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  "body": "\n## Summary\n\nDistance geometry studies sets of points through the distances between them alone.\nIts central question asks when given distances between some pairs of points can be realized by actual points in a Euclidean space.\nTools include the [[Cayley–Menger determinant|KGC5CYDF53]], [[Euclidean distance matrices|1BCJ7A73KS]] and the theory of [[rigid frameworks|V5YS9BZX0N]].\nIt has applications to molecular shape, sensor networks and the design of structures.\n\n## Explanations\n\n### L1 human\n\nSuppose you know how far apart some cities are, but you have no map.\nDistance geometry asks whether such a map exists and whether it is unique.\nFor example, three distances $3$, $4$ and $5$ fit a right triangle in the plane.\nThe distances $1$, $1$ and $3$ fit nothing, because $3 \u003e 1 + 1$ breaks the [[triangle inequality|01M6CW9VM6]].\n",
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