  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.
