Editing Distance geometry (section)

'''Distance geometry''' is the  branch of mathematics concerned with [[characterization (mathematics)|characterizing]] and studying [[Set (mathematics)|sets]] of points based ''only'' on given values of the [[distance]]s between pairs of points.<ref name="positioning" /><ref name="siam" /><ref name="DGAbook" /> More abstractly, it is the study of [[semimetric space]]s and the [[Isometry|isometric transformations]] between them. In this view, it can be considered as a subject within [[general topology]].<ref name="crippen" />

Historically, the first result in distance geometry is [[Heron's formula]] in 1st century AD. The modern theory began in 19th century with work by [[Arthur Cayley]], followed by more extensive developments in the 20th century by [[Karl Menger]] and others.

Distance geometry problems arise whenever one needs to infer the shape of a configuration of points ([[relative position]]s) from the distances between them, such as in [[biology]],<ref name="crippen" /> [[sensor network]]s,<ref name="sensors" /> [[surveying]], [[navigation]], [[cartography]], and [[physics]].