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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 328.05018

**Autor: ** Erdös, Paul; Purdy, George

**Title: ** Some extremal problems in geometry. III. (In English)

**Source: ** Proc. 6th southeast. Conf. Comb., Graph Theor., Comput.; Boca Raton 1975, 291-308 (1975).

**Review: ** [For the entire collection see Zbl 313.00004.]

In Part I, and II [both authors, J. combinat. Theory Ser. A 10, 246-252 (1971; Zbl 219.05006) and second author, Discrete Math. 7, 305-315 (1974; Zbl 283.05008)] the authors discuss the maximum number of times f^{a}_{k}(n) that the same non-zero area can occur among the triangles \Delta X_{i}X_{j}X_{l}, 1 \leq i < j < \ell \leq n, where the maximum is again taken over all choices for X_{1}, ... ,X_{n} in E_{k}. In this report they discuss the maximum number f^{i}_{k}(n) of isosceles triangles that can occur (congruent or not), the maximum number f^{e}_{k}(n) of equilateral triangles that can occur, the maximum number f^{c}_{k}(n) of pairwise congruent triangles, and the maximum number f^{s}_{k}(n) of pairwise similar triangles that can occur. All of these problems were posed at the end of Part I.

**Classif.: ** * 05B25 Finite geometries (combinatorics)

51M99 Real and complex geometry

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