A multidimensional Law of Sines

2002/11/17 by Igor Rivin, Rivin, Igor
Mathematics · Physics and Astronomy · #51F99 #52B11 #Advanced Mathematical Theories and Applications #FOS: Mathematics #General Mathematics (math.GM) #Geometric Analysis and Curvature Flows #Mathematics and Applications #Metric Geometry (math.MG) #math.GM #math.MG #msc:51F99 #msc:52B11

paper · pdf · doi:10.48550/arxiv.math/0211261

Name changed (from Theorem of Sines to Law of Sines. Some typos corrected; three dimensional identity improved (by M. Pashkevich of Novosibirsk)

openalex publication_date 2002/11/17 · arxiv created 2002/12/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend the Law of Sines to simplices in Euclidean spaces of any number of dimensions.

Related

• Some observations on the simplex
• Pythagorean Theorem, Law of Sines and Law of Cosines: alternative proofs via shape derivatives
• On the Theorem of the Three Perpendiculars
• Bürgi's "Kunstweg" - geometric approach
• Morley Trisectors and the Law of Sines with Reflections