Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  534.52007
Autor:  Erdös, Paul; Füredi, Z.
Title:  The greatest angle among n points in the d-dimensional Euclidean space. (In English)
Source:  Ann. Discrete Math. 17, 275-283 (1983).
Review:  The main result of this paper is the construction of a set P in the Euclidean space Ed with no less than (1.15)d elements, such that all angles determined by the triplets in P are acute, thus settling a long standing conjecture. For their elegant proof, the authors use a combination of geometry and probability theory. Some related results are established, and a number of interesting open questions is presented to the reader.
Reviewer:  P.Mani
Classif.:  * 52A37 Other problems of combinatorial convexity
                   52A40 Geometric inequalities, etc. (convex geometry)
Keywords:  Erdös conjecture; strictly antipodal polytopes

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