000 02905nam a22003738i 4500
001 CR9781107341029
003 UkCbUP
005 20200124160238.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 130225s2006||||enk o ||1 0|eng|d
020 _a9781107341029 (ebook)
020 _z9780521866804 (hardback)
020 _z9780521684934 (paperback)
040 _aUkCbUP
_beng
_erda
_cUkCbUP
050 0 0 _aQA639.5
_b.G37 2006
082 0 0 _a516.3/62
_222
100 1 _aGardner, Richard J.,
_eauthor.
245 1 0 _aGeometric tomography /
_cRichard J. Gardner.
250 _aSecond edition.
264 1 _aCambridge :
_bCambridge University Press,
_c2006.
300 _a1 online resource (xxi, 492 pages) :
_bdigital, PDF file(s).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aEncyclopedia of mathematics and its applications ;
_vvolume 58
500 _aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 0 _g0.
_tBackground material --
_g1.
_tParallel x-rays of planar convex bodies --
_g2.
_tParallel x-rays in n dimensions --
_g3.
_tProjections and projection functions --
_g4.
_tProjection bodies and volume inequalities --
_g5.
_tPoint x-rays --
_g6.
_tChord functions and equichordal problems --
_g7.
_tSections, section functions, and point x-rays --
_g8.
_tIntersection bodies and volume inequalities --
_g9.
_tEstimates from projection and section functions --
_gApp. A.
_tMixed volumes and dual mixed volumes --
_gApp. B.
_tInequalities --
_gApp. C.
_tIntegral transforms.
520 _aGeometric 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.
650 0 _aGeometric tomography.
776 0 8 _iPrint version:
_z9780521866804
830 0 _aEncyclopedia of mathematics and its applications ;
_vv. 58.
856 4 0 _uhttps://doi.org/10.1017/CBO9781107341029
999 _c518285
_d518283