Spherical geometry and integrable systems

TL;DR

This paper demonstrates that the cosine law for spherical triangles and tetrahedra leads to integrable systems, showcasing their multidimensional consistency and dynamical properties.

Contribution

It establishes a novel connection between spherical geometry and integrable systems, providing a new perspective on geometric laws as integrable models.

Findings

Cosine law defines integrable systems in spherical geometry.

Systems exhibit multidimensional consistency.

Dynamical systems perspective confirmed.

Abstract

We prove that the cosine law for spherical triangles and spherical tetrahedra defines integrable systems, both in the sense of multidimensional consistency and in the sense of dynamical systems.