00_BuffonsNeedle

00_BuffonsNeedle - INDIANA UNIVERSITY DEPARTMENT OF PHYSICS...

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INDIANA UNIVERSITY DEPARTMENT OF PHYSICS P309: INTERMEDIATE PHYSICS LABORATORY Introductory Laboratory 0: Buffon's Needle Introduction:  In geometry, the circumference of a circle divided by its diameter is a fundamental constant, denoted by the symbol  π . Curiously, this number has no simple form. Expressed as a decimal, the digits of  π, π  = 3.141592653589793238462643383279502884197169399375105820974944. .. continue forever without settling into a regular pattern. This mysterious contrast between the simple geometric explanation of the value of  π , and the complexity of the numerical value has inspired books, movies, and even cults. Because no simple mathematical form exists for  π , we must rely on methods which are able to to calculate  π iteratively where the approximation to its value becomes better and better with each iteration.  The first such estimate was made by Archimedes roughly 200 years BC by calculating the circumference of polygons which fit just inside and just outside of a circle. Currently, the world's best estimate of  π contains 1.24 trillion decimal places. In this introductory lab we will explore an experimental method to calculate  π introduced by the French naturalist Georges Buffon in 1733. Method:  Buffon's method for estimating the value of  π relies on the following observation. Suppose you mark a surface with parallel lines separated by a distance   d . Now imagine throwing a straight object (a needle, or a
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00_BuffonsNeedle - INDIANA UNIVERSITY DEPARTMENT OF PHYSICS...

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