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Unit distance problems
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 137, Number 1, February 2015
- pp. 251-270
- 10.1353/ajm.2015.0004
- Article
- Additional Information
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We study some discrete and continuous variants of the following problem of
Erd\H os: given a finite subset $P$ of ${\Bbb R}^2$ or ${\Bbb R}^3$, what
is the maximum number of pairs $(p_1,p_2)$ with $p_1,p_2\in P$ and $|p_1
-p_2|=1$?