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.
|Lecture 01 - Apollonius and Polarity|
We begin by going back to Apollonius of Perga (in present day Turkey, not Italy!) and his understanding of the crucial role of polarity in studying conics, in particular the circle. Given a fixed circle, to each point in the plane we associate a line called the polar, and conversely to a line we associated a point called its pole. This duality is all important for hyperbolic geometry.
Go to the Course Home or watch other lectures: