Integral Geometry and Geometric Probability [Paperback]

Classic text on integral geometry now available in paperback in the Cambridge Mathematical Library.The standard reference in the field, now available in the Cambridge Mathematical Library. Developments in integral geometry have proved to be useful in several fields ranging from pure mathematics to technical and applied disciplines. This book is a systematic exposition of the theory and a compilation of the main results in the field. It can be used to complement courses on differential geometry, Lie groups or probability or differential geometry. It is ideal both as a reference and for those wishing to enter the field.The standard reference in the field, now available in the Cambridge Mathematical Library. Developments in integral geometry have proved to be useful in several fields ranging from pure mathematics to technical and applied disciplines. This book is a systematic exposition of the theory and a compilation of the main results in the field. It can be used to complement courses on differential geometry, Lie groups or probability or differential geometry. It is ideal both as a reference and for those wishing to enter the field.Integral geometry originated with problems on geometrical probability and convex bodies. Its later developments have proved to be useful in several fields ranging from pure mathematics (measure theory, continuous groups) to technical and applied disciplines (pattern recognition, stereology). The book is a systematic exposition of the theory and a compilation of the main results in the field. The volume can be used to complement courses on differential geometry, Lie groups, or probability or differential geometry. It is ideal both as a reference and for those wishing to enter the field.Part I. Integral Geometry in the Plane: 1. Convex sets in the plane; 2. Sets of points and Poisson processes in the plane; 3. Sets of lines in the plane; 4. Pairs of points and pairs of lines; 5. Sets of strips in the plane; 6. The group of motions in the pl?