Six mathematical gems from the history of distance geometry (Q2827761)

This paper deals with the history of distance geometry focusing on six important results which are each contained in a separate section. More precisely, as mentioned in the authors' abstract, the following theorems are presented: 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 Gödel on metric spaces on the sphere, and Schoenberg's equivalence of distance and positive semidefinite matrices, which is at the basis of multidimensional scaling.