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Universal Hyperbolic Geometry

Universal Hyperbolic Geometry (UNSW). This is a collection of video lectures on Universal Hyperbolic Geometry given by Professor N. J. Wildberger. This course explains a new, simpler and more elegant theory of non-Euclidean geometry; in particular hyperbolic geometry. It is a purely algebraic approach which avoids transcendental functions like log, sin, tanh etc, relying instead on high school algebra and quadratic equations. The theory is more general, extending beyond the null circle, and connects naturally to Einstein's special theory of relativity.

This lecture introduces a simple universal analog (called the Right parallax formula) to the Angle of parallelism formula found by N. Lobachevsky and J. Bolyai in classical hyperbolic geometry. First we establish the dual laws of the main trigonometric laws for Universal Hyperbolic Geometry. The Right parallax theorem is proven using the Cross dual law, and we also show how it is related to the classical result of Lobachevsky and Bolyai.

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