB (898 words) - 19:12, 28 January 2024
Probability
...dox]] and the [[birthday problem]]. Probability can be loosely defined as the chance that an event will happen. Before reading about the following topics, a student learning about probability should learn about i

4 KB (588 words) - 12:47, 2 October 2022
Contest strategies
...ting a good night sleep can help refresh the brain, so it can be ready for the test. ...ant but don't forget to leave room to exercise. Exercise can help refresh the brain, allowing problem solvers to prepare for tests more effectively.

3 KB (538 words) - 13:13, 16 January 2021
Rearrangement Inequality
...>{b_k}</math> is also greater than or equal to exactly <math>{i}</math> of the other members <math>B</math>). ...possible interpretation of the rearrangement inequality is that sometimes, the greedy algorithm works.

5 KB (804 words) - 13:54, 26 January 2023
Divisibility rules
...her [[integer]]s. All of these rules apply for [[Base number| base-10]] ''only'' -- other bases have their own, different versions of these rules. === Divisibility Rule for 2 and Powers of 2 ===

8 KB (1,315 words) - 18:18, 2 March 2024
Orthic triangle
...d <math>C</math>, respectively. Then, <math>\triangle DEF</math> is called the '''orthic triangle''' of <math>\triangle ABC</math>. ...ABC</math> is either acute or obtuse each carry different characteristics and must be handled separately.

8 KB (1,408 words) - 11:54, 8 December 2021
Triangle
...In [[physics]], triangles are noted for their durability, since they have only three [[vertex|vertices]] around with to distort. Triangles are split into six categories; three by their [[angle]]s and three by their side lengths.

4 KB (628 words) - 17:17, 17 May 2018
Greatest common divisor
This video comprehensively explains everything related to the GCD: https://youtu.be/HboSeb_gQH8 ...o or more [[integer]]s is the largest integer that is a [[divisor]] of all the given numbers.

2 KB (288 words) - 22:40, 26 January 2021
Overcounting
...a role in incredibly important counting tools such as [[combinations]] and the [[Principle of Inclusion-Exclusion]]. ...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>

4 KB (635 words) - 12:19, 2 January 2022
Constructive counting
...unts the total possibilities of each step and assembles these to enumerate the full set. ...[casework]] and [[complementary counting]], constructive counting is among the most fundamental techniques in counting. Familiarity with constructive coun

12 KB (1,896 words) - 23:55, 27 December 2023
Jensen's Inequality
...unction]] of one real variable. Let <math>x_1,\dots,x_n\in\mathbb R</math> and let <math>a_1,\dots, a_n\ge 0</math> satisfy <math>a_1+\dots+a_n=1</math>. We only prove the case where <math>F</math> is concave. The proof for the other case is similar.

3 KB (623 words) - 13:10, 20 February 2024
Geometric probability
==Geometric Counting and Probability== ...fact that probability is the ratio of the number of successful outcomes to the number of total outcomes.

1 KB (175 words) - 23:50, 18 November 2023
Casework
...totals of each part. Casework is a very general problem-solving approach, and as such has wide applicability. Here are some examples that demonstrate casework in action. Unlike the selections in this article, most problems cannot be completely solved throu

5 KB (709 words) - 10:28, 19 February 2024
Euclidean algorithm
...CD) of two elements of a [[Euclidean domain]], the most common of which is the [[nonnegative]] [[integer]]s <math>\mathbb{Z}{\geq 0}</math>, without [[fac ==Main idea and Informal Description==

6 KB (924 words) - 21:50, 8 May 2022
Conic section
...clear from their definition, the conic sections are all [[plane curve]]s, and every conic section can be described in [[Cartesian coordinates]] by a [[po All conic sections fall into the following categories:

5 KB (891 words) - 01:14, 9 January 2023
Generating function
...e generating function) is <math>c_0 + c_1 x + c_2 x^2 + \cdots </math> and the sequence is <math>c_0, c_1, c_2,\ldots</math>. This function can be described as the number of ways we can get <math>{k}</math> heads when flipping <math>n</mat

4 KB (659 words) - 12:54, 7 March 2022
Binomial Theorem
...'' states that for [[real]] or [[complex]] <math>a</math>, <math>b</math>, and [[non-negative]] [[integer]] <math>n</math>, ...h> is expanded and like terms are collected are the same as the entries in the <math>n</math>th row of [[Pascal's Triangle]].

5 KB (935 words) - 13:11, 20 February 2024
Prime number
...nteger]] <math>p>1</math> whose only positive [[divisor | divisors]] are 1 and itself. ...ime nor [[composite number|composite]] because it is its only factor among the [[natural number|natural numbers]].

6 KB (985 words) - 12:38, 25 February 2024
Function
...ule that it takes its input value, and squares it to get an output value. One can call this function <math>f</math>. ...math>A</math> to <math>B</math>'' (written <math>f: A \to B</math>) if and only if

10 KB (1,761 words) - 03:16, 12 May 2023
Complementary counting
.... A large hint that complementary counting may lead to a quick solution is the phrase "not" or "at least" within a problem statement. ...</math>. In most instances, though, <math>A</math> is obvious from context and is committed from mention.

8 KB (1,192 words) - 17:20, 16 June 2023
Bijection
...|two-sided inverse]] exactly when it is a bijection between its [[domain]] and [[range]]. ...when dealing with arguments concerning [[infinite]] sets or in permutation and probability.

1,016 bytes (141 words) - 03:39, 29 November 2021
Combinatorial identity
...]]s <math>k</math> and <math>n</math>. Here, <math>\binom{n}{k}</math> is the binomial coefficient <math>\binom{n}{k} = {}_nC_k = C_k^n</math>. ...ys to choose <math>k-1</math> things from <math>n-1</math> things added to the number of ways to choose <math>k</math> things from <math>n-1</math> things

12 KB (1,993 words) - 23:49, 19 April 2024
Integer
...b</math> are all integers (that is, the integers are closed under addition and multiplication), but their quotient <math>a\div b</math> may or may not be For a more simple and straightforward definition, an integer is a number that is '''not''' a [[de

2 KB (296 words) - 15:04, 5 August 2022
Prime factorization
...ve integer]] has a unique prime factorization, up to changing the order of the terms. The form of a prime factorization is

3 KB (496 words) - 22:14, 5 January 2024
Composite number
...ifferent from 1 and itself. Some composite numbers are <math>4=2^2</math> and <math>12=2\times 6=3\times 4</math>. Composite numbers '''atleast have 2 di ...even [[prime number]], three is the only multiple of three that is prime, and so on.

6 KB (350 words) - 12:58, 26 September 2023
Circle
...nter]] and the distance from the center to a point on the circle is called the [[radius]]. [[Image:circle1.PNG|thumb|right|The radius and center of a circle.]]

9 KB (1,555 words) - 20:05, 2 November 2023
Ellipse
...distances from <math>P</math> to two fixed [[focus|foci]] is a constant. (The equivalence of these two definitions is a non-trivial fact.) ...to the axis of the the cone, or (in the second definition) the two foci of the ellipse coincide.

5 KB (892 words) - 21:52, 1 May 2021
Base numbers
...l]], or base-10, number system. To help explain what this means, consider the number 2746. This number can be rewritten as <math>2746_{10}=2\cdot10^3+7\ ...math>'s, the third digit tells us there are seven <math>10^2</math>'s, and the fourth digit tells us there are two <math>10^3</math>'s.

4 KB (547 words) - 17:23, 30 December 2020
Base numbers/Common bases
...is [[phinary]], which is base [[phi]]; others include "[[Fibonacci base]]" and base negative two. ...avorite among computer programmers. It has just two digits: <math>0</math> and <math>1</math>.

