Buffon's Needle Problem

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A Problem in Geometric Probability Buffons
Needle Problem
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The Plan

• Introduction to problem
• Some simple ideas from probability
• Set up the problem
• Find solution
• An approximation
• Generalization (solution known)
• Other generalizations ( solutions known?)

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Buffon's Needle ProblemStated in 1733 solution
published 1777by Geroges Louis Leclerc, Comte de
Buffon (1707-1788)
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(No Transcript)
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The Set Up
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The Solution!
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Polyá, George (1887, 1985) a good teacher
should understand and impress on his students the
view that no problem whatever is completely
exhausted. How to Solve It. Princeton Princeton
University Press. 1945.
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Something different
Let L1 and D4, then we have
Simulation
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Generalizations
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E
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Other Generalizations
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Any Uses?
Counting white blood cells!
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MATLAB CODE function pbuffon(L,D,n) cnt0 for
i1n xrand(pi/2) yrandD if y lt
(Lsin(x)) cntcnt1 end end pcnt/n
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OUTPUT EDUpi

ans3.14159265 EDU buffon(1,4,100)
ans2.9412 EDU buffon(1,4,1000) ans
2.8409 EDU buffon(1,4,3000) ans
3.1646 EDU buffon(1,4,10000) ans
3.1586 EDU buffon(1,4,100000) ans
3.1342