Test:Translation (geometry)

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.^{Fußnote [1]}

As a function

Vorlage:Messagebox

translation graphic

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

See also: Displacement (geometry)

If $\mathbf {v}$ is a fixed vector, known as the translation vector, and Fehler beim Parsen (Konvertierungsfehler. Der Server („cli“) hat berichtet: „array ( 'nohash' => array ( ), 'success' => true, '98b434d091ae15b7180667a0296aae31' => (object) array( 'speakText' => 'bold v', 'mml' => '<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="bold v"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="bold" data-semantic-annotation="clearspeak:simple" data-semantic-id="0">v</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\\displaystyle \\mathbf {v} }</annotation></semantics></math>', 'svg' => '<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.411ex" height="1.676ex" style="vertical-align: -0.338ex;" viewBox="0 -576.1 607.5 721.6" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" aria-labelledby="MathJax-SVG-1-Title"><title id="MathJax-SVG-1-Title">bold v</title><defs aria-hidden="true"><path stroke-width="1" id="E1-MJMAINB-76" d="M401 444Q413 441 495 441Q568 441 574 444H580V382H510L409 156Q348 18 339 6Q331 -4 320 -4Q318 -4 313 -4T303 -3H288Q273 -3 264 12T221 102Q206 135 197 156L96 382H26V444H34Q49 441 145 441Q252 441 270 444H279V382H231L284 264Q335 149 338 149Q338 150 389 264T442 381Q442 382 418 382H394V444H401Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)" aria-hidden="true"> <use xlink:href="#E1-MJMAINB-76" x="0" y="0"></use></g></svg>', 'width' => '1.411ex', 'height' => '1.676ex', 'style' => 'vertical-align: -0.338ex;', 'streeJson' => (object) array( 'stree' => (object) array( 'type' => 'identifier', 'role' => 'latinletter', 'font' => 'bold', 'annotation' => 'clearspeak:simple', 'id' => '0', '$t' => 'v', ), ), 'streeXml' => '<stree><identifier role="latinletter" font="bold" annotation="clearspeak:simple" id="0">v</identifier></stree>', 'success' => true, 'log' => 'success', 'mathoidStyle' => 'vertical-align: -0.338ex; width:1.411ex; height:1.676ex;', 'sanetex' => '{\\displaystyle \\mathbf {v} }', 'speech' => 'bold v', ), )“): {\displaystyle \mathbf{p}} is the initial position of some object, then the translation function Fehler beim Parsen (Konvertierungsfehler. Der Server („cli“) hat berichtet: „array ( 'nohash' => array ( ), 'success' => true, '98b434d091ae15b7180667a0296aae31' => (object) array( 'speakText' => 'bold v', 'mml' => '<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="bold v"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="bold" data-semantic-annotation="clearspeak:simple" data-semantic-id="0">v</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\\displaystyle \\mathbf {v} }</annotation></semantics></math>', 'svg' => '<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.411ex" height="1.676ex" style="vertical-align: -0.338ex;" viewBox="0 -576.1 607.5 721.6" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" aria-labelledby="MathJax-SVG-1-Title"><title id="MathJax-SVG-1-Title">bold