This video introduces stereographic and gnomonic projections of a sphere. We begin by reviewing three dimensional coordinate systems. A rational parametrization of a sphere is analogous to the rational parametrization of a circle found in MathFoundations29. 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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