Investigating Mobius addition in the Poincare Disk

Hyperbolic Geometry was discovered in the 19th Century while many mathematicians attempted to prove the Euclidean Parallel Postulate. The goal of this thesis was to further discover how theories of Euclidean Geometry could be manipulated to develop new theories in Hyperbolic Geometry. The main focus was in developing a method of determining the midpoint and any general point along a hyperbolic segment in the Poincare Disk. Fortunately this goal was achieved by applying the Mobius addition and Mobius subtraction to the Poincare Disk.