v</title><defs aria-hidden="true"><path stroke-width="1" id="E1-MJMAINB-76" d="M401 444Q413 441 495 441Q568 441 574 444H580V382H510L409 156Q348 18 339 6Q331 -4 320 -4Q318 -4 313 -4T303 -3H288Q273 -3 264 12T221 102Q206 135 197 156L96 382H26V444H34Q49 441 145 441Q252 441 270 444H279V382H231L284 264Q335 149 338 149Q338 150 389 264T442 381Q442 382 418 382H394V444H401Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)" aria-hidden="true"> <use xlink:href="#E1-MJMAINB-76" x="0" y="0"></use></g></svg>', 'width' => '1.411ex', 'height' => '1.676ex', 'style' => 'vertical-align: -0.338ex;', 'streeJson' => (object) array( 'stree' => (object) array( 'type' => 'identifier', 'role' => 'latinletter', 'font' => 'bold', 'annotation' => 'clearspeak:simple', 'id' => '0', '$t' => 'v', ), ), 'streeXml' => '<stree><identifier role="latinletter" font="bold" annotation="clearspeak:simple" id="0">v</identifier></stree>', 'success' => true, 'log' => 'success', 'mathoidStyle' => 'vertical-align: -0.338ex; width:1.411ex; height:1.676ex;', 'sanetex' => '{\\displaystyle \\mathbf {v} }', 'speech' => 'bold v', ), )“): {\displaystyle T_{\mathbf{v}} } will work as Fehler beim Parsen (Konvertierungsfehler. Der Server („cli“) hat berichtet: „array ( 'nohash' => array ( ), 'success' => true, '98b434d091ae15b7180667a0296aae31' => (object) array( 'speakText' => 'bold v', 'mml' => '<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="bold v"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="bold" data-semantic-annotation="clearspeak:simple" data-semantic-id="0">v</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\\displaystyle \\mathbf {v} }</annotation></semantics></math>', 'svg' => '<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.411ex" height="1.676ex" style="vertical-align: -0.338ex;" viewBox="0 -576.1 607.5 721.6" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" aria-labelledby="MathJax-SVG-1-Title"><title id="MathJax-SVG-1-Title">bold v</title><defs aria-hidden="true"><path stroke-width="1" id="E1-MJMAINB-76" d="M401 444Q413 441 495 441Q568 441 574 444H580V382H510L409 156Q348 18 339 6Q331 -4 320 -4Q318 -4 313 -4T303 -3H288Q273 -3 264 12T221 102Q206 135 197 156L96 382H26V444H34Q49 441 145 441Q252 441 270 444H279V382H231L284 264Q335 149 338 149Q338 150 389 264T442 381Q442 382 418 382H394V444H401Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)" aria-hidden="true"> <use xlink:href="#E1-MJMAINB-76" x="0" y="0"></use></g></svg>', 'width' => '1.411ex', 'height' => '1.676ex', 'style' => 'vertical-align: -0.338ex;', 'streeJson' => (object) array( 'stree' => (object) array( 'type' => 'identifier', 'role' => 'latinletter', 'font' => 'bold', 'annotation' => 'clearspeak:simple', 'id' => '0', '$t' => 'v', ), ), 'streeXml' => '<stree><identifier role="latinletter" font="bold" annotation="clearspeak:simple" id="0">v</identifier></stree>', 'success' => true, 'log' => 'success', 'mathoidStyle' => 'vertical-align: -0.338ex; width:1.411ex; height:1.676ex;', 'sanetex' => '{\\displaystyle \\mathbf {v} }', 'speech' => 'bold v', ), )“): {\displaystyle T_{\mathbf{v}}(\mathbf{p})=\mathbf{p}+\mathbf{v}} .

