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
© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag