https://artofproblemsolving.com/wiki/api.php?action=feedcontributions&user=Mathew1&feedformat=atomAoPS Wiki - User contributions [en]2021-08-02T20:08:22ZUser contributionsMediaWiki 1.31.1https://artofproblemsolving.com/wiki/index.php?title=Vector&diff=36577Vector2011-02-04T20:11:59Z<p>Mathew1: /* Cross (Vector) Product */</p>
<hr />
<div>The word '''vector''' has many different definitions, depending on who is defining it and in what context. Physicists will often refer to a vector as "a quantity with a direction and magnitude." For Euclidean geometers, a vector is essentially a directed line segment. In many situations, a vector is best considered as an n-tuple of numbers (often real or complex). Most generally, but also most abstractly, a vector is any object which is an element of a given vector space. <br />
<br />
A vector is usually graphically represented as an arrow. Vectors can be uniquely described in many ways. The two most common is (for 2-dimensional vectors) by describing it with its length (or magnitude) and the angle it makes with some fixed line (usually the x-axis) or by describing it as an arrow beginning at the origin and ending at the pint <math>(x,y)</math>. An <math>n</math>-dimensional vector can be described in this coordinate form as an ordered <math>n</math>-tuple of numbers within angle brackets or parentheses, <math>(x\,\,y\,\,z\,\,...)</math>. The set of vectors over a [[field]] is called a [[vector space]].<br />
<br />
== Description ==<br />
Every vector <math>\overrightarrow{PQ}</math> has a starting point <math>P\langle x_1, y_1\rangle</math> and an endpoint <math>Q\langle x_2, y_2\rangle</math>. Since the only thing that distinguishes one vector from another is its magnitude or length, and direction, vectors can be freely translated about a plane without changing. Hence, it is convenient to consider a vector as originating from the origin. This way, two vectors can be compared by only looking at their endpoints. This is why we only require <math>n</math> values for an <math>n</math> dimensional vector written in the form <math>(x\,\,y\,\,z\,\,...)</math>. The magnitude of a vector, denoted <math>\|\vec{v}\|</math>, is found simply by <br />
using the distance formula.<br />
<br />
== Addition of Vectors ==<br />
For vectors <math>\vec{v}</math> and <math>\vec{w}</math>, with angle <math>\theta</math> formed by them, <math>\|\vec{v}+\vec{w}\|^2=\|\vec{v}\|^2+\|\vec{w}\|^2+2\|\vec{v}\|\|\vec{w}\|\cos\theta</math>.<br />
{{asy image|<asy> <br />
size(150);<br />
pen p=linewidth(1);<br />
MA("\theta",(5,-1),(2,3),(4,6),0.3,9,yellow);<br />
MC("\vec v",D((0,0)--(2,3),orange+p,Arrow),NW);<br />
D((2,3)--(3,4.5));<br />
MC("\vec w",D((2,3)--(5,-1),green+p,Arrow),NE);<br />
MC(-10,"\vec{v}+\vec{w}",D((0,0)--(5,-1),red+p,Arrow),S);<br />
</asy>|right|Addition of vectors}}<br />
<br />
From this it is simple to derive that for a real number <math>c</math>, <math>c\vec{v}</math> is the vector <math>\vec{v}</math> with magnitude multiplied by <math>c</math>. Negative <math>c</math> corresponds to opposite directions.<br />
<br />
== Properties of Vectors ==<br />
Since a [[vector space]] is defined over a [[field]] <math>K</math>, it is logically inherent that vectors have the same properties as those elements in a field.<br />
<br />
For any vectors <math>\vec{x}</math>, <math>\vec{y}</math>, <math>\vec{z}</math>, and real numbers <math>a,b</math>,<br />
<br />
#<math>\vec{x}+\vec{y}=\vec{y}+\vec{x}</math> ([[Commutative]] in +)<br />
#<math>(\vec{x}+\vec{y})+\vec{z}=\vec{x}+(\vec{y}+\vec{z})</math> ([[Associative]] in +)<br />
#There exists the zero vector <math>\vec{0}</math> such that <math>\vec{x}+\vec{0}=\vec{x}</math> ([[Additive identity]])<br />
#For each <math>\vec{x}</math>, there is a vector <math>\vec{y}</math> such that <math>\vec{x}+\vec{y}=\vec{0}</math> ([[Additive inverse]])<br />
#<math>1\vec{x}=\vec{x}</math> (Unit scalar identity)<br />
#<math>(ab)\vec{x}=a(b\vec{x})</math> ([[Associative]] in scalar)<br />
#<math>a(\vec{x}+\vec{y})=a\vec{x}+a\vec{y}</math> ([[Distributive]] on vectors)<br />
#<math>(a+b)\vec{x}=a\vec{x}+b\vec{x}</math> ([[Distributive]] on scalars)<br />
<br />
== Vector Operations ==<br />
===Dot (Scalar) Product===<br />
Consider two vectors <math>\bold{a}=\langle a_1,a_2,\ldots,a_n\rangle</math> and <math>\bold{b}=\langle b_1, b_2,\ldots,b_n\rangle</math> in <math>\mathbb{R}^n</math>. The dot product is defined as <math>\bold{a}\cdot\bold{b}=\bold{b}\cdot\bold{a}=|\bold{a}| |\bold{b}|\cos\theta=a_1b_1+a_2b_2+\cdots+a_nb_n</math>, where <math>\theta</math> is the angle formed by the two vectors. This also yields the geometric interpretation of the dot product: from basic right triangle trigonometry, it follows that the dot product is equal to the length of the [[projection]] (i.e. the distance from the origin to the foot of the head of <math>\bold{a}</math> to <math>\bold{b}</math>) of <math>\bold{a}</math> onto <math>\bold{b}</math> times the length of <math>\bold{b}</math>. Note that the dot product is <math>0</math> if and only if the two vectors are perpendicular.<br />
<br />
===Cross (Vector) Product===<br />