If Fehler beim Parsen (Konvertierungsfehler. Der Server („cli“) hat berichtet: „array ( 'nohash' => array ( ), 'success' => true, '98b434d091ae15b7180667a0296aae31' => (object) array( 'speakText' => 'bold v', 'mml' => '<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="bold v"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="bold" data-semantic-annotation="clearspeak:simple" data-semantic-id="0">v</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\\displaystyle \\mathbf {v} }</annotation></semantics></math>', 'svg' => '<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.411ex" height="1.676ex" style="vertical-align: -0.338ex;" viewBox="0 -576.1 607.5 721.6" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" aria-labelledby="MathJax-SVG-1-Title"><title id="MathJax-SVG-1-Title">bold v</title><defs aria-hidden="true"><path stroke-width="1" id="E1-MJMAINB-76" d="M401 444Q413 441 495 441Q568 441 574 444H580V382H510L409 156Q348 18 339 6Q331 -4 320 -4Q318 -4 313 -4T303 -3H288Q273 -3 264 12T221 102Q206 135 197 156L96 382H26V444H34Q49 441 145 441Q252 441 270 444H279V382H231L284 264Q335 149 338 149Q338 150 389 264T442 381Q442 382 418 382H394V444H401Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)" aria-hidden="true"> <use xlink:href="#E1-MJMAINB-76" x="0" y="0"></use></g></svg>', 'width' => '1.411ex', 'height' => '1.676ex', 'style' => 'vertical-align: -0.338ex;', 'streeJson' => (object) array( 'stree' => (object) array( 'type' => 'identifier', 'role' => 'latinletter', 'font' => 'bold', 'annotation' => 'clearspeak:simple', 'id' => '0', '$t' => 'v', ), ), 'streeXml' => '<stree><identifier role="latinletter" font="bold" annotation="clearspeak:simple" id="0">v</identifier></stree>', 'success' => true, 'log' => 'success', 'mathoidStyle' => 'vertical-align: -0.338ex; width:1.411ex; height:1.676ex;', 'sanetex' => '{\\displaystyle \\mathbf {v} }', 'speech' => 'bold v', ), )“): {\displaystyle T} is a translation, then the image of a subset Fehler beim Parsen (Konvertierungsfehler. Der Server („cli“) hat berichtet: „array ( 'nohash' => array ( ), 'success' => true, '98b434d091ae15b7180667a0296aae31' => (object) array( 'speakText' => 'bold v', 'mml' => '<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="bold v"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="bold" data-semantic-annotation="clearspeak:simple" data-semantic-id="0">v</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\\displaystyle \\mathbf {v} }</annotation></semantics></math>', 'svg' => '<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.411ex" height="1.676ex" style="vertical-align: -0.338ex;" viewBox="0 -576.1 607.5 721.6" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" aria-labelledby="MathJax-SVG-1-Title"><title id="MathJax-SVG-1-Title">bold v</title><defs aria-hidden="true"><path stroke-width="1" id="E1-MJMAINB-76" d="M401 444Q413 441 495 441Q568 441 574 444H580V382H510L409 156Q348 18 339 6Q331 -4 320 -4Q318 -4 313 -4T303 -3H288Q273 -3 264 12T221 102Q206 135 197 156L96 382H26V444H34Q49 441 145 441Q252 441 270 444H279V382H231L284 264Q335 149 338 149Q338 150 389 264T442 381Q442 382 418 382H394V444H401Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)" aria-hidden="true"> <use xlink:href="#E1-MJMAINB-76" x="0" y="0"></use></g></svg>', 'width' => '1.411ex', 'height' => '1.676ex', 'style' => 'vertical-align: -0.338ex;', 'streeJson' => (object) array( 'stree' => (object) array( 'type' => 'identifier', 'role' => 'latinletter', 'font' => 'bold', 'annotation' => 'clearspeak:simple', 'id' => '0', '$t' => 'v', ), ), 'streeXml' => '<stree><identifier role="latinletter" font="bold" annotation="clearspeak:simple" id="0">v</identifier></stree>', 'success' => true, 'log' => 'success', 'mathoidStyle' => 'vertical-align: -0.338ex; width:1.411ex; height:1.676ex;', 'sanetex' => '{\\displaystyle \\mathbf {v} }', 'speech' => 'bold v', ), )“): {\displaystyle A } under the function Fehler beim