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 06 - Duality, Quadrance and Spread in Cartesian Coordinates |
This lecture connects the notions of duality, quadrance and spread to the Cartesian coordinate framework, giving explicit formulas for the dual of a point, the quadrance between points, and the spread between lines in terms of coordinates. The proofs involve some useful preliminary results on lines formed by two points on the unit circle, and the meets of two such lines.
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