Re: [MATH] Random chords

[Sonnet Nguyen <Sonnet.Nguyen@fuw.edu.pl>]

Dear lovers of math,
Your problem is very classical and interesting for young students.
Frequently, in the course of Theory of Probability, 
students have to solve similar problem:
For fixed length L = [a,b] (or more general n-box in R^{n}), and A,B
(respectively A_{1},B_{1} in x_{1}, ..., A_{n},B_{n} in x_{n} for R^{n}
case) are randomly choosed points from L.  What is the chance that
length of AB (volume, for R^{n} case) > s.
The solution is reduced to calculate a simple integral, For example in
R^{1},  this integral is follows
\frac{1}{b-a}\int_{(x,y)\in [a,b]\times [a,b] and |y-x|>s} |y-x| dx dy.

If we remind that S^{1}=[a,b]/relation, where relation is a=b, then your
problem is reduced to above problem.
For practical reason, you can calculate it by fixed one point and 
use probability "under condition" (i.e. simply, with wages) and 
solve it as "above method".

SN
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The beauty of beauty is in Math.  SN-1980
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On Sun, 15 Jun 1997, Tuan V Nguyen wrote:
> Hello Math friends,
> 
> 	I have a problem, which was brought up by one of my 
> colleagues in the mathematical hobby club. The problem is as 
> follows: 
> If a chord is selected randomly on a fixed circle, what is 
> the chance that its length is longer than the radius of the 
> circle?
> 	Any idea?