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In mathematics, a translation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x'y'-Cartesian coordinate system in which the x' axis is parallel to the x axis and k units away, and the y' axis is parallel to the y axis and h units away.
Because translation is commutative, the translation group is abelian. There are an infinite number of possible translations, so the translation group is an infinite group . In the theory of relativity , due to the treatment of space and time as a single spacetime , translations can also refer to changes in the time coordinate .
In mathematics, a translation plane is a projective plane which admits a certain group of symmetries (described below). Along with the Hughes planes and the Figueroa planes, translation planes are among the most well-studied of the known non-Desarguesian planes, and the vast majority of known non-Desarguesian planes are either translation planes, or can be obtained from a translation plane via ...
A walk can involve translation only, or translation and problem solving. For example, considering a window on a building involves first perceiving the window. After perception, there is a translation of the form of the window to mathematical language, such as the array ( w , l ) {\displaystyle (w,l)} where w {\displaystyle w} is the window's ...
Note: solving for ′ returns the resultant angle in the first quadrant (< <). To find , one must refer to the original Cartesian coordinate, determine the quadrant in which lies (for example, (3,−3) [Cartesian] lies in QIV), then use the following to solve for :
The problem observed above is that the usual directional derivative of vector calculus does not behave well under changes in the coordinate system when applied to the components of vector fields. This makes it quite difficult to describe how to translate vector fields in a parallel manner, if indeed such a notion makes any sense at all.
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This one is invariant under horizontal and vertical translation, as well as rotation by 180° (but not under reflection). In mathematics , an invariant is a property of a mathematical object (or a class of mathematical objects) which remains unchanged after operations or transformations of a certain type are applied to the objects.
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