Vol. 99, No. 1, 1982

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Projective colorings

Alfred Washington Hales and Ernst Gabor Straus

Vol. 99 (1982), No. 1, 31–43
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
Authors
Alfred Washington Hales
Ernst Gabor Straus