The cross product between two vectors <math>\bold{a}</math> and <math>\bold{b}</math> in <math>\mathbb{R}^3</math> is defined as the vector whose length is equal to the area of the parallelogram spanned by <math>\bold{a}</math> and <math>\bold{b}</math> and whose direction is in accordance with the [[right-hand rule]]. Because of this, <math>|\bold{a}\times\bold{b}|=|\bold{a}| |\bold{b}|\sin\theta</math>, where <math>\theta</math> is the angle formed by the two vectors, and from the [[right-hand rule]] condition, <math>\bold{a}\times\bold{b}=-\bold{b}\times\bold{a}</math>. Also, <math>\sin^2\theta+\cos^2\theta=1</math> gives that <math>|\bold{a}|^2|\bold{b}|^2=|\bold{a}\cdot\bold{b}|^2+|\bold{a}\times\bold{b}|^2</math>.<br />
<br />
If <math>\bold{a}=\langle a_1,a_2,a_3\rangle</math> and <math>\bold{b}=\langle b_1,b_2,b_3\rangle</math>, then the cross product of <math>\bold{a}</math> and <math>\bold{b}</math> is given by <br />
<center><math>\bold{a}\times\bold{b}=\begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3\end{vmatrix}.</math></center><br />
where <math>\hat{i},\hat{j},\hat{k}</math> are [[unit vector]]s along the coordinate axes, or equivalently, <math>\bold{a}\times\bold{b}=\langle a_2b_3-a_3b_2,a_3b_1-a_1b_3,a_1b_2-a_2b_1\rangle</math>. Also, <math>\bold{a}\times\bold{a}=\bold{0}</math><br />
<br />
===Triple Scalar Product===<br />
The triple scalar product of three vectors <math>\bold{a,b,c}</math> is defined as <math>(\bold{a}\times\bold{b})\cdot \bold{c}</math>. Geometrically, the triple scalar product gives the [[signed area]] of the [[parallelepiped]] determined by <math>\bold{a,b}</math> and <math>\bold{c}</math>. It follows that <br />
<br />
<center><math>(\bold{a}\times\bold{b})\cdot \bold{c} = (\bold{c}\times\bold{a})\cdot \bold{b} = (\bold{b}\times\bold{c})\cdot \bold{a}.</math></center><br />
<br />
It can also be shown that <br />
<br />
<center><math>(\bold{a}\times\bold{b})\cdot \bold{c} = \begin{vmatrix} a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \\ c_1 & c_2 & c_3 \end{vmatrix}.</math></center><br />
<br />
===Triple Vector Product===<br />
The vector triple product of <math>\bold{a},\bold{b},\bold{c}</math> is defined as the cross product of one vector, so that <math>\bold{a}\times(\bold{b}\times\bold{c})=\bold{b}(\bold{a}\cdot\bold{c})-\bold{c}(\bold{a}\cdot\bold{b})</math>, which can be remembered by the mnemonic "BAC-CAB" (this relationship between the cross product and dot product is called the triple product expansion, or Lagrange's formula).<br />
<br />
== See Also ==<br />
*[[Linear Algebra]]<br />
*[[Matrix]]<br />
*[http://www.artofproblemsolving.com/Forum/index.php?f=346\ Matrix-Linear Algebra AOPS forum]<br />
<br />
== Discussion ==<br />
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=89911\ This is a thread about what vectors are.]</div>Mathew1https://artofproblemsolving.com/wiki/index.php?title=Vector&diff=36576Vector2011-02-04T20:11:16Z<p>Mathew1: /* Cross (Vector) Product */</p>
<hr />
<div>The word '''vector''' has many different definitions, depending on who is defining it and in what context. Physicists will often refer to a vector as "a quantity with a direction and magnitude." For Euclidean geometers, a vector is essentially a directed line segment. In many situations, a vector is best considered as an n-tuple of numbers (often real or complex). Most generally, but also most abstractly, a vector is any object which is an element of a given vector space. <br />
<br />
A vector is usually graphically represented as an arrow. Vectors can be uniquely described in many ways. The two most common is (for 2-dimensional vectors) by describing it with its length (or magnitude) and the angle it makes with some fixed line (usually the x-axis) or by describing it as an arrow beginning at the origin and ending at the pint <math>(x,y)</math>. An <math>n</math>-dimensional vector can be described in this coordinate form as an ordered <math>n</math>-tuple of numbers within angle brackets or parentheses, <math>(x\,\,y\,\,z\,\,...)</math>. The set of vectors over a [[field]] is called a [[vector space]].<br />
<br />
== Description ==<br />
Every vector <math>\overrightarrow{PQ}</math> has a starting point <math>P\langle x_1, y_1\rangle</math> and an endpoint <math>Q\langle x_2, y_2\rangle</math>. Since the only thing that distinguishes one vector from another is its magnitude or length, and direction, vectors can be freely translated about a plane without changing. Hence, it is convenient to consider a vector as originating from the origin. This way, two vectors can be compared by only looking at their endpoints. This is why we only require <math>n</math> values for an <math>n</math> dimensional vector written in the form <math>(x\,\,y\,\,z\,\,...)</math>. The magnitude of a vector, denoted <math>\|\vec{v}\|</math>, is found simply by <br />
using the distance formula.<br />
<br />
== Addition of Vectors ==<br />
For vectors <math>\vec{v}</math> and <math>\vec{w}</math>, with angle <math>\theta</math> formed by them, <math>\|\vec{v}+\vec{w}\|^2=\|\vec{v}\|^2+\|\vec{w}\|^2+2\|\vec{v}\|\|\vec{w}\|\cos\theta</math>.<br />
{{asy image|<asy> <br />
size(150);<br />
pen p=linewidth(1);<br />
MA("\theta",(5,-1),(2,3),(4,6),0.3,9,yellow);<br />
MC("\vec v",D((0,0)--(2,3),orange+p,Arrow),NW);<br />
D((2,3)--(3,4.5));<br />
MC("\vec w",D((2,3)--(5,-1),green+p,Arrow),NE);<br />
MC(-10,"\vec{v}+\vec{w}",D((0,0)--(5,-1),red+p,Arrow),S);<br />
