#### Abstract

Finite projective planes are finite incidence structures which generalize the concept of the real projective plane. In this paper, we consider structures of points embedded in these planes. In particular, we investigate pentagons in general position, meaning no three vertices are colinear. We are interested in properties of these pentagons that are preserved by collineation of the plane, and so can be conceived as properties of the equivalence class of polygons up to collineation as a whole. Amongst these are the symmetries of a pentagon and the periodicity of the pentagon under the *pentagram map*, and a generalization of the concepts of rotational and reflective symmetry. We are also interested in counting exactly how many such equivalence classes of pentagons exist on a given projective plane.

#### Advisor

Kelvey, Robert

#### Department

Mathematics

#### Recommended Citation

Hosler, Maxwell, "Counting The Moduli Space Of Pentagons On Finite Projective Planes" (2022). *Senior Independent Study Theses.* Paper 9850.

https://openworks.wooster.edu/independentstudy/9850

#### Disciplines

Algebra | Discrete Mathematics and Combinatorics | Other Mathematics

#### Keywords

mathematics, geometry, projective geometry, abstract algebra, algebra, finite fields

#### Publication Date

2022

#### Degree Granted

Bachelor of Arts

#### Document Type

Senior Independent Study Thesis Exemplar

#### Included in

Algebra Commons, Discrete Mathematics and Combinatorics Commons, Other Mathematics Commons

© Copyright 2022 Maxwell Hosler