98-19: On the Number of Equilateral Triangles in Euclidean Spaces I

DIMACS TR: 98-19

On the Number of Equilateral Triangles in Euclidean Spaces I

Authors: Bernardo M. Abrego and Silvia Fernandez-Merchant

ABSTRACT
The following problem was posed by Erd\H{o}s and Purdy: ``What is the maximum number of equilateral triangles determined by a set of $n$ points in ${\Bbb R}^{d}$?'' New bounds for this problem are obtained for dimensions 2, 4 and 5. In addition it is shown that for $d=2$ the maximum is attained by subsets of the regular triangle lattice.

Paper Available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-19.ps.gz

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