Mathematics and Statistics Colloquium

Dr. Eugen Ionascu

The Story of a Parametrization

Thursday, October 18, 2007 at 12:30 P.M.

Howard Hall 102

Refreshments will be provided

Abstract: Equilateral triangles having vertices with integer coordinates exist only in spaces of dimension greater than three, i.e., in Z^3, Z^4,... but not in Z^2. How many such triangles are there in a bounded region like the cube {0,1,2,...,n}^3?  We denote this sequence by ET(n). We have a good idea about the growth of this sequence. For instance, ET(2007) is approximately 5.277041119 (10^16) and in general E(n) is about (n+1)^5.08. These calculations were based on a parametrization of all triangles of this type. We review some of the developments related to this parametrization and present the Maple code that implements the calculation of $E(n)$.