2000/03/01 by I. G. Korepanov, Korepanov, I. G.
Computer Science · Mathematics · Physics and Astronomy · #Computational Geometry and Mesh Generation #Digital Image Processing Techniques #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Lattice (hep-lat) #Mathematics and Applications #Metric Geometry (math.MG) #Quantum Algebra (math.QA) #gr-qc #hep-lat #math.MG #math.QA #nlin.SI
paper · pdf · doi:10.48550/arxiv.nlin/0003001
LaTeX, 2 pages. An addendum to solv-int/9911008
arxiv created 2000/03/01 · openalex publication_date 2000/03/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given five points in a three-dimensional euclidean space, one can consider five tetrahedra, using those points as vertices. We present a pentagon-like formula containing the product of three volumes of those tetrahedra in its l.h.s. and the product of the two remaining tetrahedron volumes in its r.h.s., as well as the derivative of the "discrete curvature" which arises when we slightly deform our euclidean space.