Universal Hyperbolic Geometry







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 07 – The Circle and Projective Homogeneous Coordinates
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 – Parameterizing and Projecting a Sphere
Lecture 39 – Rational Trigonometry: An Overview
Lecture 40 – Rational Trigonometry in Three Dimensions