Parsen (Konvertierungsfehler. Der Server („cli“) hat berichtet: „array ( 'nohash' => array ( ), 'success' => true, '98b434d091ae15b7180667a0296aae31' => (object) array( 'speakText' => 'bold v', 'mml' => '<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="bold v"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="bold" data-semantic-annotation="clearspeak:simple" data-semantic-id="0">v</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\\displaystyle \\mathbf {v} }</annotation></semantics></math>', 'svg' => '<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.411ex" height="1.676ex" style="vertical-align: -0.338ex;" viewBox="0 -576.1 607.5 721.6" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" aria-labelledby="MathJax-SVG-1-Title"><title id="MathJax-SVG-1-Title">bold v</title><defs aria-hidden="true"><path stroke-width="1" id="E1-MJMAINB-76" d="M401 444Q413 441 495 441Q568 441 574 444H580V382H510L409 156Q348 18 339 6Q331 -4 320 -4Q318 -4 313 -4T303 -3H288Q273 -3 264 12T221 102Q206 135 197 156L96 382H26V444H34Q49 441 145 441Q252 441 270 444H279V382H231L284 264Q335 149 338 149Q338 150 389 264T442 381Q442 382 418 382H394V444H401Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)" aria-hidden="true"> <use xlink:href="#E1-MJMAINB-76" x="0" y="0"></use></g></svg>', 'width' => '1.411ex', 'height' => '1.676ex', 'style' => 'vertical-align: -0.338ex;', 'streeJson' => (object) array( 'stree' => (object) array( 'type' => 'identifier', 'role' => 'latinletter', 'font' => 'bold', 'annotation' => 'clearspeak:simple', 'id' => '0', '$t' => 'v', ), ), 'streeXml' => '<stree><identifier role="latinletter" font="bold" annotation="clearspeak:simple" id="0">v</identifier></stree>', 'success' => true, 'log' => 'success', 'mathoidStyle' => 'vertical-align: -0.338ex; width:1.411ex; height:1.676ex;', 'sanetex' => '{\\displaystyle \\mathbf {v} }', 'speech' => 'bold v', ), )“): {\displaystyle T} is the translate of Fehler beim Parsen (Konvertierungsfehler. Der Server („cli“) hat berichtet: „array ( 'nohash' => array ( ), 'success' => true, '98b434d091ae15b7180667a0296aae31' => (object) array( 'speakText' => 'bold v', 'mml' => '<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="bold v"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="bold" data-semantic-annotation="clearspeak:simple" data-semantic-id="0">v</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\\displaystyle \\mathbf {v} }</annotation></semantics></math>', 'svg' => '<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.411ex" height="1.676ex" style="vertical-align: -0.338ex;" viewBox="0 -576.1 607.5 721.6" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" aria-labelledby="MathJax-SVG-1-Title"><title id="MathJax-SVG-1-Title">bold v</title><defs aria-hidden="true"><path stroke-width="1" id="E1-MJMAINB-76" d="M401 444Q413 441 495 441Q568 441 574 444H580V382H510L409 156Q348 18 339 6Q331 -4 320 -4Q318 -4 313 -4T303 -3H288Q273 -3 264 12T221 102Q206 135 197 156L96 382H26V444H34Q49 441 145 441Q252 441 270 444H279V382H231L284 264Q335 149 338 149Q338 150 389 264T442 381Q442 382 418 382H394V444H401Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)" aria-hidden="true"> <use xlink:href="#E1-MJMAINB-76" x="0" y="0"></use></g></svg>', 'width' => '1.411ex', 'height' => '1.676ex', 'style' => 'vertical-align: -0.338ex;', 'streeJson' => (object) array( 'stree' => (object) array( 'type' => 'identifier', 'role' => 'latinletter', 'font' => 'bold', 'annotation' => 'clearspeak:simple', 'id' => '0', '$t' => 'v', ), ), 'streeXml' => '<stree><identifier role="latinletter" font="bold" annotation="clearspeak:simple" id="0">v</identifier></stree>', 'success' => true, 'log' => 'success', 'mathoidStyle' => 'vertical-align: -0.338ex; width:1.411ex; height:1.676ex;', 'sanetex' => '{\\displaystyle \\mathbf {v} }', 'speech' => 'bold v', ), )“): {\displaystyle A } by Fehler beim Parsen (Konvertierungsfehler. Der Server („cli“) hat