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Date of Award


Document Type

Restricted Thesis: Campus only access

Degree Name

Master of Arts in Mathematics



First Reader/Committee Chair

Meyer Jeffrey


The Poincaré Disk plays a significant role in non-Euclidean geometry. Inverting points, segments, or polygons through a circle provides us with a deep vision of the link between Euclidean and non-Euclidean geometry; especially when we try to prove lemmas, constructions, or conjectures. All points inside a circle, c, represent a Poincaré Disk denoted Dc, and all "lines" in a Poincaré Disk are d-lines, which are circles orthogonal to the circle's boundary. The question that motivated my research is: how can we use the properties of the disk, its boundary, and its d-lines to construct hyperbolic polygons? We will construct center-symmetric, hyperbolic polygons in the Poincaré Disk using Euclidean and non-Euclidean geometry and trigonometry tools.