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Last updated:

September 23, 2023

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

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Description

Universal Hyperbolic Geometry (UNSW). This is a collection of video lectures on Universal Hyperbolic Geometry given by Professor N. J. Wildberger.

his 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.

Course Curriculum

  • Lecture 01 – Apollonius and Polarity Unlimited
  • Lecture 02 – Apollonius and Harmonic Conjugates Unlimited
  • Lecture 03 – Pappus’ Theorem and the Cross Ratio Unlimited
  • Lecture 04 – First Steps in Hyperbolic Geometry Unlimited
  • Lecture 05 – The Circle and Cartesian Coordinates Unlimited
  • Lecture 07 – The Circle and Projective Homogeneous Coordinates (Part A) Unlimited
  • Lecture 08 – Computations and Homogeneous Coordinates Unlimited
  • Lecture 09 – Duality and Perpendicularity Unlimited
  • Lecture 10 – Orthocenters Exist! Unlimited
  • Lecture 11 – Theorems Using Perpendicularity Unlimited
  • Lecture 12 – Null Points and Null Lines Unlimited
  • Lecture 13 – Apollonius and Polarity Revisited Unlimited
  • Lecture 14 – Reflections in Hyperbolic Geometry Unlimited
  • Lecture 15 – Reflections and Projective Linear Algebra Unlimited
  • Lecture 16 – Midpoints and Bisectors Unlimited
  • Lecture 17 – Medians, Midlines, Centroids and Circumcenters Unlimited
  • Lecture 18 – Parallels and the Double Triangle Unlimited
  • Lecture 19 – The J Function, sl(2) and the Jacobi Identity Unlimited
  • Lecture 20 – Pure and Applied Geometry – Understanding the Continuum Unlimited
  • Lecture 21 – Quadrance and Spread Unlimited
  • Lecture 22 – Pythagoras’ Theorem in Universal Hyperbolic Geometry Unlimited
  • Lecture 23 – The Triple Quad Formula in Universal Hyperbolic Geometry Unlimited
  • Lecture 24 – Visualizing Quadrance with Circles Unlimited
  • Lecture 25 – Geometer’s Sketchpad and Circles in Universal Hyperbolic Geometry Unlimited
  • Lecture 26 – Trigonometric Laws in Hyperbolic Geometry using Geometer’s Sketchpad Unlimited
  • Lecture 27 – The Spread Law in Universal Hyperbolic Geometry Unlimited
  • Lecture 28 – The Cross Law in Universal Hyperbolic Geometry Unlimited
  • Lecture 29 – Thales’ Theorem, Right Triangles and Napier’s Rules Unlimited
  • Lecture 30 – Isosceles Triangles in Hyperbolic Geometry Unlimited
  • Lecture 31 – Menelaus, Ceva and the Laws of Proportion Unlimited
  • Lecture 32 – Trigonometric Dual Laws and the Parallax Formula Unlimited
  • Lecture 33 – Spherical and Elliptic Geometries: An Introduction Unlimited
  • Lecture 34 – Spherical and elliptic geometries (cont.) Unlimited
  • Lecture 35 – Areas and Volumes for a Sphere Unlimited
  • Lecture 36 – Classical Spherical Trigonometry Unlimited
  • Lecture 37 – Perpendicularity, Polarity and Duality on a Sphere Unlimited
  • Lecture 38 – Parameterizing and Projecting a Sphere Unlimited
  • Lecture 39 – Rational Trigonometry: An Overview Unlimited
  • Lecture 40 – Rational Trigonometry in Three Dimensions Unlimited

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