[The Mathematical Atlas] [Search][Subject Index][MathMap][Tour][Help!]
[MathMap Icon]
ABOUT: [Introduction][History][Related areas][Subfields]
POINTERS: [Texts][Software][Web links][Selected topics here]

52: Convex and discrete geometry


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.


Applications and related fields

[Schematic of subareas and related areas]


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

You can reach this page through http://www.math-atlas.org/welcome.html
Last modified 2000/01/29 by Dave Rusin. Mail: