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 28 - The Cross Law in Universal Hyperbolic Geometry |
The Cross law is the fourth of the four main laws of trigonometry in the hyperbolic setting. It is also the most complicated, and the most powerful law. This lecture shows how we can prove it with the help of a remarkable polynomial identity. We also give an application to the relation between the quadrance and spread of an equilateral triangle.
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