Variation of Buffon's Needle Problem - sci.math

Message from discussion Variation of Buffon's Needle Problem

Sjoerd Job

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More options Nov 2 2009, 5:29 pm

Newsgroups: sci.math

From: Sjoerd Job <sjoerd...@sjec.nl>

Date: 02 Nov 2009 17:29:04 GMT

Local: Mon, Nov 2 2009 5:29 pm

Subject: Re: Variation of Buffon's Needle Problem

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On 2009-11-02, AI <vcpan...@gmail.com> wrote:

> You may already know about Buffon's Needle Problem
> http://mathworld.wolfram.com/BuffonsNeedleProblem.html

> I am thinking about the following variation

> Find the probability that a needle of length "l" will land on a
> circle, given a floor with equally spaced Concentric circles at a
> distance "d" apart?

> Here is the drawing which I have made for my simulation
> http://i233.photobucket.com/albums/ee201/vcpandya/NeedleProblem.jpg

This is quite an interesting problem.

When considering an infinite plane, my guess is that the probability
would be the same as for the normal problem. After all, when the needle
lands far enough from the origin, the situation is quite similar to the
original problem.

I have run trials with l = d = 1, with the tip landing in [-k,k]^2, for
various options of k. The # of trials per k was 100000.

When k gets larger, the result turns out closer to 2/pi.

Kind regards,
Sjoerd Job

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