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BibTeX entry
@Article{Johannesen:2006:BNP,
author = "Ivar G. Johannesen",
title = "The {Buffon Needle Problem} Revisited in a Pedagogical
Perspective",
journal = j-MATHEMATICA-J,
volume = "11",
number = "2",
pages = "284--299",
month = "????",
year = "2006",
CODEN = "????",
ISSN = "1047-5974 (print), 1097-1610 (electronic)",
ISSN-L = "1047-5974",
bibdate = "Sat Nov 6 13:34:51 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/mathematicaj.bib;
http://www.mathematica-journal.com/issue/v11i2/",
URL = "http://www.mathematica-journal.com/issue/v11i2/contents/Johannesen/Johannesen.pdf;
http://www.mathematica-journal.com/issue/v11i2/Johannesen.html",
abstract = "Imagine a floor marked with many equally spaced
parallel lines and a thin stick whose length exactly
equals the distance {$ L = 1 $} between the lines. If
we throw the stick on the floor, the stick may or may
not cross one of the lines. The probability for a hit
involves $ \pi $. This is surprising since there are no
circles involved; on the contrary, there are only
straight lines. If we repeat the experiment many times
and keep track of the hits, we can get an estimate of
the irrational number p. (We also consider sticks of
length {$ L > 1 $}.)\par The problem can easily be done
as an exercise in a first calculus course, where the
students are challenged to consider concepts such as
probability, definite integration, symmetry, and
inverse trigonometric functions. The solution to this
problem therefore gives many applications in a variety
of fields in calculus.\par
We continue by throwing regular polygons of different
sizes, increasing the number of edges, and at last
reach the ultimate goal of throwing circular objects.
This article illustrates the process of throwing
sticks, polygons, and circles analytically and
graphically, and how to carry out calculations for
different $n$-gons. The result always involves the
number $ \pi $, except when the circle is introduced!
We also show the circle result as a limiting value as
$n$ increases to infinity.",
acknowledgement = ack-nhfb,
journal-URL = "http://www.mathematica-journal.com/",
remark = "Proceedings of the Eighth International Mathematica
Symposium (Avignon, France, June 19 -23, 2006).",
}
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