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 31 - Menelaus, Ceva and the Laws of Proportion |
The classical theorems of Menelaus and Ceva concern a triangle together with an additional line or point, and give relations between three ratios of distances (or quadrances). These results are also valid in universal hyperbolic geometry. However we also give some other lovely and simple results: the Triangle proportions theorem and the Alternate spreads theorem.
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