Author:
Zong, Chuanming.
Imprint:New York : Springer, 1996.
Descriptionx, 158 p. : ill. ; 24 cm.
Bibliography Note:Includes bibliographical references (p. [143]-153) and index.
Note:"Zong's slender volume offers a veritable funhouse of geometrical phenomena that defy common sense, each established in a few pages, and a good deal of it within the reach of upper-division undergraduates. For example, we meet the Larman-Rogers phenomenon: two 12-dimensional convex bodies, one with larger volume yet having smaller cross-sections in every direction! Elsewhere Zong surveys results concerning packings and coverings, and in his final chapter he gives an elementary proof of Dvoretzky's once unapproachably difficult theorem on the existence of nearly spherical cross-sections of centrally symmetric convex bodies. Thompson describes other phenomena connected with convex bodies and their relation to normed spaces (this Minkowski geometry has nothing to do with that of special relativity theory!) In Euclidean space, spheres do double duty, as loci of constant distance from a center point and as bodies of a given volume with smallest surface area. Delicate issues related to the divergence of these concepts in more general normed spaces form one of several major themes of this well-written and superbly illustrated book." - Choice Reviews, May 1997.
