Geometric Tomography

A comprehensive, rigorous treatment of geometric tomography, with 66 unsolved problems, over 70 illustrations, and over 800 references.

Richard J. Gardner (Author)

9780521684934, Cambridge University Press

Paperback, published 19 June 2006

516 pages
23.4 x 15.6 x 2.9 cm, 0.79 kg

'… this book is a must for all those who are or plan to work on geometric tomography …' Acta Scientiarum Mathematicarum

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 edition includes numerous updates and improvements, with some 300 new references bringing the total to over 800.

Preface to the second edition
Preface
0. Background material
1. Parallel X-rays of planar convex bodies
2. Parallel X-rays in n dimensions
3. Projections and projection functions
4. Projection bodies and volume inequalities
5. Point X-rays
6. Chord functions and equichordal problems
7. Sections, section functions, and point X-rays
8. Intersection bodies and volume inequalities
9. Estimates from projection and section functions
Appendix A. Mixed volumes and dual mixed volumes
Appendix B. Inequalities
Appendix C. Integral transforms
References
Notation
Author index
Subject index.

Subject Areas: Geometry [PBM], Tomography [MMPJ]