國立虎尾科技大學 |

The cube : = a window to convex and discrete geometry /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	The cube :/ Chuanming Zong.
其他題名:	a window to convex and discrete geometry /
其他題名:	The Cube-A Window to Convex & Discrete Geometry
作者:	Zong, Chuanming,
面頁冊數:	1 online resource (x, 174 pages) :digital, PDF file(s). :
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Discrete geometry. -
電子資源:	https://doi.org/10.1017/CBO9780511543173
ISBN:	9780511543173 (ebook)

The cube : = a window to convex and discrete geometry /
Zong, Chuanming,

The cube :a window to convex and discrete geometry /The Cube-A Window to Convex & Discrete GeometryChuanming Zong. - 1 online resource (x, 174 pages) :digital, PDF file(s). - Cambridge tracts in mathematics ;168. - Cambridge tracts in mathematics ;203..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Basic notation -- Cross sections -- Projections -- Inscribed simplices -- Triangulations -- 0/1 polytopes -- Minkowski's conjecture -- Furtwangler's conjecture -- Keller's conjecture.

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.

ISBN: 9780511543173 (ebook)Subjects--Topical Terms:

672137
Discrete geometry.

LC Class. No.: QA639.5 / .Z64 2006

Dewey Class. No.: 516.08

The cube : = a window to convex and discrete geometry /
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505 0 $a Basic notation -- Cross sections -- Projections -- Inscribed simplices -- Triangulations -- 0/1 polytopes -- Minkowski's conjecture -- Furtwangler's conjecture -- Keller's conjecture.
520 $a 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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