✦ LIBER ✦

Another six-coloring of the plane

✍ Scribed by Ilya Hoffman; Alexander Soifer

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 92 KB
Volume: 150
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(95)00210-n

No coin nor oath required. For personal study only.

✦ Synopsis

A six-coloring of the Euclidean plane is constructed such that the distance 1 is not realized by any color except one, which does not realize the distance x/2 -1.

A 44-year-old problem due to Edward Nelson asks to find the chromatic number x(E 2) of the plane, i.e. the minimal number of colors that are required for coloring the plane so that no two points, a unit distance apart, lie on the same color. (For a history of the problem we refer the reader to .)

It has been known, since 1950, that 4 ~< z(E 2) ~< 7.

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