In modern presentations of Euclidean geometry, the points of space are defined in terms of their Cartesian coordinates, and Euclidean space itself is commonly identified with the real coordinate space "'R " "'n ".
42.
In mathematics, a "'coordinate space "'is a set ( not necessarily the same set ), collectively uniquely determine an element ( or point ) of the space in short, a space with a coordinate system.
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After this reduction in the coordinate space, the problem of maintaining a dynamic two-dimensional set of maximal points may be solved by using a van Emde Boas tree in place of the balanced binary search tree.
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In the space suggested by him ( Poincare mentions this only in passing ) where physical spacetime is " coordinatized " by, call it " coordinate space ", Lorentz transformations appear as ordinary rotations preserving the quadratic form
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Although " Unreal " is not the first major release with colored lighting ( see " Quake II " ), it is the first to have a Tim Sweeney as an ordered " texture coordinate space " dither.
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The choice of a system of affine coordinates for an affine space \ mathbb A _ k ^ n of dimension over a field induces an affine isomorphism between \ mathbb A _ k ^ n and the affine coordinate space.
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Where the latter equals to zero, the metric structure is locally Euclidean ( it means that at least some open set in the coordinate space is isometric to a piece of Euclidean space ), no matter whether coordinates are affine or curvilinear.
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The " rotation " in a plane spanned by a space unit vector and a time unit vector, while formally still a rotation in coordinate space, is a Lorentz boost in physical spacetime with " real " inertial coordinates ( see also hyperbolic rotation ).
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It is generally impossible to find a coordinate basis that is also orthonomal in any open region of a manifold, with an obvious exception of the real coordinate space } } considered as a manifold with the Euclidean metric } } at every point . }}
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The geospatial feature of Oracle Spatial and Graph provides a SQL spatial features in an Oracle database . ( The spatial component of a spatial feature consists of the geometric representation of its shape in some coordinate space referred to as its " geometry " .)
