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 21 - Quadrance and Spread |
This lecture introduces algebraic definitions of the main metrical concepts: quadrance between points and spread between lines. We first review the basics of Rational Trigonometry (RT) in the Euclidean affine setting, motivating the move to the hyperbolic projective setting. The five main laws of RT are laid out and compared with the four main laws of Universal Hyperbolic Geometry (UHG).
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