</asy>|right|Addition of vectors}}<br />
<br />
From this it is simple to derive that for a real number <math>c</math>, <math>c\vec{v}</math> is the vector <math>\vec{v}</math> with magnitude multiplied by <math>c</math>. Negative <math>c</math> corresponds to opposite directions.<br />
<br />
== Properties of Vectors ==<br />
Since a [[vector space]] is defined over a [[field]] <math>K</math>, it is logically inherent that vectors have the same properties as those elements in a field.<br />
<br />
For any vectors <math>\vec{x}</math>, <math>\vec{y}</math>, <math>\vec{z}</math>, and real numbers <math>a,b</math>,<br />
<br />
#<math>\vec{x}+\vec{y}=\vec{y}+\vec{x}</math> ([[Commutative]] in +)<br />
#<math>(\vec{x}+\vec{y})+\vec{z}=\vec{x}+(\vec{y}+\vec{z})</math> ([[Associative]] in +)<br />
#There exists the zero vector <math>\vec{0}</math> such that <math>\vec{x}+\vec{0}=\vec{x}</math> ([[Additive identity]])<br />
#For each <math>\vec{x}</math>, there is a vector <math>\vec{y}</math> such that <math>\vec{x}+\vec{y}=\vec{0}</math> ([[Additive inverse]])<br />
#<math>1\vec{x}=\vec{x}</math> (Unit scalar identity)<br />
#<math>(ab)\vec{x}=a(b\vec{x})</math> ([[Associative]] in scalar)<br />
#<math>a(\vec{x}+\vec{y})=a\vec{x}+a\vec{y}</math> ([[Distributive]] on vectors)<br />
#<math>(a+b)\vec{x}=a\vec{x}+b\vec{x}</math> ([[Distributive]] on scalars)<br />
<br />
== Vector Operations ==<br />
===Dot (Scalar) Product===<br />
Consider two vectors <math>\bold{a}=\langle a_1,a_2,\ldots,a_n\rangle</math> and <math>\bold{b}=\langle b_1, b_2,\ldots,b_n\rangle</math> in <math>\mathbb{R}^n</math>. The dot product is defined as <math>\bold{a}\cdot\bold{b}=\bold{b}\cdot\bold{a}=|\bold{a}| |\bold{b}|\cos\theta=a_1b_1+a_2b_2+\cdots+a_nb_n</math>, where <math>\theta</math> is the angle formed by the two vectors. This also yields the geometric interpretation of the dot product: from basic right triangle trigonometry, it follows that the dot product is equal to the length of the [[projection]] (i.e. the distance from the origin to the foot of the head of <math>\bold{a}</math> to <math>\bold{b}</math>) of <math>\bold{a}</math> onto <math>\bold{b}</math> times the length of <math>\bold{b}</math>. Note that the dot product is <math>0</math> if and only if the two vectors are perpendicular.<br />
<br />
===Cross (Vector) Product===<br />
The cross product between two vectors <math>\bold{a}</math> and <math>\bold{b}</math> in <math>\mathbb{R}^3</math> is defined as the vector whose length is equal to the area of the parallelogram spanned by <math>\bold{a}</math> and <math>\bold{b}</math> and whose direction is in accordance with the [[right-hand rule]]. Because of this, <math>|\bold{a}\times\bold{b}|=|\bold{a}| |\bold{b}|\sin\theta</math>, where <math>\theta</math> is the angle formed by the two vectors, and from the [[right-hand rule]] condition, <math>\bold{a}\times\bold{b}=-\bold{b}\times\bold{a}</math>. Also, <math>\sin^2\theta+\cos^2\theta=1</math> gives that <math>|\bold{a}|^2|\bold{b}|^2=|\bold{a}\cdot\bold{b}|^2+|\bold{a}\times\bold{b}|^2</math>.<br />
<br />
If <math>\bold{a}=\langle a_1,a_2,a_3\rangle</math> and <math>\bold{b}=\langle b_1,b_2,b_3\rangle</math>, then the cross product of <math>\bold{a}</math> and <math>\bold{b}</math> is given by <br />
<center><math>\bold{a}\times\bold{b}=\begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3\end{vmatrix}.</math></center><br />
where <math>\hat{i},\hat{j},\hat{k}</math> are [[unit vector]]s along the coordinate axes, or equivalently, <math>\bold{a}\times\bold{b}=\langle a_2b_3-a_3b_2,a_3b_1-a_1b_3,a_1b_2-a_2b_1\rangle</math>.<br />
<br />
Other properties of the cross product:<br />
1)<math>\bold{a}\times\bold{a}=\bold{0}</math><br />
<br />
===Triple Scalar Product===<br />
The triple scalar product of three vectors <math>\bold{a,b,c}</math> is defined as <math>(\bold{a}\times\bold{b})\cdot \bold{c}</math>. Geometrically, the triple scalar product gives the [[signed area]] of the [[parallelepiped]] determined by <math>\bold{a,b}</math> and <math>\bold{c}</math>. It follows that <br />
<br />
<center><math>(\bold{a}\times\bold{b})\cdot \bold{c} = (\bold{c}\times\bold{a})\cdot \bold{b} = (\bold{b}\times\bold{c})\cdot \bold{a}.</math></center><br />
<br />
It can also be shown that <br />
<br />
<center><math>(\bold{a}\times\bold{b})\cdot \bold{c} = \begin{vmatrix} a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \\ c_1 & c_2 & c_3 \end{vmatrix}.</math></center><br />
<br />
===Triple Vector Product===<br />
The vector triple product of <math>\bold{a},\bold{b},\bold{c}</math> is defined as the cross product of one vector, so that <math>\bold{a}\times(\bold{b}\times\bold{c})=\bold{b}(\bold{a}\cdot\bold{c})-\bold{c}(\bold{a}\cdot\bold{b})</math>, which can be remembered by the mnemonic "BAC-CAB" (this relationship between the cross product and dot product is called the triple product expansion, or Lagrange's formula).<br />
<br />
== See Also ==<br />
*[[Linear Algebra]]<br />
*[[Matrix]]<br />
*[http://www.artofproblemsolving.com/Forum/index.php?f=346\ Matrix-Linear Algebra AOPS forum]<br />
<br />
== Discussion ==<br />
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=89911\ This is a thread about what vectors are.]</div>Mathew1https://artofproblemsolving.com/wiki/index.php?title=Asymptote:_Getting_Started/Windows/Downloads_and_Installation&diff=36313Asymptote: Getting Started/Windows/Downloads and Installation2011-01-10T04:21:26Z<p>Mathew1: /* Ghostscript */</p>
