Spherical tetrahedra with rational volume, and spherical Pythagorean triples
Metric Geometry
2019-10-17 v5 Number Theory
Abstract
We study spherical tetrahedra with rational dihedral angles and rational volumes. Such tetrahedra occur in the Rational Simplex Conjecture by Cheeger and Simons, and we supply vast families, discovered by computational efforts, of positive examples that confirm this conjecture. As a by-product, we also obtain a classification of all spherical Pythagorean triples, previously found by Smith.
Keywords
Cite
@article{arxiv.1811.06598,
title = {Spherical tetrahedra with rational volume, and spherical Pythagorean triples},
author = {Alexander Kolpakov and Sinai Robins},
journal= {arXiv preprint arXiv:1811.06598},
year = {2019}
}
Comments
14 pages, 3 figures, 5 tables; to appear in Math. of Comp.; supplementary SageMath worksheets available at https://doi.org/10.7910/DVN/LJBNGO