This is the introductory lecture to a series on hyperbolic geometry which introduces a radically new and improved way of treating the subject, making it more algebraic and logical, with improved computational power and many new theorems.
In this lecture we summarize the differences between this UNIVERSAL HYPERBOLIC GEOMETRY and traditional courses taught at universities. We briefly review some of the framework introduced by Lobachevsky, Bolyai and Gauss.
This course will open up a new area of investigation into geometry, accessible to a broad audience. Let's return to those days where high school teachers and ordinary lay people could contribute to the discovery of new and beautiful facts.
Norman Wildberger is also the discoverer of Rational Trigonometry, an important new direction for classical trigonometry (and which really ought to be revolutionizing mathematics education!!)
His YouTube site Insights into Mathematics at user: njwildberger also contains series on MathFoundations, History of Mathematics, LinearAlgebra, Rational Trigonometry and even one called Elementary Mathematics (K-6) Explained.