<hr />
<div>{{Asymptote}}<br />
<br />
:'''''NOTE''': The following instructions assume that you are using a Windows machine. Instructions for MAC and Unix users can be found under Documentation <math>\rightarrow</math> Installation [http://asymptote.sourceforge.net/ here].''<br />
<br />
To begin using Asymptote, you must first download and install it. To view the eps-format images you produce, you will also need to download an eps viewer such as GSview. (GSview is convenient because it can display both eps and pdf files, and with GhostScript installed, Asymptote can easily output the images in pdf format as well.)<br />
<br />
== Asymptote ==<br />
To download and install Asymptote on your Windows machine:<br />
<br />
#Go to [http://asymptote.sourceforge.net SourceForge] and click on the Download link on the left. This will bring you to a page that has the latest file release in a box, with a green button marked "Download" on the right side of this box. Follow this link.<br />
# You will now see a box with four files, only one of which ends in <tt>.exe</tt> (it should look something like <tt>asymptote-2.00-setup.exe</tt>, depending on the number of the latest release.) Click on this link, and a download window will pop up in your browser. Choose to save the file, and take note of where on your hard drive you saved it to. Let's say you saved it to the folder <tt>D:\downloads\Asymptote</tt>. (NOTE: If you are using Windows and the green button in the previous step automatically starts downloading a file ends in ".tgz", then stop the download and return to the page with the green "Download" button. Click "View All Files" on that page, and then click the file that ends ".exe".)<br />
#When the download is complete, browse to <tt>D:\downloads\Asymptote</tt>, or wherever you saved the file, and double-click on the <tt>.exe</tt> file (<tt>asymptote-2.00-setup.exe</tt>). This will open an installer window, where you can choose the folder that Asymptote will be installed to (or simply use the default <tt>C:\Program Files\Asymptote</tt>), and choose whether you wish to have shortcuts added to the desktop and start menu. When you have finished, click Install.<br />
<br />
Asymptote is ready to start producing images, but you still need a way to view these images. (NOTE: if you already have a previewer capable of viewing .eps and .pdf files, you do not need to download the file below.)<br />
<br />
== GSview ==<br />
GSview is a standard viewer for .eps files, which is the standard output format for Asymptote images. To download and install GSview,<br />
# Go to [http://pages.cs.wisc.edu/~ghost/gsview/ this download site], and click on the "Obtaining GSView" link. Then click on the first link down, <tt>gsv49w32.exe</tt>. A download window will pop up in your browser. Choose to save the file, and take note of where on your hard drive you saved it to. Let's say you saved it to the folder <tt>D:\downloads\Ghostscript</tt>. (If you are unable to get the file <tt>gsv48w32.exe</tt> from this site, try [ftp://ftp.mirror.ac.uk/sites/mirror.cs.wisc.edu/pub/mirrors/ghost/ghostgum/ this site] instead.)<br />
# When the download is complete, browse to <tt>D:\downloads\Ghostscript</tt> in your files and double-click on the .exe file gsv48w32.exe. This will bring you to an installation window. Click Setup.<br />
# After it extracts the necessary files, there will be a new installation window. Click Next twice, and there will be two checkboxes, which can set GSview to be the default eps or pdf previewer. If you wish to use the more common Acrobat Reader, or some other pdf reader, to view pdf files, only leave the first box checked. However, you can check both if desired.<br />
# Click Next, and choose the directory in which you want GSview installed (or leave the default setting, <tt>C:\Program Files\Ghostgum</tt>). <br />
# Click Next twice, and choose the Start Menu folder to which a shortcut will be added. (The default is Ghostgum.)<br />
# Click Finish, and GSview will be installed.<br />
<br />
== Ghostscript ==<br />
Ghostscript may also need to be installed on your system. You may download it [http://pages.cs.wisc.edu/~ghost here] by clicking on the second link down, GPL Ghostscript. Then, click on the first link down, and copy the file to your computer. After that, run it to install Ghostscript. You may then need to set the version of Ghostscript in GSview. Do this by choosing the <tt>Easy Configure</tt> option in the <tt>Options</tt> menu in GSview.<br />
<br />
You now have installed everything you need to use Asymptote on the most basic level, as described in the next section.<br />
<br />
:[[Asymptote: Getting Started/Windows/Interactive Mode| Next: Interactive Mode]]</div>Mathew1https://artofproblemsolving.com/wiki/index.php?title=Asymptote:_Getting_Started/Windows/Downloads_and_Installation&diff=36312Asymptote: Getting Started/Windows/Downloads and Installation2011-01-10T04:18:55Z<p>Mathew1: /* GSview */</p>
<hr />
<div>{{Asymptote}}<br />
<br />
:'''''NOTE''': The following instructions assume that you are using a Windows machine. Instructions for MAC and Unix users can be found under Documentation <math>\rightarrow</math> Installation [http://asymptote.sourceforge.net/ here].''<br />