berichtet: „array ( 'nohash' => array ( ), 'success' => true, '98b434d091ae15b7180667a0296aae31' => (object) array( 'speakText' => 'bold v', 'mml' => '<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="bold v"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="bold" data-semantic-annotation="clearspeak:simple" data-semantic-id="0">v</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\\displaystyle \\mathbf {v} }</annotation></semantics></math>', 'svg' => '<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.411ex" height="1.676ex" style="vertical-align: -0.338ex;" viewBox="0 -576.1 607.5 721.6" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" aria-labelledby="MathJax-SVG-1-Title"><title id="MathJax-SVG-1-Title">bold v</title><defs aria-hidden="true"><path stroke-width="1" id="E1-MJMAINB-76" d="M401 444Q413 441 495 441Q568 441 574 444H580V382H510L409 156Q348 18 339 6Q331 -4 320 -4Q318 -4 313 -4T303 -3H288Q273 -3 264 12T221 102Q206 135 197 156L96 382H26V444H34Q49 441 145 441Q252 441 270 444H279V382H231L284 264Q335 149 338 149Q338 150 389 264T442 381Q442 382 418 382H394V444H401Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)" aria-hidden="true"> <use xlink:href="#E1-MJMAINB-76" x="0" y="0"></use></g></svg>', 'width' => '1.411ex', 'height' => '1.676ex', 'style' => 'vertical-align: -0.338ex;', 'streeJson' => (object) array( 'stree' => (object) array( 'type' => 'identifier', 'role' => 'latinletter', 'font' => 'bold', 'annotation' => 'clearspeak:simple', 'id' => '0', '$t' => 'v', ), ), 'streeXml' => '<stree><identifier role="latinletter" font="bold" annotation="clearspeak:simple" id="0">v</identifier></stree>', 'success' => true, 'log' => 'success', 'mathoidStyle' => 'vertical-align: -0.338ex; width:1.411ex; height:1.676ex;', 'sanetex' => '{\\displaystyle \\mathbf {v} }', 'speech' => 'bold v', ), )“): {\displaystyle T } . The translate of Fehler beim Parsen (Konvertierungsfehler. Der Server („cli“) hat berichtet: „array ( 'nohash' => array ( ), 'success' => true, '98b434d091ae15b7180667a0296aae31' => (object) array( 'speakText' => 'bold v', 'mml' => '<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="bold v"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="bold" data-semantic-annotation="clearspeak:simple" data-semantic-id="0">v</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\\displaystyle \\mathbf {v} }</annotation></semantics></math>', 'svg' => '<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.411ex" height="1.676ex" style="vertical-align: -0.338ex;" viewBox="0 -576.1 607.5 721.6" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" aria-labelledby="MathJax-SVG-1-Title"><title id="MathJax-SVG-1-Title">bold v</title><defs aria-hidden="true"><path stroke-width="1" id="E1-MJMAINB-76" d="M401 444Q413 441 495 441Q568 441 574 444H580V382H510L409 156Q348 18 339 6Q331 -4 320 -4Q318 -4 313 -4T303 -3H288Q273 -3 264 12T221 102Q206 135 197 156L96 382H26V444H34Q49 441 145 441Q252 441 270 444H279V382H231L284 264Q335 149 338 149Q338 150 389 264T442 381Q442 382 418 382H394V444H401Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)" aria-hidden="true"> <use xlink:href="#E1-MJMAINB-76" x="0" y="0"></use></g></svg>', 'width' => '1.411ex', 'height' => '1.676ex', 'style' => 'vertical-align: -0.338ex;', 'streeJson' => (object) array( 'stree' => (object) array( 'type' => 'identifier', 'role' => 'latinletter', 'font' => 'bold', 'annotation' => 'clearspeak:simple', 'id' => '0', '$t' => 'v', ), ), 'streeXml' => '<stree><identifier role="latinletter" font="bold" annotation="clearspeak:simple" id="0">v</identifier></stree>', 'success' => true, 'log' => 'success', 'mathoidStyle' => 'vertical-align: -0.338ex; width:1.411ex; height:1.676ex;', 'sanetex' => '{\\displaystyle \\mathbf {v} }', 'speech' => 'bold v', ), )“): {\displaystyle A } by Fehler beim Parsen (Konvertierungsfehler. Der Server („cli“) hat berichtet: „array ( 'nohash' => array ( ), 