Projective colorings

Alfred Washington Hales and Ernst Gabor Straus

Vol. 99 (1982), No. 1, 31–43

DOI: 10.2140/pjm.1982.99.31

Abstract

All colorings of the points of (Desarguesian) projective planes in three colors so that no straight line contains points of all three colors are characterized in terms of the valuations of the field of coordinates. Generalizations to higher dimensions and applications to the Fundamental Theorem of Projective Geometry and the division of polygons into disjoint triangles of equal areas are given. We restrict our discussion to the Pappian (commutative coordinate field) case. For the general division ring case see [3].

Mathematical Subject Classification 2000

Primary: 51A30

Milestones

Received: 2 September 1980

Revised: 15 May 1981

Published: 1 March 1982