On maximal Euclidean sets avoiding certain distance configurations
Published online by Cambridge University Press: 24 October 2008
Extract
Let us say that a set points in a Euclidean space has property
(2) if no 2 points X, Y ∈ S have X Y > 1. Then an easy observation is the following:
The maximum area (Lebesgue measure) of a plane set S with property(2) is ¼π, attained only when S is (essentially) a disc.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 89 , Issue 1 , January 1981 , pp. 79 - 88
- Copyright
- Copyright © Cambridge Philosophical Society 1981
References
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