Date of Graduation
Spring 2018
Degree
Master of Science in Mathematics
Department
Mathematics
Committee Chair
Les Reid
Abstract
In this thesis, we investigate affine and projective geometries. An affine geometry is an incidence geometry where for every line and every point not incident to it, there is a unique line parallel to the given line. Affine geometry is a generalization of the Euclidean geometry studied in high school. A projective geometry is an incidence geometry where every pair of lines meet. We study basic properties of affine and projective planes and a number of methods of constructing them. We end by prov- ing the Bruck-Ryser Theorem on the non-existence of projective planes of certain orders.
Keywords
Affine Geometry, Projective Geometry, Latin Square, Ternary Ring, Perfect Difference Set, Bruck-Ryser Theorem
Subject Categories
Geometry and Topology
Copyright
© Abraham Pascoe
Recommended Citation
Pascoe, Abraham, "Affine and Projective Planes" (2018). MSU Graduate Theses. 3233.
https://bearworks.missouristate.edu/theses/3233
