Difference between revisions of "AoPS Wiki:Sandbox"

Revision as of 18:37, 2 February 2013

Welcome to the sandbox, a location to test your newfound wiki-editing abilities.

Please note that all contributions here may be deleted periodically and without warning.

In the computer world, a sandbox is a place to test and experiment -- essentially, it's a place to play.

This is the AoPSWiki Sandbox. Feel free to experiment here.

Warning: anything you place here is subject to deletion without notice.

Test 0

Firstly, AkshajK is awesome, and is editing this.

What is $\frac{(x+y)(2x-y)(y-x)^{2}}{(x-y)(x^{2}-y^{2})(2x-y)} ???$

$x$ $x$ What is $\frac{(x+y)(2x-y)(y-x)^{2}}{(x-y)(x^{2}-y^{2})(2x-y)} ???$ oh.. donnoo

Test 1

$[asy] dot((0,0)); dot((1,0)); dot((0,1)); dot((1,1)); dot((2,0)); dot((0,2)); dot((1,2)); dot((2,1)); dot((2,2)); dot((3,0)); dot((3,1)); dot((3,2)); dot((3,3)); dot((2,3)); dot((1,3)); dot((0,3)); dot((0,4)); dot((1,4)); dot((2,4)); dot((3,4)); dot((4,4)); dot((4,3)); dot((4,2)); dot((4,1)); dot((4,0)); dot((5,0)); dot((5,1)); dot((5,2)); dot((5,3)); dot((5,4)); dot((5,5)); dot((4,5)); dot((3,5)); dot((2,5)); dot((1,5)); dot((0,5)); dot((0,6)); dot((1,6)); dot((2,6)); dot((3,6)); dot((4,6)); dot((5,6)); dot((6,6)); dot((6,5)); dot((6,4)); dot((6,3)); dot((6,2)); dot((6,1)); dot((6,0)); dot((7,0)); dot((7,1)); dot((7,2)); dot((7,3)); dot((7,4)); dot((7,5)); dot((7,6)); dot((7,7)); dot((6,7)); dot((5,7)); dot((4,7)); dot((3,7)); dot((2,7)); dot((1,7)); dot((0,7)); draw((0,1)--(1,7),red); draw((1,7)--(7,6),red); draw((7,6)--(6,0),red); draw((6,0)--(0,1),red); draw((2,7)--(7,5),blue); draw((0,2)--(2,7),blue); draw((5,0)--(0,2),blue); draw((5,0)--(7,5),blue); draw((3,7)--(7,4),yellow); draw((7,4)--(4,0),yellow); draw((4,0)--(0,3),yellow); draw((0,3)--(3,7),yellow); draw((4,7)--(7,3),green); draw((7,3)--(3,0),green); draw((3,0)--(0,4),green); draw((0,4)--(4,7),green); draw((5,7)--(7,2),black); draw((7,2)--(2,0),black); draw((2,0)--(0,5),black); draw((0,5)--(5,7),black); draw((0,6)--(1,0),purple); draw((1,0)--(7,1),purple); draw((7,1)--(6,7),purple); draw((0,6)--(6,7),purple); [/asy]$ awesome

Test 2

Test

$[asy] dot((0,0)); dot((1,0)); dot((0,1)); dot((1,1)); dot((0,2)); dot((2,0)); dot((1,2)); dot((2,1)); dot((2,2)); dot((3,0)); dot((3,1)); dot((3,2)); dot((3,3)); dot((2,3)); dot((1,3)); dot((0,3)); [/asy]$

more asy!!!!!!!!!!!! $[asy] draw((0,0)--(4,0),black); draw((4,3)--(4,0),black); draw((4,3)--(0,0),black); dot((0,0)); dot((4,0)); dot((4,3)); [/asy]$

Test 3

$[asy] dot((0,0)); dot((0,4)); dot((3,4444)); dot((3,0)); dot((1.5,2)); draw((0,0)--(3,4444),green); draw((0,4)--(3,0),green); draw((0,0)--(0,4),red); draw((0,4)--(3,4),red); draw((3,0)--(3,4),red); draw((3,0)--(0,0),red); [/asy]$

Test 4

$[asy] import graph; draw(Circle((0,0),20)); // graph - Circle [/asy]$

Test 5

n1000 is editing this. yay!

$[asy] pair A,B,C,D,E,F,G,H; A=(1,0); B=(2,0); C=(3,1); D=(3,2); E=(2,3); F=(1,3); G=(0,2); H=(0,1); path octagon,square1,square2,star,bow1,bow2; octagon=(A--B--C--D--E--F--G--H--cycle); square1=(A--C--E--G--cycle); square2=(B--D--F--H--cycle); star=(A--D--G--B--E--H--C--F--cycle); bow1=(A--B--F--E--cycle); bow2=(C--D--H--G--cycle); path[] all; all=(octagon^^square1^^square2^^star^^bow1^^bow2); draw(all); fill(octagon,blue); fill((bow1)^^(bow2),yellow); fill(all,evenodd+red); [/asy]$

Test 6

NeoMathematicalKid was here. And he broke the line of asy diagrams.

$\begin{align*}\sum^4_{k=1}\left(\sum^k_{j=1}kj\right)&=\sum^4_{k=1}\left(k\sum^k_{j=1}j\right)\\ &=\sum^4_{k=1}\left(k(1+2+\cdots +k)\right)\\ &=\sum^4_{k=1}(k+2k+\cdots +k^2)\\ &=(1)+(2+4)+(3+6+9)+(4+8+12+16)\\ &=1+6+18+40\\ &=\boxed{65} \end{align*}$ (Error compiling LaTeX. Unknown error_msg)

What is $\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{e^{1\pi}}}}}}+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{20}}}}}}$ ?!?! I got carried away.

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