This article is based on the construction of Nested Hyperbolic Polygonal Spirals. The construction uses constructible Euclidean angles to create hyperbolic polygons of five or more sides. The nested polygons are formed by connecting the midpoints of the sides of the original polygon, thus creating a spiral. The construction is included for the readers to be able to construct one for themselves as they read along. This construction, along with hyperbolic trigonometric formulas, led to the results: measures of the angles, side lengths and areas of all the parts of the spiral. Furthermore, the construction is used to prove the constructible hyperbolic regular polygons have the same number of sides as the constructible Euclidean polygons.

Author Bio

Jillian Russo is doing her student teaching this semester, Fall 2009, as well as working for the KentISD accelerated math program. She joined Pi Mu Epsilon last year, which is when she saw hyperbolic geometry for the first time. She is particularly proud of Figure 1 because the hyperbolic segments are honest and the shading turned out great.