Representing the surface of a polyhedron on a plane is not a difficult task, whereas depicting the surface of a sphere in the same manner is impossible.

For this reason, astronomers from earliest antiquity represented the starry sky by means of globes—which reproduced the constellations directly on a sphere—or by means of projection methods.

In the so-called stereographic projection, the projection plane is defined as the one crossing the celestial equator, and the projection point is the celestial south pole.

The point in which the straight line from the south pole to the star intersects the plane represents the projection of the star itself.

The projections of the stars of the northern hemisphere all fall inside the celestial equator, while the projections of the stars of the southern hemisphere all fall outside it.

The closer the stars are to the south pole, the farther their projections will be from the celestial equator. As a result, the representation was usually limited to the Tropic of Capricorn.

In the stereographic projection, all the circles of the sphere remain as such on the projection plane. This even includes the circles that are not parallel to the equator, such as the ecliptic.

The stereographic projection was widely used in the construction of the plane astrolabe: the instrument's disk, called rete, Latin for "network", carries the projections of selected bright stars; its plate, the tympanum, carries the projections of the main celestial circles.