Concept

Astrolabe

An instrument that maps the sky onto a flat brass plate by stereographic projection, with a rotating star map laid over a plate engraved for one latitude. Because circles project to circles, it answers questions of spherical astronomy, such as the time of sunrise, by lining up circles.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

One point on the sphere for every point of the plane. Lines from the north pole of a sphere through each of its points land on a plane below, matching the sphere minus one point with the whole plane.

A sphere is a plane plus one point

Remove a single point from a sphere and what is left can be flattened out to cover an infinite plane exactly. The construction is one straight line, repeated.

topology · Stereographic projection

An astrolabe is a stereographic projection in brass. Latitude 52°: 16 engraved curves, worst departure from a circle 8.88e-15; altitude-circle formulas within 2.2e-16; Cancer radius 0.6564, Capricorn 1.5235 of the equator's.

An instrument that computes with circles

An astrolabe is a stereographic projection of the sky cut in brass. Because the projection sends circles to circles, every line on it can be drawn with compasses, and turning the star map over the plate is a rotation that answers questions in spherical astronomy without a single calculation. Of the lines medieval makers engraved, one family is not a circle on the sphere — and the arcs they drew for it miss the truth by a third of a millimetre.

topology · Stereographic projection

Named alongside it

The objects these essays reach for when they reach for this one.

Circle-preserving Projection Bijection Conformal Conformal map Continuity Mobius transformation Point at infinity Riemann sphere Rotation Sphere Stereographic projection

All concepts