The volume formulas for a spherical tetrahedron
Jun Murakami
TL;DR
This paper presents two explicit formulas for calculating the volume of a spherical tetrahedron in a 3D space with constant positive curvature, using dihedral angles and edge lengths.
Contribution
It introduces two new concrete formulas for the volume of spherical tetrahedra, one based on dihedral angles and another on edge lengths.
Findings
Formulas applicable to arbitrary spherical tetrahedra.
Explicit expressions in terms of dihedral angles.
Explicit expressions in terms of edge lengths.
Abstract
The present paper gives two concrete formulas for the volume of an arbitrary spherical tetrahedron, which is in a 3-dimensional spherical space of constant curvature +1. One formula is given in terms of dihedral angles, and another one is given in terms of edge lengths.
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Taxonomy
TopicsGeometric and Algebraic Topology · Computational Geometry and Mesh Generation · Mathematics and Applications