Abstract: Constructions of tangent circles in the hyperbolic disk, interpreted in Euclidean geometry, give us examples of four mutually tangent circles. These are shown to satisfy Descartes’s Theorem for tangent circles. We also show that the Archimedes twin circles in the hyperbolic arbelos are usually not hyperbolic congruent, even though they are Euclidean congruent. We include a few construction instructions because all items under consideration require surprisingly few steps. Acknowledgements: We would like to thank those who sponsored the Mohler-Thompson Summer Research Grant for making this research experience possible. I would also like to thank Dr. Elizabeth Jensen and Dr. Chad Gunnoe for organizing the free on-campus housing for the summer’s student researchers, Dr. Michael McDaniel for including me in this project and giving me this opportunity, the referee who reviewed this paper, and David Rader, editor of the Rose-Hulman Undergraduate Mathematics Journal. PAGE 14 RHIT UNDERGRAD. MATH. J., VOL. 14, NO. 1
Publication Year: 2013
Publication Date: 2013-12-31
Language: en
Type: article
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