<br />
To begin using Asymptote, you must first download and install it. To view the eps-format images you produce, you will also need to download an eps viewer such as GSview. (GSview is convenient because it can display both eps and pdf files, and with GhostScript installed, Asymptote can easily output the images in pdf format as well.)<br />
<br />
== Asymptote ==<br />
To download and install Asymptote on your Windows machine:<br />
<br />
#Go to [http://asymptote.sourceforge.net SourceForge] and click on the Download link on the left. This will bring you to a page that has the latest file release in a box, with a green button marked "Download" on the right side of this box. Follow this link.<br />
# You will now see a box with four files, only one of which ends in <tt>.exe</tt> (it should look something like <tt>asymptote-2.00-setup.exe</tt>, depending on the number of the latest release.) Click on this link, and a download window will pop up in your browser. Choose to save the file, and take note of where on your hard drive you saved it to. Let's say you saved it to the folder <tt>D:\downloads\Asymptote</tt>. (NOTE: If you are using Windows and the green button in the previous step automatically starts downloading a file ends in ".tgz", then stop the download and return to the page with the green "Download" button. Click "View All Files" on that page, and then click the file that ends ".exe".)<br />
#When the download is complete, browse to <tt>D:\downloads\Asymptote</tt>, or wherever you saved the file, and double-click on the <tt>.exe</tt> file (<tt>asymptote-2.00-setup.exe</tt>). This will open an installer window, where you can choose the folder that Asymptote will be installed to (or simply use the default <tt>C:\Program Files\Asymptote</tt>), and choose whether you wish to have shortcuts added to the desktop and start menu. When you have finished, click Install.<br />
<br />
Asymptote is ready to start producing images, but you still need a way to view these images. (NOTE: if you already have a previewer capable of viewing .eps and .pdf files, you do not need to download the file below.)<br />
<br />
== GSview ==<br />
GSview is a standard viewer for .eps files, which is the standard output format for Asymptote images. To download and install GSview,<br />
# Go to [http://pages.cs.wisc.edu/~ghost/gsview/ this download site], and click on the "Obtaining GSView" link. Then click on the first link down, <tt>gsv49w32.exe</tt>. A download window will pop up in your browser. Choose to save the file, and take note of where on your hard drive you saved it to. Let's say you saved it to the folder <tt>D:\downloads\Ghostscript</tt>. (If you are unable to get the file <tt>gsv48w32.exe</tt> from this site, try [ftp://ftp.mirror.ac.uk/sites/mirror.cs.wisc.edu/pub/mirrors/ghost/ghostgum/ this site] instead.)<br />
# When the download is complete, browse to <tt>D:\downloads\Ghostscript</tt> in your files and double-click on the .exe file gsv48w32.exe. This will bring you to an installation window. Click Setup.<br />
# After it extracts the necessary files, there will be a new installation window. Click Next twice, and there will be two checkboxes, which can set GSview to be the default eps or pdf previewer. If you wish to use the more common Acrobat Reader, or some other pdf reader, to view pdf files, only leave the first box checked. However, you can check both if desired.<br />
# Click Next, and choose the directory in which you want GSview installed (or leave the default setting, <tt>C:\Program Files\Ghostgum</tt>). <br />
# Click Next twice, and choose the Start Menu folder to which a shortcut will be added. (The default is Ghostgum.)<br />
# Click Finish, and GSview will be installed.<br />
<br />
== Ghostscript ==<br />
Ghostscript may also need to be installed on your system. You may download it [http://pages.cs.wisc.edu/~ghost here] by clicking on the first link down, GPL Ghostscript. Then, click on the first link down, and copy the file to your computer. After that, run it to install Ghostscript. You may then need to set the version of Ghostscript in GSview. Do this by choosing the <tt>Easy Configure</tt> option in the <tt>Options</tt> menu in GSview.<br />
<br />
You now have installed everything you need to use Asymptote on the most basic level, as described in the next section.<br />
<br />
:[[Asymptote: Getting Started/Windows/Interactive Mode| Next: Interactive Mode]]</div>Mathew1https://artofproblemsolving.com/wiki/index.php?title=LaTeX:Downloads&diff=36285LaTeX:Downloads2011-01-04T19:17:38Z<p>Mathew1: /* TeXnicCenter */</p>
<hr />
<div>{{Latex}}<br />
<br />
The following are some '''downloads''' that are important to start to start writing in TeX.<br />
<br />
If you are using a [[Windows]] machine, you can download and install the following two programs ([[MiKTeX]] and [[TeXnicCenter]], in that order) to get started with LaTeX. These programs are free, and are not produced or distributed by AoPS Incorporated.<br />
<br />
''<font color="red">Note</font>: These are not the only ways to install and use LaTeX on your computer. The [http://www.tug.org TeX Users Group] has a list of other LaTeX programs, including programs for Mac and Linux computers. ''<br />
