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 13 - Apollonius and Polarity Revisited |
Armed with explicit formulas for null points and null lines, along with their meets and joins, we return to the polarity of Apollonius with which we began this series. Our aim is to establish a fundamental fact that was previously stated without proof: that the dual or polar of a point can be found by two auxiliary (interior) lines and an associated quadrangle of null points. The key point is that the diagonal line formed by the (other) diagonal points of this quadrangle depend only on the original point.
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