Geometric Tomography

Richard J. Gardner - Collection Encyclopedia of Mathematics and its Applications

514 pages, parution le 19/06/2006 (2^eme édition)

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Résumé

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.

Over 70 illustrations
Comprehensive bibliography has over 800 references
Well-written and clear; the opening chapters are accessible to advanced undergraduates

Sommaire

Background material
Parallel X-rays of planar convex bodies
Parallel X-rays in n dimensions
Projections and projection functions
Projection bodies and volume inequalities
Point X-rays
Chord functions and equichordal problems
Sections, section functions, and point X-rays
Intersection bodies and volume inequalities
Estimates from projection and section functions
Mixed volumes and dual mixed volumes
Inequalities
Integral transforms

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Richard J. Gardner
Collection	Encyclopedia of Mathematics and its Applications
Parution	19/06/2006
Édition	2^eme édition
Nb. de pages	514
Format	15,5 x 23,5
Couverture	Broché
Poids	743g
Intérieur	Noir et Blanc
EAN13	9780521684934
ISBN13	978-0-521-68493-4