<br />
== MiKTeX ==<br />
'''MiKTeX''' is the engine that does the typsetting work.<br />
<br />
Note: The MiKTeX download is a large file, about 90 MB. If you have a slow internet connection, you may prefer to buy a [http://miktex.org/cd/ MiKTeX CD] rather than downloading it for free.<br />
<br />
To download and install MiKTeX, do the following:<br />
# Click [http://miktex.org/2.9/setup here] to open the MiKTeX download site. For Mac users, you will need MacTex which can be found [http://openwetware.org/wiki/Getting_started_with_LaTeX_on_a_Mac here].<br />
# Download the basic MiKTeX system by clicking on the link that says <tt>Download "Basic MiKTeX" Installer</tt>. (This link is listed under the heading "Installing a basic system"). Clicking on that link will open a Download page. Find the 'Location' that's nearest you, then click on the 'Download' link corresponding to that location. A 'File Download' window will probably pop up after a few seconds - choose to save the file. Pay attention to where you save the file. It doesn't matter where you save it, but you will have to find it later. <br />
# After the MiKTeX system download has finished, find the downloaded file, and double-click on it to launch the installer. Follow the directions in the installer. Some things to watch out for while installing: <br />
## When it asks you for the directory in which to install the files, we recommend leaving the default <tt>C:\Program Files\MiKTeX 2.9</tt>, but if you choose to change it, make note of where you change it to: you will need this information when installing TeXnicCenter. Note: Some versions of Windows will use <tt>C:\Program Files (x86)\MiKTeX 2.9</tt> as the installation folder. Pay attention to what folder MiKTeX installs to!<br />
##It will ask you your "preferred paper size". North American users will probably want "Letter"; most users elsewhere in the world will want "A4". <br />
##When it asks "Download packages on the fly", if you choose "Ask me first", beware that this may cause bugs later. In the future, if you compile a LaTeX file and it reports producing 0 pages or that a "GUI framework cannot be initialized", know that this is because a package has not been installed. To fix this, either install the missing package yourself or change this setting to "Yes" instead of "Ask me first".<br />
<br />
At this point, MiKTeX should be installed on your computer.<br />
<br />
== TeXnicCenter ==<br />
'''TeXnicCenter''' is a visual interface and editor for producing LaTeX documents. It is not a "What You See Is What You Get" (WYSIWYG) editor, meaning your code doesn't immediately become nice math images as you type. However, it does include an easy-to-use interface for finding symbol commands, and its text editor is custom-designed to help you avoid syntax errors. To install TeXnicCenter:<br />
# Click [http://www.texniccenter.org/ here] to open the TeXnicCenter download site. (Right click on the link and open it in a new window.) <br />
# Click on "Downloads" on the top of the page. <br />
# Click on the link <tt>"TeXnicCenter Installer"</tt>.<br />
# Once the download is finished, run the program that you just downloaded. We recommend accepting the default options, except that you may wish to add a desktop shortcut icon when you are asked. <br />
# If you elected to have a shortcut on the desktop, just click the icon on the desktop. Otherwise, click <tt>Start</tt> on the main Windows window, then 'All Programs', then 'TeXnicCenter', then choose the TeXnicCenter option. <br />
# When the program starts, a Tips window will open. Click Close. The program will then walk you through the configuration wizard: <br />
#: When it asks you for the "full path of the directory where the executables" are located, type <tt>C:\Program Files\MiKTeX 2.9\miktex\bin</tt> (''Note'': if you changed the default location when installing MiKTeX, then you'll need to replace <tt>C:\Program Files\MiKTeX 2.9</tt> with the directory to which you installed MiKTeX. Your computer may also have used <tt>C:\Program Files (x86)\MiKTeX 2.9</tt> as the installation folder, in which case you'll instead have to type <tt>C:\Program Files (x86)\MiKTeX 2.9\miktex\bin</tt> as the directory for the executables.) <br />
#: If it asks you to pick a PostScript viewer, you may just leave everything blank and just click "Next". Similarly if it asks you to pick a DVI viewer, just leave everything blank and click "Next". (It may or may not ask you these things, depending on how your computer is configured.) <br />
You're now ready to use LaTeX! Progress onto your [[LaTeX:Basics| First LaTeX Document]]<br />
<br />
==See Also==<br />
*[[LaTeX:Basics|Next: Basics]]<br />
*[[LaTeX:About|Previous: About]]<br />
*[[LaTeX:About|LaTeX for Mac]]</div>Mathew1https://artofproblemsolving.com/wiki/index.php?title=LaTeX:Downloads&diff=36284LaTeX:Downloads2011-01-04T19:17:01Z<p>Mathew1: /* TeXnicCenter */</p>
<hr />
<div>{{Latex}}<br />
<br />
The following are some '''downloads''' that are important to start to start writing in TeX.<br />
<br />
If you are using a [[Windows]] machine, you can download and install the following two programs ([[MiKTeX]] and [[TeXnicCenter]], in that order) to get started with LaTeX. These programs are free, and are not produced or distributed by AoPS Incorporated.<br />
