Compass (drawing tool) in the context of "Point set"

In geometry, straightedge-and-compass construction – also known as ruler-and-compass construction, Euclidean construction, or classical construction – is the construction of lengths, angles, and other geometric figures using only an idealized ruler and a compass.

The idealized ruler, known as a straightedge, is assumed to be infinite in length, have only one edge, and no markings on it. The compass is assumed to have no maximum or minimum radius, and is assumed to "collapse" when lifted from the page, so it may not be directly used to transfer distances. (This is an unimportant restriction since, using a multi-step procedure, a distance can be transferred even with a collapsing compass; see compass equivalence theorem. Note however that whilst a non-collapsing compass held against a straightedge might seem to be equivalent to marking it, the neusis construction is still impermissible and this is what unmarked really means: see Markable rulers below.) More formally, the only permissible constructions are those granted by the first three postulates of Euclid's Elements.

In geometry, a point is an abstract idealization of an exact position, without size, in physical space, or its generalization to other kinds of mathematical spaces. As zero-dimensional objects, points are usually taken to be the fundamental indivisible elements comprising the space, of which one-dimensional curves, two-dimensional surfaces, and higher-dimensional objects consist.

In classical Euclidean geometry, a point is a primitive notion, defined as "that which has no part". Points and other primitive notions are not defined in terms of other concepts, but only by certain formal properties, called axioms, that they must satisfy; for example, "there is exactly one straight line that passes through two distinct points". As physical diagrams, geometric figures are made with tools such as a compass, scriber, or pen, whose pointed tip can mark a small dot or prick a small hole representing a point, or can be drawn across a surface to represent a curve.

Urania (/jʊəˈreɪniə/ yoor-AY-nee-ə; Ancient Greek: Οὐρανία, romanized: Ouranía; meaning "heavenly" or "of heaven") was, in Greek mythology, the muse of astronomy and astrology. Urania is the goddess of astronomy and stars, her attributes being the globe and compass.

The muse Urania is sometimes confused with Aphrodite Urania ("heavenly Aphrodite") because of their similar name.

In mathematics, the Euclidean distance between two points in a Euclidean space is the length of the line segment between them. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, and therefore is occasionally called the Pythagorean distance.

These names come from the ancient Greek mathematicians Euclid and Pythagoras. In the Greek deductive geometry exemplified by Euclid's Elements, distances were not represented as numbers but line segments of the same length, which were considered "equal". The notion of distance is inherent in the compass tool used to draw a circle, whose points all have the same distance from a common center point. The connection from the Pythagorean theorem to distance calculation was not made until the 18th century.

Perdix (Ancient Greek: Πέρδιξ meaning "partridge") was a nephew and student of Daedalus in Greek mythology, claimed to have invented the potter's wheel, the saw, and the compass. In other sources, Perdix was the name of Daedalus's sister, and her inventor son was named Talos or Attalus.

Circinus is a small, faint constellation in the southern sky, first defined in 1756 by the French astronomer Nicolas-Louis de Lacaille. Its name is Latin for compass, referring to the drafting tool used for drawing circles (it should not be confused with Pyxis, a constellation that represents a mariner's compass which points north). Its brightest star is Alpha Circini, with an apparent magnitude of 3.19. Slightly variable, it is the brightest rapidly oscillating Ap star in the night sky. AX Circini is a Cepheid variable visible with the unaided eye, and BX Circini is a faint star thought to have been formed from the merger of two white dwarfs. Two sun-like stars have planetary systems: HD 134060 has two small planets, and HD 129445 has a Jupiter-like planet. Supernova SN 185 appeared in Circinus in 185 AD and was recorded by Chinese observers. Two novae have been observed more recently, in the 20th century.

The Milky Way runs through the constellation, featuring prominent objects such as the open cluster NGC 5823 and the planetary nebula NGC 5315. Circinus hosts a notable spiral galaxy, the Circinus Galaxy, discovered in 1977; it is the closest Seyfert galaxy to the Milky Way. The Alpha Circinids (ACI), a meteor shower also discovered in 1977, radiate from this constellation.