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by wileysw
October 2nd, 2008, 6:09 am
Forum: Brainteaser Forum
Topic: expected area of triangle
Replies: 3
Views: 49954

expected area of triangle

<t>i guess the answer should not depend on what the exact shape of the triangle is. (*)so i start from an equilateral triangle. the straight line could intersect any two sides at let's say P and Q, and form a smaller triangle with any of the vertex (A, B or C). by symmetry, the expected area of the ...
by wileysw
October 1st, 2008, 12:36 am
Forum: Brainteaser Forum
Topic: Buffon’s Needle Breaks in Two!
Replies: 9
Views: 52552

Buffon’s Needle Breaks in Two!

<t>QuoteOriginally posted by: AlokitoI didn't bother doing the "k random breaks", but doing k breaks into half I get 1 - (1 - 2/(k*pi))^k wow! I think I see e! taking the limit as k => infinite breaks, I get1 - e^(-2/pi) = 47.1%Can anyone check my math?to obtain the asymptotic form when n->infty, re...
by wileysw
October 1st, 2008, 12:33 am
Forum: Brainteaser Forum
Topic: Buffon’s Needle Breaks in Two!
Replies: 9
Views: 52552

Buffon’s Needle Breaks in Two!

<t>here's my two cents for the general case:my understanding of "the needle breaks into n random lengths (with uniform probability)" is that we choose n-1 uniformly distributed numbers between 0 and 1 as the coordinates for the breaking points.the probability of a needle with length x not crossing a...
by wileysw
September 28th, 2008, 11:24 pm
Forum: Brainteaser Forum
Topic: 3 tangent circles inside a triangle
Replies: 8
Views: 54096

3 tangent circles inside a triangle

<r>QuoteOriginally posted by: ChukchiQuoteOriginally posted by: wileyswthey are so-called Malfatti circles:<URL url="http://mathworld.wolfram.com/MalfattiCircles.htmlit">http://mathworld.wolfram.com/MalfattiCircles.htmlit</URL> has an amazing history, just google "marble problem" or "Malfatti's prob...
by wileysw
September 27th, 2008, 5:27 pm
Forum: Brainteaser Forum
Topic: 3 tangent circles inside a triangle
Replies: 8
Views: 54096

3 tangent circles inside a triangle

they are so-called Malfatti circles:http://mathworld.wolfram.com/MalfattiCircles.htmlit has an amazing history, just google "marble problem" or "Malfatti's problem"
by wileysw
December 14th, 2006, 9:45 pm
Forum: Careers Forum
Topic: Is it too late for now?
Replies: 7
Views: 85329

Is it too late for now?

<t>Hi, I am a physics Ph.D. student expecting to graduate next year.I know ppl seriously considering enter this field started much earlier. So my question is:Is it too late for now as most of the vacancies are already filled, or just because i am sending resume to wrong ppl (it's also likely that my...