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| | {{AoPSWiki:Sandbox/header}} <!-- Please do not delete this line --> | | {{AoPSWiki:Sandbox/header}} <!-- Please do not delete this line --> |
| − | 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.
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| − | | |
| − | Warning: anything you place here is subject to deletion without notice.
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| − | | |
| − | == Test 0==
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| − | Firstly, AkshajK is awesome, and is editing this.
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| − | | |
| − | What is <math> \frac{(x+y)(2x-y)(y-x)^{2}}{(x-y)(x^{2}-y^{2})(2x-y)} ???</math>
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| − | | |
| − | | |
| − | <cmath>x</cmath>
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| − | <cmath>x</cmath>
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| − | What is <math> \frac{(x+y)(2x-y)(y-x)^{2}}{(x-y)(x^{2}-y^{2})(2x-y)} ???</math>
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| − | oh.. donnoo
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| − | | |
| − | ==Test 1==
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| − | | |
| − | <asy> | |
| − | | |
| − | dot((0,0));
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| − | dot((1,0));
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| − | dot((0,1));
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| − | dot((1,1));
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| − | dot((2,0));
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| − | dot((0,2));
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| − | dot((1,2));
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| − | dot((2,1));
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| − | dot((2,2));
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| − | dot((3,0));
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| − | dot((3,1));
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| − | dot((3,2));
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| − | dot((3,3));
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| − | dot((2,3));
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| − | dot((1,3));
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| − | dot((0,3));
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| − | dot((0,4));
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| − | dot((1,4));
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| − | dot((2,4));
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| − | dot((3,4));
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| − | dot((4,4));
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| − | dot((4,3));
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| − | dot((4,2));
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| − | dot((4,1));
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| − | dot((4,0));
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| − | dot((5,0));
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| − | dot((5,1));
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| − | dot((5,2));
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| − | dot((5,3));
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| − | dot((5,4));
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| − | dot((5,5));
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| − | dot((4,5));
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| − | dot((3,5));
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| − | dot((2,5));
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| − | dot((1,5));
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| − | dot((0,5));
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| − | dot((0,6));
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| − | dot((1,6));
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| − | dot((2,6));
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| − | dot((3,6));
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| − | dot((4,6));
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| − | dot((5,6));
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| − | dot((6,6));
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| − | dot((6,5));
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| − | dot((6,4));
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| − | dot((6,3));
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| − | dot((6,2));
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| − | dot((6,1));
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| − | dot((6,0));
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| − | dot((7,0));
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| − | dot((7,1));
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| − | dot((7,2));
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| − | dot((7,3));
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| − | dot((7,4));
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| − | dot((7,5));
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| − | dot((7,6));
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| − | dot((7,7));
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| − | dot((6,7));
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| − | dot((5,7));
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| − | dot((4,7));
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| − | dot((3,7));
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| − | dot((2,7));
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| − | dot((1,7));
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| − | dot((0,7));
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| − | draw((0,1)--(1,7),red);
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| − | draw((1,7)--(7,6),red);
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| − | draw((7,6)--(6,0),red);
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| − | draw((6,0)--(0,1),red);
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| − | draw((2,7)--(7,5),blue);
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| − | draw((0,2)--(2,7),blue);
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| − | draw((5,0)--(0,2),blue);
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| − | draw((5,0)--(7,5),blue);
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| − | draw((3,7)--(7,4),yellow);
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| − | draw((7,4)--(4,0),yellow);
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| − | draw((4,0)--(0,3),yellow);
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| − | draw((0,3)--(3,7),yellow);
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| − | draw((4,7)--(7,3),green);
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| − | draw((7,3)--(3,0),green);
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| − | draw((3,0)--(0,4),green);
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| − | draw((0,4)--(4,7),green);
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| − | draw((5,7)--(7,2),black);
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| − | draw((7,2)--(2,0),black);
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| − | draw((2,0)--(0,5),black);
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| − | draw((0,5)--(5,7),black);
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| − | draw((0,6)--(1,0),purple);
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| − | draw((1,0)--(7,1),purple);
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| − | draw((7,1)--(6,7),purple);
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| − | draw((0,6)--(6,7),purple);
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| − | | |
| − | </asy> | |
| − | awesome
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| − | | |
| − | ==Test 2==
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| − | <b>Test</b>
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| − | | |
| − | <asy>
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| − | | |
| − | dot((0,0));
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| − | dot((1,0));
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| − | dot((0,1));
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| − | dot((1,1));
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| − | dot((0,2));
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| − | dot((2,0));
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| − | dot((1,2));
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| − | dot((2,1));
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| − | dot((2,2));
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| − | dot((3,0));
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| − | dot((3,1));
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| − | dot((3,2));
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| − | dot((3,3));
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| − | dot((2,3));
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| − | dot((1,3));
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| − | dot((0,3));
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| − | | |
| − | </asy>
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| − | | |
| − | more asy!!!!!!!!!!!!
