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Sphere Packings (Hardcover, 1999 ed.): John Talbot Sphere Packings (Hardcover, 1999 ed.)
John Talbot; Chuanming Zong
R2,065 R1,593 Discovery Miles 15 930 Save R472 (23%) Ships in 12 - 17 working days

Preliminary Text. Do not use. Sphere Packings is one of the most attractive and challenging subjects in mathematics. Almost 4 centuries ago, Kepler studied the densities of sphere packings and made his famous conjecture. In the course of centuries, many exciting results have been obtained, ingenious methods created, related challenging problems proposed, and many surprising connections with othe subjects found. Thus, though some of its original problems are still open, sphere packings has been developed into an important discipline. This book tries to give a full account of this fascinating subject, especially its local aspects, discrete aspects and its proof methods.

Sphere Packings (Paperback, Softcover reprint of the original 1st ed. 1999): John Talbot Sphere Packings (Paperback, Softcover reprint of the original 1st ed. 1999)
John Talbot; Chuanming Zong
R1,459 Discovery Miles 14 590 Ships in 10 - 15 working days

Sphere Packings is one of the most attractive and challenging subjects in mathematics. Almost 4 centuries ago, Kepler studied the densities of sphere packings and made his famous conjecture. In the course of centuries, many exciting results have been obtained, ingenious methods created, related challenging problems proposed, and many surprising connections with othe subjects found. Thus, though some of its original problems are still open, sphere packings has been developed into an important discipline. This book tries to give a full account of this fascinating subject, especially its local aspects, discrete aspects and its proof methods.

Strange Phenomena in Convex and Discrete Geometry (Paperback, Softcover reprint of the original 1st ed. 1996): Chuanming Zong Strange Phenomena in Convex and Discrete Geometry (Paperback, Softcover reprint of the original 1st ed. 1996)
Chuanming Zong
R1,433 Discovery Miles 14 330 Ships in 10 - 15 working days

Convex and discrete geometry is one of the most intuitive subjects in mathematics. One can explain many of its problems, even the most difficult - such as the sphere-packing problem (what is the densest possible arrangement of spheres in an n-dimensional space?) and the Borsuk problem (is it possible to partition any bounded set in an n-dimensional space into n+1 subsets, each of which is strictly smaller in "extent" than the full set?) - in terms that a layman can understand; and one can reasonably make conjectures about their solutions with little training in mathematics.

The Cube-A Window to Convex and Discrete Geometry (Hardcover): Chuanming Zong The Cube-A Window to Convex and Discrete Geometry (Hardcover)
Chuanming Zong
R3,067 Discovery Miles 30 670 Ships in 12 - 17 working days

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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