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

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

2007-10-03

arxiv.org/abs/0710.0708v1

Mathematics

Number Theory

8 pages, 3 figures, continuation of previous work

Scientific paper

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 $\{0,1,2,...,n\}^3$ (A 102698) is given and the asymptotic behavior of this sequence is analyzed.

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