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 04 - First Steps in Hyperbolic Geometry |
This lecture outlines the basic framework of universal hyperbolic geometry - as the projective study of a circle, or later on the projective study of relativistic geometry. Perpendicularity is defined in terms of duality. We state the main formulas: Pythagoras' theorem, the Triple quad formula, Pythagoras' dual theorem, the Triple spread formula, the Spread law and the Cross law and its dual.
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