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Line 6: :Suppose we have a [[floor]] made of [[Parallel (geometry)\|parallel]] strips of [[wood]], each the same width, and we drop a [[Sewing needle\|needle]] onto the floor. What is the [[probability]] that the needle will lie across a line between two strips? Buffon's needle was the earliest problem in [[geometric probability]] to be solved;<ref>{{Cite journal \|~~last~~last1=Seneta \|~~first~~first1=Eugene \|last2=Parshall \|first2=Karen Hunger \|last3=Jongmans \|first3=François \|date=2001 \|title=Nineteenth-Century Developments in Geometric Probability: J. J. Sylvester, M. W. Crofton, J.-É. Barbier, and J. Bertrand \|url=https://www.jstor.org/stable/41134124 \|journal=Archive for History of Exact Sciences \|volume=55 \|issue=6 \|pages=501–524 \|doi=10.1007/s004070100038 \|jstor=41134124 \|s2cid=124429237 \|issn=0003-9519}}</ref> it can be solved using [[integral geometry]]. The solution for the sought probability ''p'', in the case where the needle length ''ℓ'' is not greater than the width ''t'' of the strips, is :<math>p=\frac{2}{\pi} \cdot \frac\ell t.</math> Line 129: * {{cite journal\|last = Ramaley\|first = J. F.\|title = Buffon's Noodle Problem\|journal = The American Mathematical Monthly\|volume = 76\|issue = 8\|date=October 1969\|pages = 916–918\|doi = 10.2307/2317945\|jstor = 2317945\|publisher = Mathematical Association of America}} * {{cite book\|last = Mathai\|first = A. M.\|title = An Introduction to Geometrical Probability\|year = 1999\|publisher = Gordon & Breach\|location = Newark\|url = https://books.google.com/books?id=FV6XncZgfcwC \| isbn=978-90-5699-681-9 \|page=5}} * {{cite journal\| last = Dell\|first = Zachary\| author2 = Franklin, Scott V.\|title = The Buffon-Laplace needle problem in three dimensions\|journal = Journal of Statistical Mechanics: Theory and Experiment\|date=September 2009\| volume = 2009\| issue = 9\| pages = 010\| doi = 10.1088/1742-5468/2009/09/P09010\| bibcode = 2009JSMTE..09..010D\| s2cid=32470555 }} * Schroeder, L. (1974). "Buffon's needle problem: An exciting application of many mathematical concepts". ''Mathematics Teacher'', 67 (2), 183–6.

Buffon's needle problem: Difference between revisions