Odd Distances in Colourings of the Plane

We prove that every finite colouring of the plane contains a monochromatic pair of points at an odd distance from each other.

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Bibliographic Details
Published inGeometric and functional analysis Vol. 34; no. 1; pp. 19 - 31
Main Author Davies, James
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.02.2024
Springer Nature B.V
Subjects
Analysis
Coloring
Mathematics
Mathematics and Statistics
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Summary:We prove that every finite colouring of the plane contains a monochromatic pair of points at an odd distance from each other.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:1016-443X
1420-8970
DOI:10.1007/s00039-024-00659-w