Spherical Heron triangles and elliptic curves
Number Theory
2021-12-15 v1 Metric Geometry
Abstract
We define spherical Heron triangles (spherical triangles with "rational" side-lengths and angles) and parametrize them via rational points of certain families of elliptic curves. We show that the congruent number problem has infinitely many solutions for most areas in the spherical setting and we find a spherical Heron triangle with rational medians. We also explore the question of spherical triangles with a single rational median or a single a rational area bisector (median splitting the triangle in half), and discuss various problems involving isosceles spherical triangles.
Cite
@article{arxiv.2112.07058,
title = {Spherical Heron triangles and elliptic curves},
author = {Tinghao Huang and Matilde Lalín and Olivier Mila},
journal= {arXiv preprint arXiv:2112.07058},
year = {2021}
}
Comments
22 pages, 2 figures