Isometries of the Hyperbolic Plane
Nicholas Wade Stout
Classical geometry bases its foundation on five postulates from Euclid. However, mathematicians were always troubled by Euclid's fifth postulate, as it seemed that it should be derivable from the other four, and many made attempts to prove it using the other four postulates. Their efforts proved in vain, as it was later shown that other geometries exist which do not satisfy Euclid's fifth postulate. One of these, which will be the focus of this presentation, is hyperbolic geometry. We will examine two common models for the hyperbolic plane: the disk model and the upper half-plane model, with a particular emphasis on the isometries of the hyperbolic plane. Time permitting, we will also discuss tilings of the hyperbolic plane.
George E. Todd
Primary Advisor's Department
Stander Symposium project, College of Arts and Sciences
"Isometries of the Hyperbolic Plane" (2022). Stander Symposium Projects. 2531.