Translation (mathematics)

In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure or a space by the same amount in a given direction.

In Euclidean geometry a transformation is a one-to-one correspondence between two sets of points or a mapping from one plane to another.) A translation can be described as a rigid motion: the other rigid motions are rotations, reflections and glide reflections.

A translation can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system.

A translation operator is an operator ${\displaystyle T_{\mathbf {\delta } }}$ such that ${\displaystyle T_{\mathbf {\delta } }f(\mathbf {v} )=f(\mathbf {v} +\mathbf {\delta } ).}$

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