Geometric tomography

by Richard J. Gardner

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. In part, it is a geometric relative of computerized tomography, which reconstructs an image from X-rays of a human patient. Geometric tomography overlaps with convex geometry and employs many tools from that area, including some formulas from integral geometry. It also has connections to geometric probing in robotics and to stereology. The main text of this book contains a rigorous treatment of the subject and supplies background for the 72 unsolved problems stated. Brief introductions, suitable for advanced undergraduates, are provided to the basic concepts required, and many figures are included. Each chapter ends with extensive notes, including historical remarks and some biographies, and the bibliography comprises over 500 references.