Unit Distance Problems

2012/09/28 by Oberlin, Daniel, Oberlin, Richard
#11B30 #28E99 #42B10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1209.6537

Abstract

We study some discrete and continuous variants of the following problem of Erdos: given a finite subset P of R² or R³, what is the maximum number of pairs (p₁,p₂) with p₁,p₂ in P and |p₁ -p₂ |=1?

Related

• On the Number of Discrete Chains
• Unit and distinct distances in typical norms
• On some non-rigid unit distance patterns
• Erdős's unit distance problem and rigidity
• Almost sharp bounds on the number of discrete chains in the plane