Zong C. Strange Phenomena in Convex and Discrete Geometry

New York: Spriger, 1996. — 166 p.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.Borsuk’s Problem
Finite Packing Problems
The Venkov-McMullen Theorem and Stein’s Phenomenon
Local Packing Phenomena
Category Phenomena
The Busemann-Petty Problem
Dvoretzky’s Theorem