Circular arc in the context of "Point (geometry)"

The Randstad (Dutch pronunciation: [ˈrɑntstɑt] ; "Rim City" or "Edge City") is a roughly crescent- or arc-shaped conurbation in the Netherlands, that includes almost half the country's population. With a central-western location, it connects and comprises the Netherlands' four biggest cities (Amsterdam, Rotterdam, The Hague, and Utrecht), their suburbs, and many towns in between, that all grew and merged into each other. Among other things, it includes the Port of Rotterdam (the world's busiest seaport outside Asia), the Port of Amsterdam (Europe's fourth-busiest seaport), and Amsterdam Airport Schiphol (Europe's fourth-busiest airport). With a population of approximately 8.4 million people it is one of the largest metropolitan regions in Europe, comparable in population size to the Rhine-Ruhr metropolitan region or the San Francisco Bay Area, and covers an area of approximately 11,372 km (4,391 sq mi). The Randstad had a gross regional domestic product of €510 billion in 2022, making it the second most productive region in the European Union, only behind the Paris metropolitan area. It encompasses both the Amsterdam metropolitan area and Rotterdam–The Hague metropolitan area. It is part of the larger Blue Banana megalopolis.

The Randstad's main cities are Almere, Amsterdam, Delft, Dordrecht, Haarlem, The Hague, Leiden, Rotterdam, and Utrecht. Other cities and towns include Alkmaar, Alphen aan den Rijn, Amersfoort, Amstelveen, Capelle aan den IJssel, Gouda, Heerhugowaard, Hilversum, Hoofddorp, Hoorn, Lelystad, Nieuwegein, Purmerend, Rijswijk, Schiedam, Spijkenisse, Vlaardingen, Zaandam, Zeist, and Zoetermeer.

This list covers all known stars, white dwarfs, brown dwarfs, and sub-brown dwarfs/rogue planets within 20 light-years (6.13 parsecs) of the Sun. So far, 131 such objects have been found. Only 22 are bright enough to be visible without a telescope, for which the star's visible light needs to reach or exceed the dimmest brightness visible to the naked eye from Earth, which is typically around 6.5 apparent magnitude.

The known 131 objects are bound in 94 stellar systems. Of those, 103 are main sequence stars: 80 red dwarfs and 23 "typical" stars having greater mass. Additionally, astronomers have found 6 white dwarfs (stars that have exhausted all fusible hydrogen), 21 brown dwarfs, as well as 1 sub-brown dwarf, WISE 0855−0714 (possibly a rogue planet). The closest system is Alpha Centauri, with Proxima Centauri as the closest star in that system, at 4.2465 light-years from Earth. The brightest, most massive and most luminous object among those 131 is Sirius A, which is also the brightest star in Earth's night sky; its white dwarf companion Sirius B is the hottest object among them. The largest object within the 20 light-years is Procyon.

In geometry, an angle subtended (from Latin for "stretched under") by a line segment at an arbitrary vertex is formed by the two rays between the vertex and each endpoint of the segment. For example, a side of a triangle subtends the opposite angle.

More generally, an angle subtended by an arc of a curve is the angle subtended by the corresponding chord of the arc.For example, a circular arc subtends the central angle formed by the two radii through the arc endpoints.

The horizon is the border between the surface of a celestial body and its sky when viewed from the perspective of an observer on or above the surface of the celestial body. This concept is further refined as -

There is also an imaginary astronomical, celestial, or theoretical horizon, part of the horizontal coordinate system, which is an infinite eye-level plane perpendicular to a line that runs (a) from the center of a celestial body (b) through the observer and (c) out to space (see graphic). It is used to calculate "horizon dip," which is the difference between the astronomical horizon and the sea horizon measured in arcs. Horizon dip is one factor taken into account in navigation by the stars.

In geometry, the lune of Hippocrates, named after Hippocrates of Chios, is a lune bounded by arcs of two circles, the smaller of which has as its diameter a chord spanning a right angle on the larger circle. Equivalently, it is a non-convex plane region bounded by one 180-degree circular arc and one 90-degree circular arc. It was the first curved figure to have its exact area calculated mathematically.

The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. It is defined such that one radian is the angle subtended at the center of a plane circle by an arc that is equal in length to the radius. The unit is defined in the SI as the coherent unit for plane angle, as well as for phase angle. Angles without explicitly specified units are generally assumed to be measured in radians, especially in mathematical writing.

A chord (from the Latin chorda, meaning "catgut or string") of a circle is a straight line segment whose endpoints both lie on a circular arc. If a chord were to be extended infinitely on both directions into a line, the object is a secant line. The perpendicular line passing through the chord's midpoint is called sagitta (Latin for "arrow").

More generally, a chord is a line segment joining two points on any curve, for instance, on an ellipse. A chord that passes through a circle's center point is the circle's diameter.

In mathematics (and more specifically geometry), a semicircle is a one-dimensional locus of points that forms half of a circle. It is a circular arc that measures 180° (equivalently, π radians, or a half-turn). It only has one line of symmetry (reflection symmetry).

In non-technical usage, the term "semicircle" is sometimes used to refer to either a closed curve that also includes the diameter segment from one end of the arc to the other or to the half-disk, which is a two-dimensional geometric region that further includes all the interior points.