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The Cube-A Window to Convex and Discrete Geometry (Hardcover)
Loot Price: R1,929
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The Cube-A Window to Convex and Discrete Geometry (Hardcover)
Series: Cambridge Tracts in Mathematics
Expected to ship within 12 - 17 working days
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This tract has two purposes: to show what is known about the
n-dimensional unit cubes and to demonstrate how Analysis, Algebra,
Combinatorics, Graph Theory, Hyperbolic Geometry, Number Theory,
can be applied to the study of them. The unit cubes, from any point
of view, are among the most important and fascinating objects in an
n-dimensional Euclidean space. However, our knowledge about them is
still quite limited and many basic problems remain unsolved. In
this Tract eight topics about the unit cubes are introduced: cross
sections, projections, inscribed simplices, triangulations, 0/1
polytopes, Minkowski's conjecture, Furtwangler's conjecture, and
Keller's conjecture. In particular the author demonstrates how deep
analysis like log concave measure and the Brascamp-Lieb inequality
can deal with the cross section problem, how Hyperbolic Geometry
helps with the triangulation problem, how group rings can deal with
Minkowski's conjecture and Furtwangler's conjecture, and how Graph
Theory handles Keller's conjecture.
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