'success' => true, '98b434d091ae15b7180667a0296aae31' => (object) array( 'speakText' => 'bold v', 'mml' => '<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="bold v"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="bold" data-semantic-annotation="clearspeak:simple" data-semantic-id="0">v</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\\displaystyle \\mathbf {v} }</annotation></semantics></math>', 'svg' => '<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.411ex" height="1.676ex" style="vertical-align: -0.338ex;" viewBox="0 -576.1 607.5 721.6" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" aria-labelledby="MathJax-SVG-1-Title"><title id="MathJax-SVG-1-Title">bold v</title><defs aria-hidden="true"><path stroke-width="1" id="E1-MJMAINB-76" d="M401 444Q413 441 495 441Q568 441 574 444H580V382H510L409 156Q348 18 339 6Q331 -4 320 -4Q318 -4 313 -4T303 -3H288Q273 -3 264 12T221 102Q206 135 197 156L96 382H26V444H34Q49 441 145 441Q252 441 270 444H279V382H231L284 264Q335 149 338 149Q338 150 389 264T442 381Q442 382 418 382H394V444H401Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)" aria-hidden="true"> <use xlink:href="#E1-MJMAINB-76" x="0" y="0"></use></g></svg>', 'width' => '1.411ex', 'height' => '1.676ex', 'style' => 'vertical-align: -0.338ex;', 'streeJson' => (object) array( 'stree' => (object) array( 'type' => 'identifier', 'role' => 'latinletter', 'font' => 'bold', 'annotation' => 'clearspeak:simple', 'id' => '0', '$t' => 'v', ), ), 'streeXml' => '<stree><identifier role="latinletter" font="bold" annotation="clearspeak:simple" id="0">v</identifier></stree>', 'success' => true, 'log' => 'success', 'mathoidStyle' => 'vertical-align: -0.338ex; width:1.411ex; height:1.676ex;', 'sanetex' => '{\\displaystyle \\mathbf {v} }', 'speech' => 'bold v', ), )“): {\displaystyle T_{\mathbf{v}} } is often written Fehler beim Parsen (Konvertierungsfehler. Der Server („cli“) hat berichtet: „array ( 'nohash' => array ( ), 'success' => true, '98b434d091ae15b7180667a0296aae31' => (object) array( 'speakText' => 'bold v', 'mml' => '<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="bold v"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="bold" data-semantic-annotation="clearspeak:simple" data-semantic-id="0">v</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\\displaystyle \\mathbf {v} }</annotation></semantics></math>', 'svg' => '<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.411ex" height="1.676ex" style="vertical-align: -0.338ex;" viewBox="0 -576.1 607.5 721.6" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" aria-labelledby="MathJax-SVG-1-Title"><title id="MathJax-SVG-1-Title">bold v</title><defs aria-hidden="true"><path stroke-width="1" id="E1-MJMAINB-76" d="M401 444Q413 441 495 441Q568 441 574 444H580V382H510L409 156Q348 18 339 6Q331 -4 320 -4Q318 -4 313 -4T303 -3H288Q273 -3 264 12T221 102Q206 135 197 156L96 382H26V444H34Q49 441 145 441Q252 441 270 444H279V382H231L284 264Q335 149 338 149Q338 150 389 264T442 381Q442 382 418 382H394V444H401Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)" aria-hidden="true"> <use xlink:href="#E1-MJMAINB-76" x="0" y="0"></use></g></svg>', 'width' => '1.411ex', 'height' => '1.676ex', 'style' => 'vertical-align: -0.338ex;', 'streeJson' => (object) array( 'stree' => (object) array( 'type' => 'identifier', 'role' => 'latinletter', 'font' => 'bold', 'annotation' => 'clearspeak:simple', 'id' => '0', '$t' => 'v', ), ), 'streeXml' => '<stree><identifier role="latinletter" font="bold" annotation="clearspeak:simple" id="0">v</identifier></stree>', 'success' => true, 'log' => 'success', 'mathoidStyle' => 'vertical-align: -0.338ex; width:1.411ex; height:1.676ex;', 'sanetex' => '{\\displaystyle \\mathbf {v} }', 'speech' => 'bold v', ), )“): {\displaystyle A+\mathbf{v} } .

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

Translation (geometry)-50289677

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

Fußnote [1]