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 27 - The Spread Law in Universal Hyperbolic Geometry|
The spread between two lines in hyperbolic geometry is exactly dual to the notion of the quadrance between two points. The Spread law is the third of the four main laws of trigonometry in universal hyperbolic geometry. Its proof also relies on a remarkable polynomial identity, just as did the proofs of Pythagoras' theorem and the Triple quad formula. We review the definition of spread, give an example relating it to the spread between lines in Euclidean geometry, and give a proof.
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