2 KB (351 words) - 10:39, 1 October 2015
Henstock-Kurzweil integral
...ple and elegant idea. It was developed independently by [[Ralph Henstock]] and [[Jaroslav Kurzweil]]. ...</math> is ''Generalized Riemann Integrable'' on <math>[a,b]</math> if and only if, <math>\forall\epsilon>0</math>, there exists a [[gauge]] <math>\delta:[

2 KB (401 words) - 09:46, 31 January 2018
Mathematical Kangaroo
...coring students per grade at the national level. High scoring students in the US that are ranked high within their state will also be awarded as a state ==Registration and Eligibility==

6 KB (936 words) - 15:38, 22 February 2024
Least common multiple
...gers has an [[infinite]] number of [[common multiple]]s, but only one LCM. The LCM of a set of numbers <math>\{a_1,a_2,\cdots,a_n\}</math> is conventional ...4 and 6. We would begin by listing the multiples of 4 and 6 until we find the smallest number in both lists, as shown below.

2 KB (383 words) - 10:49, 4 September 2022
Math Day at the Beach
'''Math Day at the Beach''' is a [[mathematical problem solving]] festival for Southern Califo ...nd team competition. Teams represent high schools and have 6 members each. The competition takes place on a Saturday in March.

4 KB (644 words) - 12:56, 29 March 2017
Ptolemy's Inequality
'''Ptolemy's Inequality''' is a famous inequality attributed to the Greek mathematician Ptolemy. The inequality states that in for four points <math>A, B, C, D </math> in the plane,

3 KB (602 words) - 09:01, 7 June 2023
Pi
...act, [[transcendental number]], as proved by Lindemann in 1882) denoted by the Greek letter <math>\pi </math>. ...on]]al approximations for pi are <math>\frac{22}{7} \approx 3.14285</math> and <math>\frac{355}{113} \approx 3.1415929</math>.

8 KB (1,469 words) - 21:11, 16 September 2022
Phi
...iting, often to represent the constant <math>\frac{1+\sqrt{5}}{2}</math>. (The Greek letter [[Tau]] (<math>\tau</math>) was also used for this purpose in ...e terms of the [[Fibonacci sequence]], as well as the positive solution of the [[quadratic equation]] <math>x^2-x-1=0</math>.

2 KB (302 words) - 14:04, 1 January 2024
Fibonacci sequence
...h equal to 1 and each subsequent term is the sum of the two preceding it. The first few terms are <math>1, 1, 2, 3, 5, 8, 13, 21, 34, 55,...</math>. ...> and <math>F_n=F_{n-1}+F_{n-2}</math> for <math>n \geq 3</math>. This is the simplest nontrivial example of a [[linear recursion]] with constant coeffic

6 KB (957 words) - 23:49, 7 March 2024
Muirhead's Inequality
The inequality is easier to understand given an example. Since the sequence <math>(5,1)</math> majorizes <math>(4,2)</math> (as <math>5>4, 5+1 ...erify that an inequality ''can'' be proved with AM-GM before demonstrating the full AM-GM proof.

8 KB (1,346 words) - 12:53, 8 October 2023
Cardinality
...of <math>\{1, \{2, 3\}, \{1, 2, 3\}\}</math> is 3, and the cardinality of the [[empty set]] is 0. ...is <math>|\{3, 4\}| = 2</math>. Sometimes, the notations <math>n(A)</math> and <math>\# (A)</math> are used.

2 KB (263 words) - 00:54, 17 November 2019
Injection
...or which every value in the [[range]] is the image of exactly one value in the [[domain]]. .../math> and <math>|Y|\leq|Z|</math> implies <math>|X|\leq|Z|</math> because the composition of injections is again an injection.

1 KB (228 words) - 01:01, 17 November 2019
Polygon
...ine segment]]s. There are two types of polygons: [[convex polygon|convex]] and [[concave polygon|concave]]. ...ular]] or irregular. A polygon is regular if all sides are the same length and all angles are [[congruent]].

2 KB (372 words) - 19:04, 30 May 2015
Writing scholarships
...rship programs in other countries. Just make that reorganization as clear and as clean as possible. Additions to this list are welcomed and encouraged. Please don't be stingy about letting students in on how they c

7 KB (1,039 words) - 18:45, 18 January 2024

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