<br />
''<font color="red">Note</font>: These are not the only ways to install and use LaTeX on your computer. The [http://www.tug.org TeX Users Group] has a list of other LaTeX programs, including programs for Mac and Linux computers. ''<br />
<br />
== MiKTeX ==<br />
'''MiKTeX''' is the engine that does the typsetting work.<br />
<br />
Note: The MiKTeX download is a large file, about 90 MB. If you have a slow internet connection, you may prefer to buy a [http://miktex.org/cd/ MiKTeX CD] rather than downloading it for free.<br />
<br />
To download and install MiKTeX, do the following:<br />
# Click [http://miktex.org/2.9/setup here] to open the MiKTeX download site. For Mac users, you will need MacTex which can be found [http://openwetware.org/wiki/Getting_started_with_LaTeX_on_a_Mac here].<br />
# Download the basic MiKTeX system by clicking on the link that says <tt>Download "Basic MiKTeX" Installer</tt>. (This link is listed under the heading "Installing a basic system"). Clicking on that link will open a Download page. Find the 'Location' that's nearest you, then click on the 'Download' link corresponding to that location. A 'File Download' window will probably pop up after a few seconds - choose to save the file. Pay attention to where you save the file. It doesn't matter where you save it, but you will have to find it later. <br />
# After the MiKTeX system download has finished, find the downloaded file, and double-click on it to launch the installer. Follow the directions in the installer. Some things to watch out for while installing: <br />
## When it asks you for the directory in which to install the files, we recommend leaving the default <tt>C:\Program Files\MiKTeX 2.9</tt>, but if you choose to change it, make note of where you change it to: you will need this information when installing TeXnicCenter. Note: Some versions of Windows will use <tt>C:\Program Files (x86)\MiKTeX 2.9</tt> as the installation folder. Pay attention to what folder MiKTeX installs to!<br />
##It will ask you your "preferred paper size". North American users will probably want "Letter"; most users elsewhere in the world will want "A4". <br />
##When it asks "Download packages on the fly", if you choose "Ask me first", beware that this may cause bugs later. In the future, if you compile a LaTeX file and it reports producing 0 pages or that a "GUI framework cannot be initialized", know that this is because a package has not been installed. To fix this, either install the missing package yourself or change this setting to "Yes" instead of "Ask me first".<br />
<br />
At this point, MiKTeX should be installed on your computer.<br />
<br />
== TeXnicCenter ==<br />
'''TeXnicCenter''' is a visual interface and editor for producing LaTeX documents. It is not a "What You See Is What You Get" (WYSIWYG) editor, meaning your code doesn't immediately become nice math images as you type. However, it does include an easy-to-use interface for finding symbol commands, and its text editor is custom-designed to help you avoid syntax errors. To install TeXnicCenter:<br />
# Click [http://www.texniccenter.org/ here] to open the TeXnicCenter download site. (Right click on the link and open it in a new window.) <br />
# Click on "Downloads" on the top of the page. <br />
# Click on the link <tt>"TeXnicCenter Installer"</tt>.<br />
# Once the download is finished, run the program that you just downloaded. We recommend accepting the default options, except that you may wish to add a desktop shortcut icon when you are asked. <br />
# If you elected to have a shortcut on the desktop, just click the icon on the desktop. Otherwise, click <tt>Start</tt> on the main Windows window, then 'All Programs', then 'TeXnicCenter', then choose the TeXnicCenter option. <br />
# When the program starts, a Tips window will open. Click Close. The program will then walk you through the configuration wizard: <br />
#: When it asks you for the "full path of the directory where the executables" are located, type <tt>C:\Program Files\MiKTeX 2.9\miktex\bin</tt> (''Note'': if you changed the default location when installing MiKTeX, then you'll need to replace <tt>C:\Program Files\MiKTeX 2.8</tt> with the directory to which you installed MiKTeX. Your computer may also have used <tt>C:\Program Files (x86)\MiKTeX 2.9</tt> as the installation folder, in which case you'll instead have to type <tt>C:\Program Files (x86)\MiKTeX 2.9\miktex\bin</tt> as the directory for the executables.) <br />
#: If it asks you to pick a PostScript viewer, you may just leave everything blank and just click "Next". Similarly if it asks you to pick a DVI viewer, just leave everything blank and click "Next". (It may or may not ask you these things, depending on how your computer is configured.) <br />
You're now ready to use LaTeX! Progress onto your [[LaTeX:Basics| First LaTeX Document]]<br />
<br />
==See Also==<br />
*[[LaTeX:Basics|Next: Basics]]<br />
*[[LaTeX:About|Previous: About]]<br />
*[[LaTeX:About|LaTeX for Mac]]</div>Mathew1https://artofproblemsolving.com/wiki/index.php?title=LaTeX:Downloads&diff=36283LaTeX:Downloads2011-01-04T19:07:20Z<p>Mathew1: /* MiKTeX */</p>
<hr />
<div>{{Latex}}<br />
<br />
The following are some '''downloads''' that are important to start to start writing in TeX.<br />
