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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.

Introduction


Lecture 01 - Apollonius and Polarity
Lecture 02 - Apollonius and Harmonic Conjugates
Lecture 03 - Pappus' Theorem and the Cross Ratio
Lecture 04 - First Steps in Hyperbolic Geometry
Lecture 05 - The Circle and Cartesian Coordinates
Lecture 06 - Duality, Quadrance and Spread in Cartesian Coordinates
Lecture 7a - The Circle and Projective Homogeneous Coordinates
Lecture 7b - The Circle and Projective Homogeneous Coordinates (cont.)
Lecture 08 - Computations and Homogeneous Coordinates
Lecture 09 - Duality and Perpendicularity
Lecture 10 - Orthocenters Exist!
Lecture 11 - Theorems Using Perpendicularity
Lecture 12 - Null Points and Null Lines
Lecture 13 - Apollonius and Polarity Revisited
Lecture 14 - Reflections in Hyperbolic Geometry
Lecture 15 - Reflections and Projective Linear Algebra
Lecture 16 - Midpoints and Bisectors
Lecture 17 - Medians, Midlines, Centroids and Circumcenters
Lecture 18 - Parallels and the Double Triangle
Lecture 19 - The J Function, sl(2) and the Jacobi Identity
Lecture 20 - Pure and Applied Geometry - Understanding the Continuum
Lecture 21 - Quadrance and Spread
Lecture 22 - Pythagoras' Theorem in Universal Hyperbolic Geometry
Lecture 23 - The Triple Quad Formula in Universal Hyperbolic Geometry
Lecture 24 - Visualizing Quadrance with Circles
Lecture 25 - Geometer's Sketchpad and Circles in Universal Hyperbolic Geometry
Lecture 26 - Trigonometric Laws in Hyperbolic Geometry using Geometer's Sketchpad
Lecture 27 - The Spread Law in Universal Hyperbolic Geometry
Lecture 28 - The Cross Law in Universal Hyperbolic Geometry
Lecture 29 - Thales' Theorem, Right Triangles and Napier's Rules
Lecture 30 - Isosceles Triangles in Hyperbolic Geometry
Lecture 31 - Menelaus, Ceva and the Laws of Proportion
Lecture 32 - Trigonometric Dual Laws and the Parallax Formula
Lecture 33 - Spherical and Elliptic Geometries: An Introduction
Lecture 34 - Spherical and Elliptic Geometries (cont.)
Lecture 35 - Areas and Volumes for a Sphere
Lecture 36 - Classical Spherical Trigonometry
Lecture 37 - Perpendicularity, Polarity and Duality on a Sphere
Lecture 38 - Parametrizing and Projecting a Sphere
Lecture 39 - Rational Trigonometry: An Overview
Lecture 40 - Rational Trigonometry in Three Dimensions