![]() Lecture 19 - The J Function, sl(2) and the Jacobi Identity ![]() Lecture 18 - Parallels and the Double Triangle Lecture 17 - Medians, Midlines, Centroids and Circumcenters Lecture 15 - Reflections and Projective Linear Algebra Lecture 14 - Reflections in Hyperbolic Geometry Lecture 13 - Apollonius and Polarity Revisited 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: Together these allow us to state a very simple form for Napier's rules in this algebraic setting. Besides Pythagoras' theorem, there is a simple result called Thales' theorem, giving a formula for a spread as a ratio of two quadrances. This lecture establishes important results for right triangles in universal hyperbolic geometry - these are triangles where at least two sides are perpendicular. Lecture 29 - Thales' Theorem, Right Triangles and Napier's Rules 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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