In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine and standardize the position of the points or other geometric elements on a manifold such as Euclidean space. The coordinates are not interchangeable; they are commonly distinguished by their position in an ordered tuple, or by a label, such as in "the x-coordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a commutative ring. The use of a coordinate system allows problems in geometry to be translated into problems about numbers and vice versa; this is the basis of analytic geometry.
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👉 Coordinate axis in the context of Integral
In mathematics, an integral is the continuous analog of a sum, and is used to calculate areas, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental operations of calculus, the other being differentiation. Integration was initially used to solve problems in mathematics and physics, such as finding the area under a curve, or determining displacement from velocity. Usage of integration expanded to a wide variety of scientific fields thereafter.
A definite integral computes the signed area of the region in the plane that is bounded by the graph of a given function between two points in the real line. Conventionally, areas above the horizontal axis of the plane are positive while areas below are negative. Integrals also refer to the concept of an antiderivative, a function whose derivative is the given function; in this case, they are also called indefinite integrals. The fundamental theorem of calculus relates definite integration to differentiation and provides a method to compute the definite integral of a function when its antiderivative is known; differentiation and integration are inverse operations.
In this Dossier
- ⭐ Core Definition: Coordinate axis
- 👉 Coordinate axis in the context of Integral
- Coordinate axis in the context of Political spectrum
- Coordinate axis in the context of Six degrees of freedom
- Coordinate axis in the context of Coaxial
- Coordinate axis in the context of Altazimuth mount
- Coordinate axis in the context of Political compass
- Coordinate axis in the context of Triple helix
Coordinate axis in the context of Political spectrum
A political spectrum is a system to characterize and classify different political positions in relation to one another. These positions sit upon one or more geometric axes that represent independent political dimensions. The expressions political compass and political map are used to refer to the political spectrum as well, especially to popular two-dimensional models of it.
Most long-standing spectra include the left–right dimension as a measure of social, political and economic hierarchy which originally referred to seating arrangements in the French parliament after the Revolution (1789–1799), with radicals on the left and aristocrats on the right. While communism and socialism are usually regarded internationally as being on the left, conservatism and reactionism are generally regarded as being on the right. Liberalism can mean different things in different contexts, being sometimes on the left (social liberalism) and other times on the right (conservative liberalism or classical liberalism). Those with an intermediate outlook are sometimes classified as centrists. Politics that rejects the conventional left–right spectrum is often known as syncretic politics. This form of politics has been criticized as tending to mischaracterize positions that have a logical location on a two-axis spectrum because they seem randomly brought together on a one-axis left–right spectrum.
Coordinate axis in the context of Six degrees of freedom
Six degrees of freedom (6DOF), or sometimes six degrees of movement, refers to the six mechanical degrees of freedom of movement of a rigid body in three-dimensional space. Specifically, the body is free to change position as forward/backward (surge), up/down (heave), left/right (sway) translation in three perpendicular axes, combined with changes in orientation through rotation about three perpendicular axes, often termed yaw (normal axis), pitch (transverse axis), and roll (longitudinal axis).
Three degrees of freedom (3DOF), a term often used in the context of virtual reality, typically refers to tracking of rotational motion only: pitch, yaw, and roll.
Coordinate axis in the context of Coaxial
In geometry, coaxial means that several three-dimensional linear or planar forms share a common axis. The two-dimensional analogue is concentric.
Coordinate axis in the context of Altazimuth mount
An altazimuth mount or alt-azimuth mount is a simple two-axis mount for supporting and rotating an instrument about two perpendicular axes – one vertical and the other horizontal. Rotation about the vertical axis varies the azimuth (compass bearing) of the pointing direction of the instrument. Rotation about the horizontal axis varies the altitude angle (angle of elevation) of the pointing direction.
These mounts are used, for example, with telescopes, cameras, radio antennas, heliostat mirrors, solar panels, and guns and similar weapons.
Coordinate axis in the context of Political compass
A political spectrum is a system to characterize and classify different political positions in relation to one another. These positions are typically placed on one or more geometric axes that represent independent political dimensions. The expressions political compass and political map are used to refer to the political spectrum as well, especially to popular two-dimensional models of it.
Most long-standing spectra include the left–right dimension as a measure of social, political, and economic hierarchy which originally referred to seating arrangements in the French parliament after the Revolution (1789–1799), with radicals on the left and aristocrats on the right. While communism and socialism are usually regarded internationally as being on the left, conservatism and reactionism are generally regarded as being on the right. Liberalism can mean different things in different contexts, being sometimes on the left (social liberalism) and other times on the right (conservative liberalism or classical liberalism). Those with an intermediate outlook are sometimes classified as centrists. Politics that rejects the conventional left–right spectrum is often known as syncretic politics. This form of politics has been criticized for tending to mischaracterize positions that have a logical location on a two-axis spectrum because they seem randomly brought together on a one-axis left–right spectrum.
Coordinate axis in the context of Triple helix
In the fields of geometry and biochemistry, a triple helix (pl.: triple helices) is a set of three congruent geometrical helices with the same axis, differing by a translation along the axis. This means that each of the helices keeps the same distance from the central axis. As with a single helix, a triple helix may be characterized by its pitch, diameter, and handedness. Examples of triple helices include triplex DNA, triplex RNA, the collagen helix, and collagen-like proteins.