## 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 fak(n) that the same non-zero area can occur among the triangles \Delta XiXjXl, 1 \leq i < j < \ell \leq n, where the maximum is again taken over all choices for X1, ... ,Xn in Ek. In this report they discuss the maximum number fik(n) of isosceles triangles that can occur (congruent or not), the maximum number fek(n) of equilateral triangles that can occur, the maximum number fck(n) of pairwise congruent triangles, and the maximum number fsk(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

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag