%0 Journal Article
%T On the ErdÖs Distance Conjecture in  Geometry
%A Amir Jafari
%A Amin Najafi Amin
%J Open Journal of Discrete Mathematics
%P 109-160
%@ 2161-7643
%D 2016
%I Scientific Research Publishing
%R 10.4236/ojdm.2016.63012
%X Erd<span style=\"font-family:Verdana, Helvetica, Arial;line-height:18px;white-space:normal;background-color:#FFFFFF;\">&amp;#214;</span>s 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¡Üi¡Ün-1 ) there is a distance determined by the points that occur exactly i times. So far some examples have been discovered for 2¡Ün¡Ü8 [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.
%K Erd&amp
%K #214
%K s Distance Problem
%K General Position
%K Graph Pattern
%K Distance Distribution
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=67516