Rational Distances with Rational Angles

Details Rational Distances with Rational Angles Rational Distances with Rational Angles

2010-08-22

arxiv.org/abs/1008.3671v2

Mathematics

Combinatorics

12 pages; corrected typos, updated references; corrected results in Sections 3 and 4; added/updated statement of main results

Scientific paper

In 1946 Erd\H os asked for the maximum number of unit distances, $u(n)$, among $n$ points in the plane. He showed that $u(n)> n^{1+c/\log\log n}$ and conjectured that this was the true magnitude. The best known upper bound is $u(n)

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