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In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction. 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 Transformation Approach to Tenth Grade Geometry, The Mathematics Teacher, Vol. 65, No. 1 (January 1972), pp. 21-30. Zalman P. Usiskin. The Effects of Teaching Euclidean Geometry via Transformations on Student Achievement and Attitudes in Tenth-Grade Geometry, Journal for Research in Mathematics Education, Vol. 3, No. 4 (Nov., 1972), pp. 249-259.
A composition of four mappings coded in SVG, which transforms a rectangular repetitive pattern into a rhombic pattern. The four transformations are linear.. In mathematics, a transformation, transform, or self-map [1] is a function f, usually with some geometrical underpinning, that maps a set X to itself, i.e. f: X → X.
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.
Affine transformation (Euclidean geometry); Bäcklund transform; Bilinear transform; Box–Muller transform; Burrows–Wheeler transform (data compression); Chirplet transform ...
In mathematics, and in particular functional analysis, the shift operator, also known as the translation operator, is an operator that takes a function x ↦ f(x) to its translation x ↦ f(x + a). [1] In time series analysis, the shift operator is called the lag operator.
2. In geometry and linear algebra, denotes the cross product. 3. In set theory and category theory, denotes the Cartesian product and the direct product. See also × in § Set theory. · 1. Denotes multiplication and is read as times; for example, 3 ⋅ 2. 2. In geometry and linear algebra, denotes the dot product. 3.
Geometric transformations can be distinguished into two types: active or alibi transformations which change the physical position of a set of points relative to a fixed frame of reference or coordinate system (alibi meaning "being somewhere else at the same time"); and passive or alias transformations which leave points fixed but change the ...