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 02 - Apollonius and Harmonic Conjugates |
Apollonius introduced the important idea of harmonic conjugates, concerning four points on a line. He showed that the pole polar duality associated with a circle produces a family of such harmonic ranges, one for every line through the pole of a line. Harmonic ranges also occur in the context of vertex bisectors, as combinations of vectors, and associated with the sides of a quadrangle.
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