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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