![]() ![]() ![]() ![]() Lecture 11 - Theorems Using Perpendicularity Lecture 09 - Duality and Perpendicularity Lecture 08 - Computations and Homogeneous Coordinates Lecture 07 - The Circle and Projective Homogeneous Coordinates Lecture 06 - Duality, Quadrance and Spread in Cartesian Coordinates Lecture 05 - The Circle and Cartesian Coordinates Lecture 04 - First Steps in Hyperbolic Geometry Lecture 03 - Pappus' Theorem and the Cross Ratio Lecture 02 - Apollonius and Harmonic Conjugates Go to the Course Home or watch other lectures: We review the basic measurement of quadrance (not distance!) between points. 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. Pythagoras' theorem in the Euclidean plane is easily the most important theorem in geometry, and indeed in all of mathematics. Lecture 22 - Pythagoras' Theorem in Universal Hyperbolic Geometry The theory is more general, extending beyond the null circle, and connects naturally to Einstein's special theory of relativity. It is a purely algebraic approach which avoids transcendental functions like log, sin, tanh etc, relying instead on high school algebra and quadratic equations. This course explains a new, simpler and more elegant theory of non-Euclidean geometry in particular hyperbolic geometry. This is a collection of video lectures on Universal Hyperbolic Geometry given by Professor N. ![]()
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