AbstractsMathematics

The main aim of this thesis is to define and investigate the parabola in hyperbolic geometry using the algebraic setting of Universal Hyperbolic Geometry (UHG), developed by N. J. Wildberger, with an emphasis on duality and the use of our new notion of sydpoints of a side. We use a projective linear algebra approach together with our carefully chosen parabolic standard coordinates to develop a rich library of formulas for important points, lines and conics associated to a hyperbolic parabola.