Up: Math 53 Selected Course Notes

# Stereographic Projection:

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This movie shows a circle on a sphere projected stereographically onto the plane from a point at the north pole of the sphere. The circle is initially at the south pole, then grows to the equator, and then shrinks toward the south pole. The light rays are shown to help you see the projection. Once the circle reaches the top, the light rays are removed and the circle moves again to the south pole.
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This movie shows a another squence of circles projected from the sphere. This time, the circles enlarge until one of them passes through the light source. The image of this circle is a straight line in the plane. All the other images are circles in the plane, though some are so large that you can't see them entirely in the picture.
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This movie shows a small circle that starts at the bottom of the sphere and them travels up the side and over the top of the sphere.
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This movie shows circles on the sphere that all go through the south pole. They grow larger until they pass over the north pole and return again to the bottom. Note that as the circle passes over the top, the image becomes a straight line; the image goes from being a circle on one side of this line to a circle on the other side.
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This movie shows circles on the sphere that all go through the north pole. They grow larger until they pass under the south pole and return again to the top. Note that the image of every such circle is a straight line.

Up: Math 53 Selected Course Notes