| 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 |
