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Geometric tomography / Richard J. Gardner

Author
Gardner, Richard J.
Published
Cambridge ; New York : Cambridge University Press, 2006.
Edition
2nd ed.
Physical Description
1 online resource (xxi, 492 pages) : illustrations
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Contents
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 -- App. A. Mixed volumes and dual mixed volumes -- App. B. Inequalities -- App. C. Integral transforms.
Summary
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.
Subject(s)
ISBN
9781461938323 (electronic bk.)
1461938325 (electronic bk.)
9781107341029 (electronic bk.)
1107341027 (electronic bk.)
9781107387560 (e-book)
1107387566 (e-book)
9781139883368 (e-book)
1139883364
0521866804
9780521866804
0521684935
9780521684934
Bibliography Note
Includes bibliographical references (pages 437-469) and indexes.
View MARC record | catkey: 43624939