Isometries of Spherical Geometry

Gryphon Balentine

For centuries after Euclid wrote his books, mathematicians were constantly trying to prove Postulate Five’s dependence on the other four postulates. While all were unsuccessful, these attempts at proving the dependency of Postulate Five eventually led to the creation of the idea of non-Euclidean geometries. In this talk, we will discuss analogs of Euclidean geometry topics on the surfaces of spheres. We will begin by looking at and discussing the known isometries of the Euclidean geometry and then discover what analogs we can make in the Spherical plane.

• Gryphon Balentine graduated from Emerald High School in Greenwood. He is completing his last year at Lander University before transferring to Clemson University in the fall as a part of the Bridge program to pursue studies to become a mechanical engineer.