Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  403.52006
Autor:  Erdös, Paul; Purdy, George
Title:  Some extremal problems in geometry. V. (In English)
Source:  Proc. 8th southeast. Conf. on Combinatorics, graph theory, and computing, Baton Rouge 1977, 569-578 (1977).
Review:  [For the entire collection see Zbl 396.00002.]
The authors continue their investigation of bounds for several functions occuring in problems of Combinatorial Geometry (for part IV, see Proc. 7th south-east. Conf. Comb., Graph Theory, Comput.; Baton Rouge 1976, 307-322 (1976; Zbl 345.52007). Their results concern the number of different volumes of simplices formed from n given points in a Euclidean space, the number of planes determined by n given points, and the number of triangles determined by n points in the plane. Examples: Given n points in E3, no three on a line, not all on a plane, there are at least cn3/4 distinct volumes of simplices formed from these points, where c is a constant. Then n vertices of polyhedron in E3 determine at least \binom{n-2}{2}+1 planes, provided n \geq 552.
Reviewer:  R.Schneider
Classif.:  * 52A37 Other problems of combinatorial convexity
Keywords:  simplices formed from n given points; number of different volumes of simplices; Euclidean space
Citations:  Zbl.396.00002; Zbl.345.52007

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