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 05 - The Circle and Cartesian Coordinates|
This lecture introduces basic facts about points, lines and the unit circle in terms of Cartesian coordinates. We determine the line joining two points, the condition for colinearity of three points (using the determinant), the point where two non-parallel lines meet and the the condition for concurrency of three lines. We state the rational parametrization of the circle and show that a line meets a circle in either 1,2 or 0 points.
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