Inverse Stereographic Projection of the Logarithmic Spiral

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This Demonstration shows the inverse stereographic projection of a logarithmic spiral onto the unit sphere. You can move the spiral in the plane; it maps on the sphere as a loxodrome.

Contributed by: Erik Mahieu (March 2011)
Open content licensed under CC BY-NC-SA


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The inverse stereographic projection of the point to the unit sphere is the point .

A logarithmic or equiangular spiral is defined as a two-dimensional curve that cuts all radial lines at a constant angle. Its polar equation is given by .

A loxodrome on a sphere (spherical spiral) is a curve that cuts all meridians at the same angle. The stereographic projection of a loxodrome is a logarithmic spiral.



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