Hyperbolic Spirals and Spiral Patterns

Douglas Dunham
Meeting Alhambra, ISAMA-BRIDGES Conference Proceedings (2003)
Pages 521–528


Starting many centuries ago, artists in a number of cultures have created spiral patterns on flat surfaces, and even on spheres. Mathematicians have given precise definitions of spirals in the Euclidean plane and have studied them for centuries. Yet no one seems to have studied spirals in the hyperbolic plane, and until recently, no one had created hyperbolic spiral patterns. In this paper, we investigate both areas.