Introduction to Geometric Probability [Paperback]

The basic ideas of the subject and the analogues with enumerative combinatorics are described and exploited.Elementary geometry in n-dimensional Euclidean space is a subject that, under the stimulus of computational geometry, is regaining its former position. This is the first textbook that addresses some fundamental problems of Euclidean geometry that have been solved over the last half-century. The authors, who have made significant contributions to the subject, have taken pains to keep the exposition elementary, making the relationship between it and combinatorics transparent. It should be required reading of anyone in mathematics or computer science who deals with the visual display of information.Elementary geometry in n-dimensional Euclidean space is a subject that, under the stimulus of computational geometry, is regaining its former position. This is the first textbook that addresses some fundamental problems of Euclidean geometry that have been solved over the last half-century. The authors, who have made significant contributions to the subject, have taken pains to keep the exposition elementary, making the relationship between it and combinatorics transparent. It should be required reading of anyone in mathematics or computer science who deals with the visual display of information.Here is the first modern introduction to geometric probability, also known as integral geometry, presented at an elementary level, requiring little more than first-year graduate mathematics. Klein and Rota present the theory of intrinsic volumes due to Hadwiger, McMullen, Santaló and others, along with a complete and elementary proof of Hadwiger's characterization theorem of invariant measures in Euclidean n-space. They develop the theory of the Euler characteristic from an integral-geometric point of view. The authors then prove the fundamental theorem of integral geometry, namely, the kinematic formula. Finally, the analogies between invariant measures on polyconvex lS(