Projective Planes and Groups

Projective planes are geometrical structures that grew out of projective art, in which the 2-dimensional plane is extended so that any two lines will always intersect. In projective geometry, we follow rules that are quite different from the “normal” Euclidean geometry that most mathematicians work with. Instead, the leading players of projective geometry are lines and points – defined differently than their Euclidean counterparts – and the incidence relations between them. We will discuss projective planes through various mathematical “lenses”, use group theory to further study the properties of these structures, and reach some fascinating conclusions.