Spherical tetrahedra with rational volume, and spherical Pythagorean triples

Kolpakov, Alexander; Robins, Sinai

doi:10.1090/mcom/3496

Spherical tetrahedra with rational volume, and spherical Pythagorean triples
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by Alexander Kolpakov and Sinai Robins HTML | PDF

Math. Comp. 89 (2020), 2031-2046

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.

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