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Strange Phenomena in Convex and Discrete Geometry (Universitext) - Softcover

Zong, Chuanming

 
9780387947341: Strange Phenomena in Convex and Discrete Geometry (Universitext)

Inhaltsangabe

Convex and discrete geometry is one of the most intuitive subjects in mathematics. One can explain many of its problems, even the most difficult - such as the sphere-packing problem (what is the densest possible arrangement of spheres in an n-dimensional space?) and the Borsuk problem (is it possible to partition any bounded set in an n-dimensional space into n+1 subsets, each of which is strictly smaller in "extent" than the full set?) - in terms that a layman can understand; and one can reasonably make conjectures about their solutions with little training in mathematics.

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This book presents some of the most famous problems of convex and discrete geometry - such as Borsuk's problem (is it possible to partition any bounded set in an n-dimensional Euclidean space into n+1 subsets, each of which is strictly smaller in diameter than the full set?) and the finite sphere-packing problem (how can one arrange m nonoverlapping congruent spheres in an n-dimensional Euclidean space to minimize the volume or surface area of their convex hull?) - as well as their (at times astonishing) answers. Though covering some of the most recent developments in the field, the book is self-contained, and can be understood by any trained mathematician.

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