On Sets of Distances of n Points

@article{Erds1946OnSO,
  title={On Sets of Distances of n Points},
  author={Paul Erd{\"o}s},
  journal={American Mathematical Monthly},
  year={1946},
  volume={53},
  pages={248-250}
}
  • P. Erdös
  • Published 1946
  • Mathematics
  • American Mathematical Monthly
1. The function f(n). Let [P. ] be the class of all planar subsets P. of n points and denote by f(n) the minimum number of different distances determined by its n points for P,, an element of { P. }. Clearly, f(3) = 1 (with the three points forming the vertices of an equilateral triangle) f(4) = 2, f(5) = 2. The following theorem establishes rough bounds for arbitrary n. Though I have sought to improve this result for many years, I have not been able to do so. 
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On Sets of Distances of N Points in Euclidean Space
Let [Pg)] he the clans of all subsets Pjlc, of the Ic dimensional space consisting of TZ distinct points and having diameter 1. Denote by g,Jn, T) the maximum number of times a given distance r canExpand
On sets of distances of 7t points, this MONTHLY
  • 1946
On a problem of Sidon, jour
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