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 11 - Theorems Using Perpendicularity|
We review how perpendicularity in hyperbolic geometry comes from duality, and then introduce duality for triangles and trilaterals. Then we discuss the orthic triangle and its dual, defining the important base center point. We introduce a general strategy for approaching theorems in the subject, and introduce our Standard Triangle 1: which will be used to algebraically illustrate many concepts and as an arena for numerical investigations.
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