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| − | <asy>
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| − | draw((0,0)--(4,0),black);
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| − | draw((4,3)--(4,0),black);
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| − | draw((4,3)--(0,0),black);
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| − | dot((0,0));
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| − | dot((4,0));
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| − | dot((4,3));
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| − | </asy>
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| − | | |
| − | ==Test 3==
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| − | <asy>
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| − | dot((0,0));
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| − | dot((0,4));
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| − | dot((3,4444));
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| − | dot((3,0));
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| − | dot((1.5,2));
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| − | draw((0,0)--(3,4444),green);
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| − | draw((0,4)--(3,0),green);
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| − | draw((0,0)--(0,4),red);
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| − | draw((0,4)--(3,4),red);
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| − | draw((3,0)--(3,4),red);
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| − | draw((3,0)--(0,0),red);
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| − | </asy>
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| − | | |
| − | | |
| − | ==Test 4==
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| − | | |
| − | <asy>
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| − | import graph;
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| − | draw(Circle((0,0),20)); // graph - Circle
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| − | </asy>
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| − | | |
| − | ==Test 5==
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| − | | |
| − | n1000 is editing this.
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| − | yay!
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| − | | |
| − | <asy>
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| − | pair A,B,C,D,E,F,G,H;
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| − | | |
| − | A=(1,0);
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| − | B=(2,0);
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| − | C=(3,1);
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| − | D=(3,2);
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| − | E=(2,3);
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| − | F=(1,3);
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| − | G=(0,2);
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| − | H=(0,1);
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| − | | |
| − | path octagon,square1,square2,star,bow1,bow2;
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| − | octagon=(A--B--C--D--E--F--G--H--cycle);
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| − | square1=(A--C--E--G--cycle);
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| − | square2=(B--D--F--H--cycle);
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| − | star=(A--D--G--B--E--H--C--F--cycle);
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| − | bow1=(A--B--F--E--cycle);
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| − | bow2=(C--D--H--G--cycle);
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| − | | |
| − | path[] all;
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| − | all=(octagon^^square1^^square2^^star^^bow1^^bow2);
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| − | | |
| − | draw(all);
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| − | | |
| − | fill(octagon,blue);
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| − | fill((bow1)^^(bow2),yellow);
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| − | fill(all,evenodd+red);
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| − | | |
| − | </asy> | |
| − | | |
| − | ==Test 6==
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| − | | |
| − | NeoMathematicalKid was here. And he broke the line of asy diagrams.
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| − | | |
| − | <math>\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)\\
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| − | &=\sum^4_{k=1}(k+2k+\cdots +k^2)\\
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| − | &=(1)+(2+4)+(3+6+9)+(4+8+12+16)\\
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| − | &=1+6+18+40\\
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| − | &=\boxed{65}
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| − | \end{align*}</math>
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| − | | |
| − | What is <math>\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}}}}}}</math>?!?! I got carried away.
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