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 in the context of Two-dimensional
A two-dimensional space is a mathematical space with two dimensions, meaning points have two degrees of freedom: their locations can be locally described with two coordinates or they can move in two independent directions. Common two-dimensional spaces are often called planes, or, more generally, surfaces. These include analogs to physical spaces, like flat planes, and curved surfaces like spheres, cylinders, and cones, which can be infinite or finite. Some two-dimensional mathematical spaces are not used to represent physical positions, like an affine plane or complex plane.
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Coordinate in the context of One-dimensional space
A one-dimensional space (1D space) is a mathematical space in which location can be specified with a single coordinate. An example is the number line, each point of which is described by a single real number. Any straight line or smooth curve is a one-dimensional space, regardless of the dimension of the ambient space in which the line or curve is embedded. Examples include the circle on a plane, or a parametric space curve.In physical space, a 1D subspace is called a "linear dimension" (rectilinear or curvilinear), with units of length (e.g., metre).
In algebraic geometry there are several structures that are one-dimensional spaces but are usually referred to by more specific terms. Any field is a one-dimensional vector space over itself. The projective line over denoted is a one-dimensional space. In particular, if the field is the complex numbers then the complex projective line is one-dimensional with respect to (but is sometimes called the Riemann sphere, as it is a model of the sphere, two-dimensional with respect to real-number coordinates).
Coordinate in the context of Mare Undarum
Mare Undarum /ʌnˈdɛərəm/ (Latin undārum, the "sea of waves") is a shallow, irregular lunar mare located just north of Mare Spumans on the lunar near side, between the crater Firmicus and the eastern limb. It lies within a trough between the third and fourth raised rings formed by the impact that created the Mare Crisium. The selenographic coordinates of this mare are 7.5° N, 68.7° E. It has a maximum diameter of 245 km.
There are five known lunar domes within the mare. The surrounding basin material is of the Nectarian epoch, with the mare basalt being of the Upper Imbrian epoch. The crater Dubyago can be seen on the southern edge of the mare. On the northeastern edge of the mare is the crater Condorcet P.
Coordinate in the context of Sinus Successus
The lunar feature Sinus Successus /ˈsaɪnəs səkˈsɛsəs/ (Latin sinus successūs "Bay of Success") lies along the eastern edge of Mare Fecunditatis. It is an outward bulge that forms a type of bay. The selenographic coordinates of Sinus Successus are 0.9° N, 59.0° E, and the diameter is 132 km.
Along the eastern edge of the bay is the flooded crater Condon, and the crater Webb forms the southern end of the area. There are no other features of significance on the bay. However the terrain just to the northwest of Sinus Successus was the landing site for the Soviet Luna 18 and Luna 20 probes.
Coordinate in the context of Ordinate
In mathematics, the abscissa (/æbˈsɪs.ə/; plural abscissae or abscissas) and the ordinate are respectively the first and second coordinate of a point in a Cartesian coordinate system:
Together they form an ordered pair which defines the location of a point in two-dimensional rectangular space.
Coordinate in the context of Cosmic time
Cosmic time, or cosmological time, is the time coordinate used in the Big Bang models of physical cosmology. This concept of time avoids some issues related to relativity by being defined within a solution to the equations of general relativity widely used in cosmology.