Geodesic
The Maximal Number of Triangles of Maximal Perimeter Length Determined by a Finite Set
Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 49-50

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Suppose there are N not necessarily distinct points on a plane in such a position that any triangle (degenerate or non-degenerate) determined by these points has perimeter length at most 1. Denote by m the number of triangles with maximal perimeter length, (briefly, the number of maximal triangles), and put f(N) = max m where the maximum is taken over all permissible configurations. At the Colloquim on Graph Theory in Calgary, 1969, P. Erdös proposed the problem of determining f(N). He conjectured that the following construction gives the maximal number: place approximately half of the points at a point A and the others at B where AB = 1/2. The aim of this note is to prove this conjecture. 
Bollobás, Béla. The Maximal Number of Triangles of Maximal Perimeter Length Determined by a Finite Set. Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 49-50. doi: 10.4153/CMB-1970-009-9
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     year = {1970},
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     doi = {10.4153/CMB-1970-009-9},
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