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.
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Discusses two types of problems: Borsuk's partition problem and the illumination problem, and shows how closely related these problems are. -- Book Description
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Text: English, Russian (translation)
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3
books
cite this book:
- The Contest Problem Book V: American High School Mathematics Examinations (AHSME) / American Invitational Mathematics Examinations (AIME) 1983-1988 (Anneli Lax New Mathematical Library) by George Berzsenyi in Back Matter
- The Gohberg Anniversary Collection Vol 1: The Calgary Conference and Matrix Theory Papers (Operator Theory: Advances and Applications v40) (v. 1) by Seymour Goldberg on page 84
- Combinatorial Geometry by J?nos Pach in Back Matter
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