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 29 - Thales' Theorem, Right Triangles and Napier's Rules |
This lecture establishes important results for right triangles in universal hyperbolic geometry - these are triangles where at least two sides are perpendicular. Besides Pythagoras' theorem, there is a simple result called Thales' theorem, giving a formula for a spread as a ratio of two quadrances. Together these allow us to state a very simple form for Napier's rules in this algebraic setting.
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