Six mathematical gems from the history of Distance Geometry

Por • 29 abr, 2015 • Sección: Educacion

Leo Liberti, Carlile 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 semi-metric spaces, a result of Goedel on metric spaces on the sphere, and Schoenberg’s equivalence of distance and positive semidefinite matrices, which is at the basis of Multidimensional Scaling.

arXiv:1502.02816v1 [math.HO]

History and Overview (math.HO); Combinatorics (math.CO); Metric Geometry (math.MG); Optimization and Control (math.OC)

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