Euclidean and non-Euclidean geometry

Prerequisites: Only the courses that are common requirements for MAT292.

Description: Euclidean geometry, which is the "regular" intuitive geometry that we think about, is based on several postulates and axioms. One of these is the parallel postulate, best known today in the form of "through every point away from a line passes exactly one line that is parallel to the original". In the 1800s, other geometries were developed that were not built upon the parallel postulate and are therefore call non-Euclidean, namely, hyperbolic geometry and elliptic or spherical geometry. In this project, the student will present the most important properties in Euclidean, hyperbolic and elliptic geometry, and the historical background of their development.

This project is suitable for students who are interested in the history of mathematics and who want to immerse themselves in a somewhat broader and more general course than what they might be going to do at a master's degree level, and develop their geometric intuition.

References:

[1] Gans, David; An introduction to non-Euclidean geometry. Academic Press. New York-London, 1973.
[2] Martin, George E.; The foundations of geometry and the non-Euclidean plane. Undergraduate Texts in Mathematics. Springer-Verlag, New York-Berlin, 1982.