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52: Convex and discrete geometry


Introduction

Convex and discrete geometry includes the study of convex subsets of Euclidean space. A wealth of famous results distinguishes this family of sets (e.g. Brouwer's fixed-point theorem, the isoperimetric problems). This classification also includes the study of polygons and polyhedra, and frequently overlaps discrete mathematics and group theory; through piece-wise linear manifolds, it intersects topology. This area also includes tilings and packings in Euclidean space.

History

Applications and related fields

[Schematic of subareas and related areas]

Subfields

Browse all (old) classifications for this area at the AMS.


Textbooks, reference works, and tutorials

Klee, Victor: "What is a convex set?", Amer. Math. Monthly 78 1971 616--631. MR44#3202

Miyazaki, Koji: "An adventure in multidimensional space. The art and geometry of polygons, polyhedra, and polytopes", John Wiley & Sons, Inc., New York, 1986. 112 pp. ISBN 0-471-81648-5 MR87m:00001

Tilings: There are two books by Grünbaum, Branko and Shephard, G. C. entitled "Tilings and patterns", both published by W. H. Freeman and Company, New York: the first (1987. 700 pp. ISBN 0-7167-1193-1) followed by one subtitled "An introduction" (1989. 446 pp. ISBN 0-7167-1998-3) (The two authors have a long history of collaboration in this area.)

Software and tables

LEDA can perform calculations with geometric and combinatorial objects.

Other web sites with this focus

Selected Topics at this site


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Last modified 2000/01/29 by Dave Rusin. Mail: