Some Lemmas to Hopefully Enable Search Methods to Find Short and Human Readable Proofs for Incidence Theorems of Projective Geometry

Abstract

Search methods provide short and human readable proofs, i.e. with few algebra, of most of the theorems of the Euclidean plane. They are less succesful and convincing for incidence theorems of projective geometry, which has received less attention up to now. This is due to the fact that basic notions, like angles and distances, which are relevant for Euclidean geometry, are no more relevant for projective geometry. This article suggests that search methods can also provide short and human readable proofs of incidence theorems of projective geometry with well chosen notions, rules or lemmas. This article proposes such lemmas, and show that they indeed permit to find by hand short proofs of some theorems of projective geometry.