Geometric Tomography
Seiten
1995
Cambridge University Press (Verlag)
978-0-521-45126-0 (ISBN)
Cambridge University Press (Verlag)
978-0-521-45126-0 (ISBN)
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A research text which makes unsolved problems accessible to advanced undergraduates. It rigorously develops the new subject of geometric tomography, which deals with the retrieval of information about a geometric object from data concerning its projections on planes or cross-sections by planes.
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 computerised tomography, which reconstructs an image from X-rays of a human patient. It overlaps with convex geometry, and employs many tools from that area, including integral geometry. It also has connections to geometric probing in robotics and to stereology. The main text contains a rigorous treatment of the subject starting from basic concepts and moving up to the research frontier: 72 unsolved problems are stated. Each chapter ends with extensive notes, historical remarks, and some biographies. The bibliography comprises over 500 references. This comprehensive study will be invaluable to specialists in geometry and tomography; the opening chapters can also be read by advanced undergraduate students.
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 computerised tomography, which reconstructs an image from X-rays of a human patient. It overlaps with convex geometry, and employs many tools from that area, including integral geometry. It also has connections to geometric probing in robotics and to stereology. The main text contains a rigorous treatment of the subject starting from basic concepts and moving up to the research frontier: 72 unsolved problems are stated. Each chapter ends with extensive notes, historical remarks, and some biographies. The bibliography comprises over 500 references. This comprehensive study will be invaluable to specialists in geometry and tomography; the opening chapters can also be read by advanced undergraduate students.
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.
| Erscheint lt. Verlag | 29.9.1995 |
|---|---|
| Reihe/Serie | Encyclopedia of Mathematics and its Applications |
| Zusatzinfo | 7 Halftones, unspecified; 50 Line drawings, unspecified |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 162 x 240 mm |
| Gewicht | 752 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 0-521-45126-4 / 0521451264 |
| ISBN-13 | 978-0-521-45126-0 / 9780521451260 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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