Parametrizing and Projecting a Sphere - Universal Hyperbolic Geometry
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Overview
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This video introduces stereographic and gnomonic projections of a sphere, including three-dimensional coordinate systems, spherical coordinates, and a rational parametrization formula. It also explains the algebraic underpinnings and the relationship between gnomonic projection and elliptic geometry.
Syllabus
Introduction
Stereographic projection
Recall parametrization of a circle
Algebraic underpinnings
Parametrization formula for a sphere
Spherical co-ordinates
Gnomonic projection
Gnomonic projection works more naturally with elliptic geometry
Taught by
Insights into Mathematics