Difference between revisions of "AoPS Wiki:Sandbox"

Revision as of 09:53, 5 August 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.

[This was deleted due to its inappropriateness.]

Test 1

$[asy] dot((0,0)); dot((1,0)); dot((0,1)); dot((1,1)); dot((2,0)); dot((0,2)); dot((1,2)); dot((2,1)); dot((2,2)); dot((3,0)); dot((3,1)); dot((3,2)); dot((3,3)); dot((2,3)); dot((1,3)); dot((0,3)); dot((0,4)); dot((1,4)); dot((2,4)); dot((3,4)); dot((4,4)); dot((4,3)); dot((4,2)); dot((4,1)); dot((4,0)); dot((5,0)); dot((5,1)); dot((5,2)); dot((5,3)); dot((5,4)); dot((5,5)); dot((4,5)); dot((3,5)); dot((2,5)); dot((1,5)); dot((0,5)); dot((0,6)); dot((1,6)); dot((2,6)); dot((3,6)); dot((4,6)); dot((5,6)); dot((6,6)); dot((6,5)); dot((6,4)); dot((6,3)); dot((6,2)); dot((6,1)); dot((6,0)); dot((7,0)); dot((7,1)); dot((7,2)); dot((7,3)); dot((7,4)); dot((7,5)); dot((7,6)); dot((7,7)); dot((6,7)); dot((5,7)); dot((4,7)); dot((3,7)); dot((2,7)); dot((1,7)); dot((0,7)); draw((0,1)--(1,7),pink); draw((1,7)--(7,6),red); draw((7,6)--(6,0),red); draw((6,0)--(0,1),pink); draw((2,7)--(7,5),blue); draw((0,2)--(2,7),blue); draw((5,0)--(0,2),blue); draw((5,0)--(7,5),red); draw((3,7)--(7,4),green); draw((7,4)--(4,0),black); draw((4,0)--(0,3),green); draw((0,3)--(3,7),pink); draw((4,7)--(7,3),green); draw((7,3)--(3,0),green); draw((3,0)--(0,4),red); draw((0,4)--(4,7),green); draw((5,7)--(7,2),black); draw((7,2)--(2,0),black); draw((2,0)--(0,5),orange); draw((0,5)--(5,7),black); draw((0,6)--(1,0),green); draw((1,0)--(7,1),brown); draw((7,1)--(6,7),brown); draw((0,6)--(6,7),brown); [/asy]$ Hi there yall

Test 2

Test

$[asy] dot((50,1)); dot((2,1)); dot((3,1)); dot((4,1)); dot((5,1)); dot((6,1)); dot((7,1)); dot((1,2)); dot((2,2)); dot((3,2)); dot((4,2)); dot((5,2)); dot((6,2)); dot((7,2)); dot((1,3)); dot((2,3)); dot((3,3)); dot((4,3)); dot((5,3)); dot((6,3)); dot((7,3)); dot((1,4)); dot((2,4)); dot((3,4)); dot((4,4)); dot((5,4)); dot((6,4)); dot((7,4)); dot((1,5)); dot((2,5)); dot((3,5)); dot((4,5)); dot((5,5)); dot((6,5)); dot((7,5)); dot((1,6)); dot((2,6)); dot((3,6)); dot((4,6)); dot((5,6)); dot((6,6)); dot((7,6)); dot((1,7)); dot((2,7)); dot((3,7)); dot((4,7)); dot((5,7)); dot((6,7)); dot((7,7)); draw((1,1)--(1,3)--(3,3),red); draw((1,4)--(3,4)--(3,2),yellow); draw((4,4)--(4,2)--(2,2),green); draw((4,1)--(2,1)--(2,3),blue); draw((7,1)--(7,3)--(5,3),red); draw((7,4)--(5,4)--(5,2),yellow); draw((4,2)--(6,2),green); draw((4,1)--(6,1)--(6,3),blue); draw((1,7)--(1,5)--(3,5),red); draw((3,4)--(3,6),yellow); draw((4,4)--(4,6)--(2,6),green); draw((4,7)--(2,7)--(2,5),blue); draw((7,7)--(7,5)--(5,5),red); draw((5,4)--(5,6),yellow); draw((4,6)--(6,6),green); draw((4,7)--(6,7)--(6,5),blue); [/asy]$

This is what epicness looks like.

BUT JEFFCHEN WOULDN'T KNOW

<asy2>unitsize(33);pair A,B,C,D,I;A=origin; B=1.6*right; C=1.6*dir(60); D=0.8*right; I=incenter(A,B,C); draw(A--B--C--cycle);draw(incircle(A,B,C)); draw(C--D); </asy2>

Test 3

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

Test 4.0000000000000000000000000000000000000000000000000000000000000000000

$\binom{\binom{3}{2}}{/binom{6}{2}}$ $\sqrt{5}=50$

Test 5

n1000 is editing this. yay! (Made better by AoPS)

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

Who loves me? only $x^2$

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) notice how the square root signs are becoming progressively less slanted... What is $\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{e^{1\pi\pi\sqrtpi}}}}}}+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{20}}}}}}$ (Error compiling LaTeX. Unknown error_msg)?!?! I got carried away.

Test 7

$\text{Use a calculator:}$

$\int_{-\frac{877\pi}{7e^{e^{e^e}}}}^{1492.558} \sum^{9000!}_{k=0} \left(\cfrac{k^{kx+e}-\cfrac{1}{x^e-\cfrac{k-x}{k^{1337^e}+\cfrac{1}{k-x+\pi-42}}}}{x^{122.8}+\cfrac{71^k}{k+x+\cfrac{\sqrt{\sqrt{\pi^{12000.4x}}}}{94.5^{89x}}}-k^{100}100^xx^k}+2\right)\frac{d}{dx}+10^{10^{76}}$ !

silentazn's trillion dollar question

bobthesmartypants's answer: There is not enough space in the observable universe to write this number down, so there s no valid answer. my answer: There's not enough matter in the observable universe to store this number in memory, so you don't know the valid answer.

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