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Geometric ProbabilityGeometric Probability

Herbert Solomon



CBMS-NSF Regional Conference Series in Applied Mathematics 28

Topics include: ways modern statistical procedures can yield estimates of pi more precisely than the original Buffon procedure traditionally used; the question of density and measure for random geometric elements that leave probability and expectation statements invariant under translation and rotation; the number of random line intersections in a plane and their angles of intersection; developments due to W. L. Stevens's ingenious solution for evaluating the probability that n random arcs of size a cover a unit circumference completely; the development of M. W. Crofton's mean value theorem and its applications in classical problems; and an interesting problem in geometrical probability presented by a karyograph.

Contents

Buffon Needle Problem, Extensions, and Estimation of pi; Density and Measure for Random Geometric Elements; Random Lines in the Plane and Applications; Covering a Circle Circumference and a Sphere Surface; Crofton's Theorem and Sylvester's Problem in Two and Three Dimensions; Random Chords in the Circle and the Sphere.

1978 / vi + 174 pages / Softcover / ISBN-13: 978-0-898710-25-0 / ISBN-10: 0-89871-025-1 /
List Price $71.00 / SIAM/CBMS Member Price $49.70 / Order Code CB28
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Banner art adapted from a figure by Hinke M. Osinga and Bernd Krauskopf (University of Auckland, NZ.)