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.
| Lecture 25 - Geometer's Sketchpad and Circles in Universal Hyperbolic Geometry |
We describe Geometer's Sketchpad (GSP): a dynamic software package that we use to illustrate constructions and measurements in universal hyperbolic geometry. Starting with basic properties of GSP, we then explain custom tools and how to make them. In particular we show how to construct the dual of a point, with respect to the standard null circle. For our main application, we illustrate various circles in hyperbolic geometry.
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