Reflections and Their Images
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This paper investigates the applications of linear algebra in the field of projective geometry, using Coxeter’s “Projective Geometry” as a source material. It examines the relationship between reflections in Euclidean Geometry as rigid symmetries and harmonic homologies, period two functions in the projective plane. Of particular interest is the ways in which a reflection in a plane can be written as a linear transformation called T. From here, a method for finding the image of T called T’ is found using a projection. Finally, a method is developed by which one can take a harmonic homology and show that it is the image of a family of reflections.
Franklin and Marshall College Archives, Undergraduate Honors Thesis 2013
- F&M Theses Collection