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Type: Artigo
Title: Six Mathematical Gems From The History Of Distance Geometry
Author: Liberti
Leo; Lavor
Abstract: This is a partial account of the fascinating history of distance geometry. We make no claim to completeness, but we do promise a dazzling display of beautiful, elementary mathematics. We prove Heron's formula, Cauchy's theorem on the rigidity of polyhedra, Cayley's generalization of Heron's formula to higher dimensions, Menger's characterization of abstract semimetric spaces, a result of Godel on metric spaces on the sphere, and Schoenberg's equivalence of distance and positive semidefinite matrices, which is at the basis of multidimensional scaling.
Subject: Euler's Conjecture
Cayley-menger Determinants
Multidimensional Scaling
Euclidean Distance Matrix
Editor: Wiley-Blackwell
Rights: fechado
Identifier DOI: 10.1111/itor.12170
Date Issue: 2016
Appears in Collections:Unicamp - Artigos e Outros Documentos

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