Results and Problems in Combinatorial Geometry

by Vladimir G. Boltyansky, Israel Gohberg, A. Harris (Translator)

In this short book, the authors discuss three types of problems from combinatorial geometry: Borsuk's partition problem, covering convex bodies by smaller homothetic bodies, and the illumination problem. They show how closely related these problems are to each other. The presentation is elementary, with no more than high-school mathematics and an interest in geometry required to follow the arguments. Most of the discussion is restricted to two- and three-dimensional Euclidean space, though sometimes more general results and problems are given. Thus even the mathematically unsophisticated reader can grasp some of the results of a branch of twentieth-century mathematics that has applications in such disciplines as mathematical programming, operations research and theoretical computer science. At the end of the book the authors have collected together a set of unsolved and partially solved problems that a sixth-form student should be able to understand and even attempt to solve.

120 pages, Paperback

First published October 10, 1985

About the author

Vladimir Grigorevich Boltyansky (Russian: Влади́мир Григо́рьевич Болтя́нский ), also transliterated as Boltyanski, Boltyanskii, or Boltjansky, is a Soviet and Russian mathematician, educator and author of popular mathematical books and articles. He is best known for his books on topology, combinatorial geometry and Hilbert's third problem.
https://en.wikipedia.org/wiki/Vladimi...