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 37 - Perpendicularity, Polarity and Duality on a Sphere |
This lecture discusses perpendicularity on a sphere, associating two poles to every great circle, and one polar line (great circle) to every point. We introduce the polar triangle of a triangle, and explain the supplementary relation between angles and sides in a triangle and sides and angles in the polar triangle. Then we extend the duality of Apollonius from the case of a circle to the case of a sphere.
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