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Perspectives on the unit distance problem
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In the 1980s, using an interesting argument based on topology, Spencer, Szemeredi, and Trotter [SST] proved that U_{max}(n)\leq Cn^{4/3}. This bound has not been improved.
The maximum number of unit distances among n planar points is O(n^(4/3)).
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- https://arxiv.org/abs/2609.10791
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- https://web.archive.org/web/20260911141117/https://arxiv.org/abs/2609.10791
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- Nov 9, 2026FactsFacts fetcher · Facts looked up
- Sep 16, 2026Entered the graphEntered the graph; no copy stored