Test:Translation (geometry): Difference between revisions

Latest revision as of 11:21, 16 September 2022

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. In a Euclidean space, any translation is an isometry.^[1]

As a function

Note:This is a translation.

translation graphic — A translation moves every point of a figure or a space by the same amount in a given direction.

Horizontal and vertical translations

In geometry, a vertical translation (also known as vertical shift) is a translation of a geometric object in a direction parallel to the vertical axis of the Cartesian coordinate system.

Drawio

Attachments

External links

Translation Transform
Geometric Translation (Interactive Animation) at Math Is Fun
Understanding 2D Translation and Understanding 3D Translation by Roger Germundsson, The Wolfram Dmonstrations Project.

References

↑ Zazkis, R., Liljedahl, P., & Gadowsky, K. Conceptions of function translation: obstacles, intuitions, and rerouting. Journal of Mathematical Behavior, 22, 437-450. Retrieved April 29, 2014, from www.elsevier.com/locate/jmath

[1] Zazkis, R., Liljedahl, P., & Gadowsky, K. Conceptions of function translation: obstacles, intuitions, and rerouting. Journal of Mathematical Behavior, 22, 437-450. Retrieved April 29, 2014, from www.elsevier.com/locate/jmath

[1]

@@ Line 1: / Line 1: @@
-[[File:Test:Traslazione OK.svg|alt=translation graphic|thumb|<span style="color: rgb(32, 33, 34)">A translation moves every point of a figure or a space by the same amount in a given direction.</span>]]
-{{Short description|Planar movement within a Euclidean space without rotation}}
 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. In a Euclidean space, any translation is an isometry.<ref>Zazkis, R., Liljedahl, P., & Gadowsky, K. Conceptions of function translation: obstacles, intuitions, and rerouting. Journal of Mathematical Behavior, 22, 437-450. Retrieved April 29, 2014, from www.elsevier.com/locate/jmath</ref>
-==As a function==
-{{see also|Displacement (geometry)}}
 == As a function ==
+{{Messagebox|boxtype=note|icon=|Note text=This is a translation.|bgcolor=}}[[File:Test:Traslazione OK.svg|alt=translation graphic|thumb|<span style="color: rgb(32, 33, 34)">A translation moves every point of a figure or a space by the same amount in a given direction.</span>]]
 See also: Displacement (geometry)
-<nowiki>If {\displaystyle \mathbf {v} }{\displaystyle \mathbf {v} } is a fixed vector, known as the translation vector, and {\displaystyle \mathbf {p} }\mathbf {p}  is the initial position of some object, then the translation function {\displaystyle T_{\mathbf {v} }}{\displaystyle T_{\mathbf {v} }} will work as {\displaystyle T_{\mathbf {v} }(\mathbf {p} )=\mathbf {p} +\mathbf {v} }{\displaystyle T_{\mathbf {v} }(\mathbf {p} )=\mathbf {p} +\mathbf {v} }.</nowiki>
+If <math>\mathbf{v} </math> is a fixed vector, known as the ''translation vector'', and <math>\mathbf{p}</math> is the initial position of some object, then the translation function <math>T_{\mathbf{v}} </math> will work as <math> T_{\mathbf{v}}(\mathbf{p})=\mathbf{p}+\mathbf{v}</math>.
-<nowiki>If {\displaystyle T} T is a translation, then the image of a subset {\displaystyle A}A under the function {\displaystyle T} T is the translate of {\displaystyle A}A by {\displaystyle T}T. The translate of {\displaystyle A}A by {\displaystyle T_{\mathbf {v} }}{\displaystyle T_{\mathbf {v} }} is often written {\displaystyle A+\mathbf {v} }{\displaystyle A+\mathbf {v} }.</nowiki>
+If <math> T</math> is a translation, then the image of a subset <math> A </math> under the function <math> T</math> is the '''translate''' of <math> A </math> by <math> T </math>. The translate of <math>A </math> by <math>T_{\mathbf{v}} </math> is often written <math>A+\mathbf{v} </math>.
 === Horizontal and vertical translations ===
 In geometry, a vertical translation (also known as vertical shift) is a translation of a geometric object in a direction parallel to the vertical axis of the Cartesian coordinate system.
+== Drawio ==
+<bs:drawio filename="Translation (geometry)-50289677" />
+== Attachments ==
+<attachments>
+* [[Media:Rasperry_pi.pdf]]
+</attachments>
 ==See also==
 * [[Advection]]
 * [[Parallel transport]]
-* [[Rotation matrix]]
-* [[Scaling (geometry)]]
-* [[Transformation matrix]]
-* [[Translational symmetry]]
 ==External links==
-{{Commons category|Translation (geometry)}}
-* [http://www.cut-the-knot.org/Curriculum/Geometry/Translation.shtml Translation Transform] at [[cut-the-knot]]
+* [http://www.cut-the-knot.org/Curriculum/Geometry/Translation.shtml Translation Transform]
 * [http://www.mathsisfun.com/geometry/translation.html Geometric Translation (Interactive Animation)] at Math Is Fun
-* [http://demonstrations.wolfram.com/Understanding2DTranslation/ Understanding 2D Translation] and [http://demonstrations.wolfram.com/Understanding3DTranslation/ Understanding 3D Translation] by Roger Germundsson, [[The Wolfram Demonstrations Project]].
+* [http://demonstrations.wolfram.com/Understanding2DTranslation/ Understanding 2D Translation] and [http://demonstrations.wolfram.com/Understanding3DTranslation/ Understanding 3D Translation] by Roger Germundsson, The Wolfram Dmonstrations Project.
 ==References==
-{{reflist}}
 {{DEFAULTSORT:Translation (Geometry)}}
 [[Category:Euclidean symmetries]]