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 22 - Pythagoras' Theorem in Universal Hyperbolic Geometry|
Pythagoras' theorem in the Euclidean plane is easily the most important theorem in geometry, and indeed in all of mathematics. The hyperbolic version, stated in terms of hyperbolic quadrances, is a deformation of the Euclidean result, and is also the most important theorem of hyperbolic geometry. We review the basic measurement of quadrance (not distance!) between points.
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