AoPS Wiki:Sandbox: Difference between revisions

Revision as of 12:28, 13 January 2008

Template:AoPSWiki:Sandbox/header 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.

Sandbox Area

$[asy] size(220pt); defaultpen(1); pair A=(0,0), B=(220,0), C=(18.7723,118.523); pair D=(72.6,0); pair Ia=incenter(A,D,C), Ib=incenter(B,D,C); pair Ta=(24.9758,52.5775),Tb=(86.6196,67.4129); pair E=IntersectionPoint((Ta--Tb),(C--D)); path Oa=circle(Ia,inradius(A,D,C)); path Ob=circle(Ib,inradius(B,D,C)); pair Da=IP(Oa,A--B), Db=IP(Ob,A--B); draw(D--C--A--B--C); draw(Ta--Tb); draw(Oa); draw(Ob); dot(A,linewidth(4)); dot(B,linewidth(4)); dot(C,linewidth(4)); dot(D,linewidth(4)); dot(E,linewidth(4)); dot(Ta,linewidth(4)); dot(Tb,linewidth(4)); label("A",A,SW); label("<math>B</math>",B,SE); label("<math>C</math>",C,W); label("<math>D</math>",D,S); label("<math>E</math>",E,NNE); [/asy]$

---

test <problem> <contest>AIME</contest> <version>I</version> <year>2007</year> <probnum>3</probnum> <question> Prove that $a^2+b^2=c^2$ in a right triangle. </question> <solution> "Because I said so" -- Pythagoras </solution> </problem>

If anybody knows how to embed XML tags in a Wiki page so that they don't display, but are still there, please post here.

$\mathrm{Test\;of\;mathrm}$ I am also testing dollars signs: $x+3=5$ $5+3=x$ Testing dollar signs $x^2 + 3 = 4$

Testing multiple dollar signs: $r^2+2 = 7$ and then, $r^3-2 = 9$

$\$ $x^2 + 3 = 4$

Dollar signs. $\dfrac{y}{r}=\sin \theta$ $\frac{m}{n}$ $cheesecake$ LaTeX didn't show up in the previews because the last } was missing.

$\frac{\sqrt{b^2-4aq}}{2\pi+3\pi+4\pi}$

test

testing asy

$[asy] pair A,B; A=(0,0); B=(1,1); draw(A--B); dot((0,0)); dot((1,1)); label("<math>A</math>",A,W); label("<math>B</math>",B,N); [/asy]$

A proof without words that $sin'=cos$ and $cos'=-sin$ . --Dustball 19:39, 6 January 2008 (EST)

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AoPS Wiki:Sandbox: Difference between revisions

Revision as of 12:28, 13 January 2008

Sandbox Area

@@ Line 7: / Line 7: @@
 === Sandbox Area ===
+<asy>
+size(220pt);
+defaultpen(1);
+pair A=(0,0), B=(220,0), C=(18.7723,118.523);
+pair D=(72.6,0);
+pair Ia=incenter(A,D,C), Ib=incenter(B,D,C);
+pair Ta=(24.9758,52.5775),Tb=(86.6196,67.4129);
+pair E=IntersectionPoint((Ta--Tb),(C--D));
+path Oa=circle(Ia,inradius(A,D,C));
+path Ob=circle(Ib,inradius(B,D,C));
+pair Da=IP(Oa,A--B), Db=IP(Ob,A--B);
+draw(D--C--A--B--C);
+draw(Ta--Tb);
+draw(Oa);
+draw(Ob);
+dot(A,linewidth(4));
+dot(B,linewidth(4));
+dot(C,linewidth(4));
+dot(D,linewidth(4));
+dot(E,linewidth(4));
+dot(Ta,linewidth(4));
+dot(Tb,linewidth(4));
+label("A",A,SW);
+label("<math>B</math>",B,SE);
+label("<math>C</math>",C,W);
+label("<math>D</math>",D,S);
+label("<math>E</math>",E,NNE);
+</asy>
+---
 test
 <problem>