Results and Problems in Combinatorial Geometry by Vladimir G. Boltjansky (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review Discusses two types of problems: Borsuk’s partition problem and the illumination problem, and shows how closely related these problems are. — Book Description Book Description In this short book, the authors discuss three types of problems from combinatorial geometry.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐A beautiful small book containing three general geometric problems, which are shown to be intimately related. The discussion is entirely elementary, using only early high school level mathematics, but the book highlights deep connections between disparate fields and ends with difficult open problems.

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