Geometric Tomography (Encyclopedia of Mathematics and its Applications) by Richard J. Gardner

Encyclopedia of Mathematics and its Applications #58

by Richard J. Gardner

Geometric tomography deals with the retrieval of information about a geometric object from data concerning its projections (shadows) on planes or cross-sections by planes. It is a geometric relative of computerized tomography, which reconstructs an image from X-rays of a human patient. The subject overlaps with convex geometry and employs many tools from that area, including some formulas from integral geometry. It also has connections to discrete tomography, geometric probing in robotics and to stereology. This comprehensive study provides a rigorous treatment of the subject. Although primarily meant for researchers and graduate students in geometry and tomography, brief introductions, suitable for advanced undergraduates, are provided to the basic concepts. More than 70 illustrations are used to clarify the text. The book also presents 66 unsolved problems. Each chapter ends with extensive notes, historical remarks, and some biographies. This new edition includes numerous updates and improvements, with some 300 new references bringing the total to over 800.

Paperback

First published January 1, 2006

Reviews

[Nadav Har'El · Rating 5 out of 5]

My MSc research was in the subject of Geometric Tomography (more specifically, parallel X-rays of connected sets), and Richard Gardner's book was an invaluable reference book to me during my research, especially chapter 1 (Parallel X-rays of planar convex bodies) and 2 (Parallel X-rays in n dimensions).

But this book covers much more - everything that could be considered "Geometric Tomography". It assumes no prior knowledge of the subject, and then builds the entire theory of Geometric Tomography (to which Gardner has been one of the most important contributers), step by step, building on and referring to almost 550 journal articles and books.
Gardner's "Geometric Tomography" is an invaluable tool to anybody who is seriously interested in the subject of Geometric Tomography, and and must-have to any serious Mathematics library.