English

A characterization of all equilateral triangles in \Bbb Z^3

Number Theory 2007-10-04 v1

Abstract

This paper is a continuation of previous work of the authors. We extend one of the theorems that gave a way to construct equilateral triangles whose vertices have integer coordinates to the general situation. An approximate extrapolation formula for the sequence ET(n) of all equilateral triangles with vertices in {0,1,2,...,n}3\{0,1,2,...,n\}^3 (A 102698) is given and the asymptotic behavior of this sequence is analyzed.

Keywords

Cite

@article{arxiv.0710.0708,
  title  = {A characterization of all equilateral triangles in \Bbb Z^3},
  author = {Ray Chandler and Eugen J. Ionascu},
  journal= {arXiv preprint arXiv:0710.0708},
  year   = {2007}
}

Comments

8 pages, 3 figures, continuation of previous work

R2 v1 2026-06-21T09:25:49.414Z