## 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

DIMACS Home Page