Cool

Yesterday, at 5:21 pm, by AIME15

I talked to our Congressman today.

roflmao

Thu Dec 03, 2009 7:48 am, by AIME15

http://www.artofproblemsolving.com/Forum/profile.php?mode=viewprofile&u=73076

Mandelbrot

Wed Dec 02, 2009 7:03 am, by AIME15

Maybe today I won't fail.

Failed

Wed Nov 25, 2009 6:11 pm, by AIME15

Darn, the WOOT Olympiad had geometry Sad

Yes.

Mon Nov 23, 2009 10:13 pm, by AIME15

Got my caffeine. Time to do math.

Note to Self

Mon Nov 23, 2009 5:18 pm, by AIME15

1992 1993 2000 2001 2004 2007

Rain

Fri Nov 20, 2009 3:26 pm, by AceOfDiamonds

It rained today.
When I was going home.
I don't like rain.
My longboard's bearings are all wet and rusty now.
And my pant sleeves are wet.
And my socks.
And my shoes.

T-50 WH

Thu Nov 19, 2009 9:47 am, by AIME15

Average a bit over 15.4 this time. Of course, some memming went on, and some cheating, but it's not that bad considering the amount of 1-digit results.

FAIL

Sat Nov 14, 2009 3:53 pm, by AIME15

I won with a 165. ROFL.

Problems

Thu Nov 12, 2009 8:27 pm, by AIME15

1. Inside a unit square lie several circles with the sum of their circumferences equal to 10. Prove that there exist infinitely many lines, each of which intersect at least four circles.

2. Let S be a convex set in the plane that contains three non-collinear points. The points of S are colored by p colors, p > 1. Prove that for any n \ge 3 there exist infinitely many isometric n-gons whose vertices are all colored by the same color.

3. Draw the diagonals of a 21-gon. Prove that in doing so, at least one angle less than 1^\circ is formed.

Geometry

Tue Nov 10, 2009 7:03 pm, by AIME15

[ Currently: Not non-trivial. ]

Circle \omega is inscribed in convex quadrilateral ABCD, and it touches sides AB, BC, CD, and DA at A_1, B_1, C_1, and D_1, respectively. Let E, F, G, and H be the midpoints of A_1B_1, B_1C_1, C_1D_1, and D_1A_1, respectively. Prove that quadrilateral EFGH is a rectangle if and only if ABCD is cyclic.

Solution

Since HG and EF are midlines of triangles A_1C_1D_1 and A_1B_1C_1, they are both parallel to A_1C_1. Similarly, both HE and GF are parallel to B_1D_1. Thus, it suffices to show that A_1C_1 \perp B_1D_1 if and only if ABCD is cyclic.

Let T be the intersection of the segments A_1C_1 and B_1D_1. We have

\begin{align*} \angle A + \angle C &= 180^\circ - 2 \angle AA_1D_1+180^\circ - 2\angle CB_1C_1 \\ & = 360^\circ - \st...

Thus, \angle A + \angle C = 180^\circ if and only if \angle D_1TC_1=90^\circ. The result follows.

Trig

Sat Nov 07, 2009 2:10 pm, by AIME15

1. Prove that for any positive integer n,
\cot ^2 \dfrac{\pi}{2n + 1} + \cot^2 \dfrac{2\pi}{2n + 1} + \dots + \cot^2 \dfrac{n \pi}{2n + 1} = \dfrac{n(2n - 1)}{3}.
2. Solve the following system in positive real numbers:
\left (x_1 + \dots + x_k \right ) \left (x_k + \dots + x_{10} \right ) = 1
for k = 1,\dots,10.

Express the solutions in the form \dfrac{a\sqrt {b} - c\sqrt {d}}{e}, where a,b,c,d,e are positive integers, b,c are square-free, and \gcd (a,c,e) = 1.

Twenty-One

Thu Nov 05, 2009 9:37 pm, by AIME15

Indeed.

Awesomeness

Tue Nov 03, 2009 9:12 pm, by AIME15

I think this is self-explanatory.

Image

World Series

Mon Nov 02, 2009 8:27 pm, by AIME15

Yay, Game 6 is needed Mr. Green

Eh, Yankees are gonna win either way...

Won.

Sat Oct 31, 2009 2:22 pm, by AIME15

Our team won also. Woohoo!

Unfortunately I lost the countdown. And the game. Multiple times.

Mathleague 10/31

Fri Oct 30, 2009 5:38 pm, by AceOfDiamonds

Harvest Park won.
I couldn't do anything to prevent it.
I'm sorry Julia Sad

Q1

Thu Oct 29, 2009 4:49 pm, by AIME15

Over. 3-day weekend. Woohoo!

AYE

Tue Oct 27, 2009 8:39 pm, by AIME15

[ Currently: AYE ]

AYE

Frost MATHCOUNTS Competition #1

Sat Oct 24, 2009 11:10 am, by AIME15

Sprint: 29/30 in 21:30.
Target: 8/8, each pair in 2:00.
Team: 9/10 in 10:00.

Not bad, one misread each on Sprint and Team.

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  • u should start PoTD/W/M again Mr. Green

    By BarbieRocks, on Mon Nov 30, 2009 6:22 pm

  • lol

    By randomguy64, on Mon Nov 30, 2009 5:55 pm

  • do you delete all my shouts?????? Mad

    By BarbieRocks, on Thu Nov 26, 2009 7:12 am

  • m places. Inside joke.

    By PhireKaLk6781, on Sun Nov 08, 2009 10:22 am

  • Merry Halloween Everybody! Very Happy

    By BarbieRocks, on Sat Oct 31, 2009 7:24 am

  • Aay. Also known as Aye/Nay depending on the situation. Hahaha.

    By randomguy64, on Wed Oct 28, 2009 7:06 pm

  • aye

    By BarbieRocks, on Wed Oct 28, 2009 2:52 pm

  • everyone who enjoys listening to birds sing say 'aye' without the ''.

    By AceOfDiamonds, on Tue Oct 27, 2009 7:45 pm

  • Wow... way to go with your signature lol Rotfl Rotfl Rotfl

    By SonyWii, on Fri Oct 23, 2009 4:16 pm

  • wow...that was mean

    By gauss1181, on Thu Oct 22, 2009 7:36 am

158 Shouts

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  • Joined: 24 Mar 2008
  • Location: Pleasanton, TX

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  • Blog started: 21 Mar 2009
  • Total entries: 69
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