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 38 - Parameterizing and Projecting a Sphere |
This lecture introduces stereographic and gnomonic projections of a sphere. We begin by reviewing three dimensional coordinate systems. Stereographic projection projects from the south pole of the sphere through the equatorial plane. Gnomonic projection projects from the center of the sphere through a tangent plane. Both are very important. Gnomonic projection works more naturally in the elliptic framework, where we identify antipodal points on a sphere.
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