Abstract. 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. Acknowledgements: We thank the Dennison and Marguerite Mohler Fund for creating a summer research experience for my advisor, Dr. Michael McDaniel, and me. Dr. Aaron Cinzori’s talk on geometric spirals at our Math Club inspired our hyperbolic version. We appreciate the referee’s directions, which helped clarify the article. RHIT Undergrad. Math. J., Vol. 11, No. 2 Page 197 1