SCHEMATIZING (37)

By: Joshua Glenn
June 9, 2024

One in a series of posts via which HILOBROW’S Josh Glenn will attempt to depict the intellectual and emotional highs and lows of developing a semiotic schema.

3D illustration of a stereographic projection from the north pole onto a plane below the sphere

In mathematics, a 3D sphere can be represented in 2D by means of a stereographic projection — which is to say a perspective projection of the sphere, through a specific point on the sphere (the pole or center of projection), onto a plane (the projection plane) perpendicular to the diameter through the point. This is a one-to-one mapping that allows us to study the sphere by studying the plane instead. The idea is to point a light source at the north pole, and look at the shadows of points on the sphere as they appear on the plane below.

Stereographic projection is believed to have been discovered by Ancient Greek astronomers, who used it to project the celestial sphere to a plane — so that the motions of stars and planets could be analyzed using plane geometry. Its earliest extant description is found in Ptolemy’s Planisphere (2nd century AD).

Can’t wrap your head around the principle of perspective projection (of which stereographic projection is a special case)? Here’s a helpful illustration — by Rubens — demonstrating perspective projection. It’s from François d’Aguilon’s Opticorum libri sex philosophis juxta ac mathematicis utiles (1613; Six Books of Optics, useful for philosophers and mathematicians alike).

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SCHEMATIZING (37)

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