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A Euclidean Ramsey theorem

✍ Scribed by M. Bóna

Publisher: Elsevier Science
Year: 1993
Tongue: English
Weight: 168 KB
Volume: 122
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)90308-g

No coin nor oath required. For personal study only.

✦ Synopsis

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 a 12.coloration of the space in which there is no copy of T with monochromatic vertices.

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