In this note we shall prove a geometric Ramsey theorem. Let T be a triangle with angles 30, 60 and 90 degrees, and with hypotenus of unit length. Then the theorem says that if one threecolors the 3-space, then there is always a copy of T with monochromatic vertices. We shall also show that there is
β¦ LIBER β¦
A Euclidean Ramsey Problem
β Scribed by Exoo
- Publisher
- Springer
- Year
- 2003
- Tongue
- English
- Weight
- 55 KB
- Volume
- 29
- Category
- Article
- ISSN
- 0179-5376
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## Abstract Let us call a finite subset __X__ of a Euclidean __m__βspace E^m^ __Ramsey__ if for any positive integer __r__ there is an integer __n__ = __n__(__X;r__) such that in any partition of E^n^ into __r__ classes __C__~1~,β¦, __C~r~__, some __C~i~__ contains a set __X__' which is the image of
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