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**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 E_{d} 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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