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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.

Here we introduce basic aspects of triangle geometry into the superior framework of universal hyperbolic geometry, a purely algebraic setting valid over the rational numbers. We begin by reviewing the centroid and circumcenter in the Euclidean setting. In the hyperbolic plane, midpoints of a side don't always exist. If we consider a triangle in which each side has midpoints, there are then 6 medians, and their dual lines, called midlines here, although they play the role of perpendicular bisectors. The medians meet in 4 centroids. The midlines meet in 4 circumcenters.

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