Unit Distances in Three Dimensions

Details Unit Distances in Three Dimensions Unit Distances in Three Dimensions

Publishing date

2011-07-06

URL

arxiv.org/abs/1107.1077v1

Science

Mathematics

Field

Combinatorics

Additional info

13 pages

Type

Scientific paper

Abstract

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 et al. established in 1990. The new proof uses the recently introduced polynomial partitioning technique of Guth and Katz [arXiv:1011.4105]. While this paper was still in a draft stage, a similar proof of our main result was posted to the arXiv by Joshua Zahl [arXiv:1104.4987].

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