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arXiv · 2504.04208

Many unit distances requires many directions

Gabriel Currier·József Solymosi
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Abstract

In this note, we show that in planar pointsets determining many unit distances, these unit distances must span many directions. Specifically, we show that a set of $n$ points can determine only $o(n^{4/3})$ unit distances from a set of at most $O(n^{1/3})$ directions.

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Gabriel Currier, József Solymosi. 2025-04-05. Many unit distances requires many directions. https://arxiv.org/abs/2504.04208

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