# Spherical Trigonometry on a Gnomonic Projection

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A gnomonic projection is obtained by projecting points on the surface of a sphere from the sphere's center to a plane tangent to the sphere. In this Demonstration, the tangent point is taken as the North Pole, so that loci of constant are circles, while those of constant are radial spokes. This projection can be used to project slightly less than one hemisphere at a time onto a finite plane. The transformation equations are , . A gnomonic projection is neither conformal nor area-preserving, but has the distinctive feature that great circle arcs are mapped into straight lines. This suggests that it might be instructive to apply the gnomonic projection to spherical trigonometry.

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Contributed by: S. M. Blinder (March 2011)

Open content licensed under CC BY-NC-SA

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