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Spherical tetrahedra with rational volume, and spherical Pythagorean triples


Authors: Alexander Kolpakov and Sinai Robins
Journal: Math. Comp. 89 (2020), 2031-2046
MSC (2010): Primary 51F15, 11H06
DOI: https://doi.org/10.1090/mcom/3496
Published electronically: December 17, 2019
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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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Additional Information

Alexander Kolpakov
Affiliation: Institut de Mathématiques, Université de Neuchâtel, Suisse/Switzerland
Email: kolpakov.alexander@gmail.com

Sinai Robins
Affiliation: Departamento de ciência da computação, Instituto de Matemática e Estatistica, Universidade de São Paulo, Brasil/Brazil
Email: sinai.robins@gmail.com

DOI: https://doi.org/10.1090/mcom/3496
Received by editor(s): November 15, 2018
Received by editor(s) in revised form: October 5, 2019
Published electronically: December 17, 2019
Additional Notes: The first author was supported by the Swiss National Science Foundation - SNSF project no. PP00P2-170560
The second author was supported by the São Paulo Research Foundation - FAPESP project no. 15/10323-7
Article copyright: © Copyright 2019 Alexander Kolpakov and Sinai Robins