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.
Share and Cite:
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.