<br />
If you are using a [[Windows]] machine, you can download and install the following two programs ([[MiKTeX]] and [[TeXnicCenter]], in that order) to get started with LaTeX. These programs are free, and are not produced or distributed by AoPS Incorporated.<br />
<br />
''<font color="red">Note</font>: These are not the only ways to install and use LaTeX on your computer. The [http://www.tug.org TeX Users Group] has a list of other LaTeX programs, including programs for Mac and Linux computers. ''<br />
<br />
== MiKTeX ==<br />
'''MiKTeX''' is the engine that does the typsetting work.<br />
<br />
Note: The MiKTeX download is a large file, about 90 MB. If you have a slow internet connection, you may prefer to buy a [http://miktex.org/cd/ MiKTeX CD] rather than downloading it for free.<br />
<br />
To download and install MiKTeX, do the following:<br />
# Click [http://miktex.org/2.9/setup here] to open the MiKTeX download site. For Mac users, you will need MacTex which can be found [http://openwetware.org/wiki/Getting_started_with_LaTeX_on_a_Mac here].<br />
# Download the basic MiKTeX system by clicking on the link that says <tt>Download "Basic MiKTeX" Installer</tt>. (This link is listed under the heading "Installing a basic system"). Clicking on that link will open a Download page. Find the 'Location' that's nearest you, then click on the 'Download' link corresponding to that location. A 'File Download' window will probably pop up after a few seconds - choose to save the file. Pay attention to where you save the file. It doesn't matter where you save it, but you will have to find it later. <br />
# After the MiKTeX system download has finished, find the downloaded file, and double-click on it to launch the installer. Follow the directions in the installer. Some things to watch out for while installing: <br />
## When it asks you for the directory in which to install the files, we recommend leaving the default <tt>C:\Program Files\MiKTeX 2.9</tt>, but if you choose to change it, make note of where you change it to: you will need this information when installing TeXnicCenter. Note: Some versions of Windows will use <tt>C:\Program Files (x86)\MiKTeX 2.9</tt> as the installation folder. Pay attention to what folder MiKTeX installs to!<br />
##It will ask you your "preferred paper size". North American users will probably want "Letter"; most users elsewhere in the world will want "A4". <br />
##When it asks "Download packages on the fly", if you choose "Ask me first", beware that this may cause bugs later. In the future, if you compile a LaTeX file and it reports producing 0 pages or that a "GUI framework cannot be initialized", know that this is because a package has not been installed. To fix this, either install the missing package yourself or change this setting to "Yes" instead of "Ask me first".<br />
<br />
At this point, MiKTeX should be installed on your computer.<br />
<br />
== TeXnicCenter ==<br />
'''TeXnicCenter''' is a visual interface and editor for producing LaTeX documents. It is not a "What You See Is What You Get" (WYSIWYG) editor, meaning your code doesn't immediately become nice math images as you type. However, it does include an easy-to-use interface for finding symbol commands, and its text editor is custom-designed to help you avoid syntax errors. To install TeXnicCenter:<br />
# Click [http://www.texniccenter.org/ here] to open the TeXnicCenter download site. (Right click on the link and open it in a new window.) <br />
# Click on "Downloads" on the top of the page. <br />
# Click on the link <tt>"TeXnicCenter Installer"</tt>.<br />
# Once the download is finished, run the program that you just downloaded. We recommend accepting the default options, except that you may wish to add a desktop shortcut icon when you are asked. <br />
# If you elected to have a shortcut on the desktop, just click the icon on the desktop. Otherwise, click <tt>Start</tt> on the main Windows window, then 'All Programs', then 'TeXnicCenter', then choose the TeXnicCenter option. <br />
# When the program starts, a Tips window will open. Click Close. The program will then walk you through the configuration wizard: <br />
#: When it asks you for the "full path of the directory where the executables" are located, type <tt>C:\Program Files\MiKTeX 2.8\miktex\bin</tt> (''Note'': if you changed the default location when installing MiKTeX, then you'll need to replace <tt>C:\Program Files\MiKTeX 2.8</tt> with the directory to which you installed MiKTeX. Your computer may also have used <tt>C:\Program Files (x86)\MiKTeX 2.8</tt> as the installation folder, in which case you'll instead have to type <tt>C:\Program Files (x86)\MiKTeX 2.8\miktex\bin</tt> as the directory for the executables.) <br />
#: If it asks you to pick a PostScript viewer, you may just leave everything blank and just click "Next". Similarly if it asks you to pick a DVI viewer, just leave everything blank and click "Next". (It may or may not ask you these things, depending on how your computer is configured.) <br />
You're now ready to use LaTeX! Progress onto your [[LaTeX:Basics| First LaTeX Document]]<br />
<br />
==See Also==<br />
*[[LaTeX:Basics|Next: Basics]]<br />
*[[LaTeX:About|Previous: About]]<br />
*[[LaTeX:About|LaTeX for Mac]]</div>Mathew1