Isometries of the Hyperbolic Plane

Classical geometry bases its foundation on five postulates from Euclid. However, mathematicians were always troubled by Euclid\u27s 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\u27s 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.https://ecommons.udayton.edu/stander_posters/3532/thumbnail.jp