Axiomatic Foundations of Projective Geometry

Igor Minevich

November 12, 2008

Projective geometry can be studied in many different ways, one of which is a strictly axiomatic approach. In fact, coordinates are never necessary in this approach, though they can be used to help prove (or verify) theorems. We introduce these axiomatic foundations, develop just enough projective geometry to taste its flavor, and discuss the implications of projective geometry for Euclidean space. Some attractive concepts projective geometry has to offer are abstractions to "points and lines at infinity," complete duality between points and lines, and its wealth of symmetry.