Unit Distances in Three Dimensions
Unit Distances in Three Dimensions
We show that the number of unit distances determined by n points in ℝ 3 is O ( n 3/2 ), slightly improving the bound of Clarkson, Edelsbrunner, Guibas, Sharir and Welzl [5], established in 1990. The new proof uses the recently introduced polynomial partitioning technique of Guth and Katz …