# Six mathematical gems from the history of Distance Geometry

arXiv: https://arxiv.org/abs/1502.02816 · HTML: https://mlsanity.com/paper/1502.02816/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Feb 2015.

## Built on by (most cited first, 1 of 1)

- [Mathematics with large language models as provers and verifiers](https://mlsanity.com/paper/2510.12829/) (2025)

## Abstract (arXiv)

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.