Projective Rectangles: A New Kind of Incidence Structure
arXiv:2307.04079
Abstract
A projective rectangle is like a projective plane that has different lengths in two directions. We develop the basic theory of projective rectangles including incidence properties, projective subplanes, configuration counts, a partial Desargues's theorem, a construction from projective planes, and alternative formulations. In sequels we study harmonic conjugation and the graphs of lines and subplanes.
33 pp., 8 figures. V2: Major revisions, corrections, new title; 41 pp., 15 figures. V3: Rev. sects. 1 & 6; 40 pp., 15 figures