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.

Author Bio

Megan Ternes is a Mathematics and German major from Aquinas College, class of 2013. This work was done during the summer after her sophomore year at Aquinas. She is interested in attending grad school to further her mathematical education. In her spare time she enjoys reading.