A characterization of all equilateral triangles in \Bbb Z³

2007/10/03 by Ray Chandler, Chandler, Ray, Eugen J. Ionaşcu +2
Mathematics · #11A67 #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematics and Applications #Number Theory (math.NT) #math.NT #msc:11A67

paper · pdf · doi:10.48550/arxiv.0710.0708

8 pages, 3 figures, continuation of previous work

arxiv created 2007/10/03 · openalex publication_date 2007/10/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 (A 102698) is given and the asymptotic behavior of this sequence is analyzed.

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