Model of Stereographic Projection by Richard P. Baker, Baker #443

A stereographic projection maps a sphere (or, in this case, a portion of a sphere) onto a plane. One assumes that the eye of an observer is one of the poles of the sphere, one draws line segments between that pole and points of the sphere, and the points where the line segments intersect the plane are the points of the projection. Baker’s wire model on a wooden base shows a sphere with two poles, five latitude circles, and eight longitude circles. The observer is supposed to be at the top pole. The lower three latitude circles project onto circles penciled on the base (the upper latitude circles also would project into circles, but these would be outside the base of the existing model). The longitude circles project onto lines on the base (only part of these lines shows – they extend indefinitely from the lower pole). Also shown is the projection of a point on the sphere onto the base and a projection of a triangle on the sphere onto a triangle on the base.

A typed paper tag on the bottom of the base of the model reads: Mx No. 443 (/) Stereographic Projection.

Scientific instruments known as astrolabes – which were outdated by Baker’s time - used stereographic projection. In them, the eye of the observer is presumed to be at the celestial south pole. The center of the projection is the celestial north pole, and the circles are those on a celestial sphere. To explain the projection in surviving astrolabes, it would be easiest to invert Baker’s model.

Reference:

R. P. Baker, Mathematical Models, Iowa City, Iowa, 1931, p. 17.

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