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arXiv · 1502.02816

Six mathematical gems from the history of Distance Geometry

Leo Liberti·Carlile Lavor
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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.

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Leo Liberti, Carlile Lavor. 2015-02-10. Six mathematical gems from the history of Distance Geometry. https://arxiv.org/abs/1502.02816

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