Breaking the 3/2 barrier for unit distances in three dimensions

06/16/2017

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by   Joshua Zahl, et al.

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We prove that every set of n points in R^3 spans O(n^295/197+ϵ) unit distances. This is an improvement over the previous bound of O(n^3/2). A key ingredient in the proof is a new result for cutting circles in R^3 into pseudo-segments.