Alexander Ryba, Queens College, City University of New York

Abstract

A well known example of an incidence theorem is Pappus' Hexagon Theorem that: If the six vertices of a hexagon lie alternately on two straight lines, then the three intersection points of opposite sides are collinear. We shall consider a simple computer program that outputs incidence theorems of a similar nature. Some of its theorems are easily understood in terms of standard human geometrical concepts, but others are decidedly strange. However, all of its proposed theorems are undoubtedly true (although this particular program does not find a proof) and more importantly are theorems rather than trivialities in the sense that we feel they do require some sort of a proof.