Distance geometry

Distance geometry is the branch of mathematics concerned with characterizing and studying sets of points based only on given values of the distances between pairs of points.^[1]^[2]^[3] More abstractly, it is the study of semimetric spaces and the isometric transformations between them. In this view, it can be considered as a subject within general topology.^[4]

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 positions) from the distances between them, such as in biology,^[4] sensor networks,^[5] surveying, navigation, cartography, and physics.

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