OJDM  Vol.6 No.3 , July 2016
On the ErdÖs Distance Conjecture in Geometry
Abstract: ErdÖs asks if it is possible to have n points in general position in the plane (no three on a line or four on a circle) such that for every i (1≤i≤n-1 ) there is a distance determined by the points that occur exactly i times. So far some examples have been discovered for 2≤n≤8 [1] [2]. A solution for the 8 point is provided by I. Palasti [3]. Here two other possible solutions for the 8 point case as well as all possible answers to 4 - 7 point cases are provided and finally a brief discussion on the generalization of the problem to higher dimensions is given.
Cite this paper: Jafari, A. and Amin, A. (2016) On the ErdÖs Distance Conjecture in Geometry. Open Journal of Discrete Mathematics, 6, 109-160. doi: 10.4236/ojdm.2016.63012.

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