Constructing Hyperbolic Polygons in the Poincaré Disk

Author

Akram Zakaria SamweilFollow

Date of Award

8-2023

Document Type

Thesis

Degree Name

Master of Arts in Mathematics

Department

Mathematics

First Reader/Committee Chair

Meyer Jeffrey

Abstract

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 D_c, 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.

Recommended Citation

Samweil, Akram Zakaria, "Constructing Hyperbolic Polygons in the Poincaré Disk" (2023). Electronic Theses, Projects, and Dissertations. 1763.
https://scholarworks.lib.csusb.edu/etd/1763