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In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry . Analytic geometry is used in physics and engineering , and also in aviation , rocketry , space science , and spaceflight .
In coordination chemistry, a coordinate covalent bond, [1] also known as a dative bond, [2] dipolar bond, [1] or coordinate bond [3] is a kind of two-center, two-electron covalent bond in which the two electrons derive from the same atom. The bonding of metal ions to ligands involves this kind of interaction. [4]
Coordinate charts are mathematical objects of topological manifolds, and they have multiple applications in theoretical and applied mathematics. When a differentiable structure and a metric are defined, greater structure exists, and this allows the definition of constructs such as integration and geodesics .
The coordination geometry of an atom is the geometrical pattern defined by the atoms around the central atom. The term is commonly applied in the field of inorganic chemistry, where diverse structures are observed. The coordination geometry depends on the number, not the type, of ligands bonded to the metal centre as well as their locations.
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
In mathematics, a Euclidean plane is a Euclidean space of dimension two, denoted or . It is a geometric space in which two real numbers are required to determine the position of each point . It is an affine space , which includes in particular the concept of parallel lines .
Coordinate bonds are useful in such supramolecular self-assembly because of their versatile geometries. [1] However, there is controversy over calling coordinate bonds noncovalent, as they are typically strong bonds and have covalent character. [2] The combination of a coordination cage and a guest is a type of inclusion compound. Coordination ...
In mathematics, particularly topology, an atlas is a concept used to describe a manifold. An atlas consists of individual charts that, roughly speaking, describe individual regions of the manifold. In general, the notion of atlas underlies the formal definition of a manifold and related structures such as vector bundles and other fiber bundles.