Date of Award

Spring 1-1-2012

Document Type


Degree Name

Master of Science (MS)


Computer Science

First Advisor

Michael Eisenberg

Second Advisor

Sriram Sankaranarayanan

Third Advisor

Clayton H. Lewis


Turtle geometry has for decades played an engaging role as a constructivist tool for teaching Euclidean mathematical concepts and introductory computer programming to school-aged children at nearly all educational levels. Recent advances in computing power and display technologies have enabled the full implementation of a turtle geometry world on a spherical surface, whose geometric properties are inherently different than in the Euclidian world. Until now, spherical geometry has remained only shallowly explored using turtle geometry, largely because no easily accessible surface existed upon which to implement such a system. This paper describes the concept, implementation and working examples of a spherical turtle geometry system named Geometry on a Sphere (GOS) that makes use of any personal computer and the National Oceanic and Atmospheric Administration (NOAA)'s Science on a Sphere (SOS) display technology, or any similar spherical rendering device. The GOS system is a functioning prototype interactive system, designed to finally "bring the turtle off the plane."