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id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Início</div> </a> </li> <li id="toc-Ver_também" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ver_também"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Ver também</span> </div> </a> <ul id="toc-Ver_também-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Referências" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Referências"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Referências</span> </div> </a> <ul id="toc-Referências-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Conteúdo" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Alternar o índice" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Alternar o índice</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Translação</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Ir para um artigo noutra língua. Disponível em 22 línguas" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-22" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">22 línguas</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9F%D0%B0%D1%81%D1%82%D1%83%D0%BF%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D1%80%D1%83%D1%85" title="Паступальны рух — bielorrusso" lang="be" hreflang="be" data-title="Паступальны рух" data-language-autonym="Беларуская" data-language-local-name="bielorrusso" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9F%D0%B0%D1%81%D1%82%D1%83%D0%BF%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D1%80%D1%83%D1%85" title="Паступальны рух — Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Паступальны рух" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Translaci%C3%B3_(f%C3%ADsica)" title="Translació (física) — catalão" lang="ca" hreflang="ca" data-title="Translació (física)" data-language-autonym="Català" data-language-local-name="catalão" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Posuvn%C3%BD_pohyb" title="Posuvný pohyb — checo" lang="cs" hreflang="cs" data-title="Posuvný pohyb" data-language-autonym="Čeština" data-language-local-name="checo" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A2%D0%B0%D0%BF%D1%80%D0%B0%D0%BD%D1%83%D0%BB%D0%BB%C4%83_%D0%BA%D1%83%C3%A7%C4%83%D0%BC" title="Тапрануллă куçăм — chuvash" lang="cv" hreflang="cv" data-title="Тапрануллă куçăм" data-language-autonym="Чӑвашла" data-language-local-name="chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Translation_(Physik)" title="Translation (Physik) — alemão" lang="de" hreflang="de" data-title="Translation (Physik)" data-language-autonym="Deutsch" data-language-local-name="alemão" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en badge-Q70893996 mw-list-item" title=""><a href="https://en.wikipedia.org/wiki/Translational_motion" title="Translational motion — inglês" lang="en" hreflang="en" data-title="Translational motion" data-language-autonym="English" data-language-local-name="inglês" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Traslaci%C3%B3n_(f%C3%ADsica)" title="Traslación (física) — espanhol" lang="es" hreflang="es" data-title="Traslación (física)" data-language-autonym="Español" data-language-local-name="espanhol" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Kulgliikumine" title="Kulgliikumine — estónio" lang="et" hreflang="et" data-title="Kulgliikumine" data-language-autonym="Eesti" data-language-local-name="estónio" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AC%D8%A7%D8%A8%D9%87%E2%80%8C%D8%AC%D8%A7%DB%8C%DB%8C" title="جابه‌جایی — persa" lang="fa" hreflang="fa" data-title="جابه‌جایی" data-language-autonym="فارسی" data-language-local-name="persa" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%80%D5%A1%D5%B4%D5%A8%D5%B6%D5%A9%D5%A1%D6%81_%D5%B7%D5%A1%D6%80%D5%AA%D5%B8%D6%82%D5%B4" title="Համընթաց շարժում — arménio" lang="hy" hreflang="hy" data-title="Համընթաց շարժում" data-language-autonym="Հայերեն" data-language-local-name="arménio" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%86%D0%BB%D0%B3%D0%B5%D1%80%D1%96%D0%BB%D0%B5%D0%BC%D0%B5%D0%BB%D1%96_%D2%9B%D0%BE%D0%B7%D2%93%D0%B0%D0%BB%D1%8B%D1%81" title="Ілгерілемелі қозғалыс — cazaque" lang="kk" hreflang="kk" data-title="Ілгерілемелі қозғалыс" data-language-autonym="Қазақша" data-language-local-name="cazaque" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Virzes_kust%C4%ABba" title="Virzes kustība — letão" lang="lv" hreflang="lv" data-title="Virzes kustība" data-language-autonym="Latviešu" data-language-local-name="letão" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Translatie_(natuurkunde)" title="Translatie (natuurkunde) — neerlandês" lang="nl" hreflang="nl" data-title="Translatie (natuurkunde)" data-language-autonym="Nederlands" data-language-local-name="neerlandês" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Translasjon_(fysikk)" title="Translasjon (fysikk) — norueguês bokmål" lang="nb" hreflang="nb" data-title="Translasjon (fysikk)" data-language-autonym="Norsk bokmål" data-language-local-name="norueguês bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Ruch_post%C4%99powy" title="Ruch postępowy — polaco" lang="pl" hreflang="pl" data-title="Ruch postępowy" data-language-autonym="Polski" data-language-local-name="polaco" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9F%D0%BE%D1%81%D1%82%D1%83%D0%BF%D0%B0%D1%82%D0%B5%D0%BB%D1%8C%D0%BD%D0%BE%D0%B5_%D0%B4%D0%B2%D0%B8%D0%B6%D0%B5%D0%BD%D0%B8%D0%B5" title="Поступательное движение — russo" lang="ru" hreflang="ru" data-title="Поступательное движение" data-language-autonym="Русский" data-language-local-name="russo" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Posuvn%C3%BD_pohyb" title="Posuvný pohyb — eslovaco" lang="sk" hreflang="sk" data-title="Posuvný pohyb" data-language-autonym="Slovenčina" data-language-local-name="eslovaco" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Translacija" title="Translacija — esloveno" lang="sl" hreflang="sl" data-title="Translacija" data-language-autonym="Slovenščina" data-language-local-name="esloveno" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Gerak_lempeng" title="Gerak lempeng — sundanês" lang="su" hreflang="su" data-title="Gerak lempeng" data-language-autonym="Sunda" data-language-local-name="sundanês" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9F%D0%BE%D1%81%D1%82%D1%83%D0%BF%D0%B0%D0%BB%D1%8C%D0%BD%D0%B8%D0%B9_%D1%80%D1%83%D1%85" title="Поступальний рух — ucraniano" lang="uk" hreflang="uk" data-title="Поступальний рух" data-language-autonym="Українська" data-language-local-name="ucraniano" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%B9%B3%E7%A7%BB%E8%BF%90%E5%8A%A8" title="平移运动 — chinês" lang="zh" hreflang="zh" data-title="平移运动" data-language-autonym="中文" data-language-local-name="chinês" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q1129632#sitelinks-wikipedia" title="Editar hiperligações interlínguas" class="wbc-editpage">Editar hiperligações</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Espaços nominais"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Transla%C3%A7%C3%A3o" title="Ver a página de conteúdo [c]" accesskey="c"><span>Artigo</span></a></li><li id="ca-talk" 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mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Imprimir/exportar </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Especial:Livro&bookcmd=book_creator&referer=Transla%C3%A7%C3%A3o"><span>Criar um livro</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Especial:DownloadAsPdf&page=Transla%C3%A7%C3%A3o&action=show-download-screen"><span>Descarregar como PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Transla%C3%A7%C3%A3o&printable=yes" title="Versão para impressão desta página [p]" accesskey="p"><span>Versão para impressão</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> Noutros projetos </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q1129632" title="Hiperligação para o elemento do repositório de dados [g]" accesskey="g"><span>Elemento Wikidata</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Ferramentas de página"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Aspeto"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Aspeto</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">mover para a barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">ocultar</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Origem: Wikipédia, a enciclopédia livre.</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="pt" dir="ltr"><div class="hatnote"><span typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Disambig_grey.svg/20px-Disambig_grey.svg.png" decoding="async" width="20" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Disambig_grey.svg/30px-Disambig_grey.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Disambig_grey.svg/40px-Disambig_grey.svg.png 2x" data-file-width="260" data-file-height="200" /></span></span> <b>Nota:</b> Para a translação na geometria euclidiana, veja <a href="/wiki/Transla%C3%A7%C3%A3o_(geometria)" title="Translação (geometria)">Translação (geometria)</a>.</div> <style data-mw-deduplicate="TemplateStyles:r68971778">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output 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#c0c090}.mw-parser-output .tmbox-style{border:2px solid #fc3}.mw-parser-output .tmbox-move{border:2px solid #9932cc}.mw-parser-output .tmbox .mbox-text{border:none;padding:0.25em 0.9em;width:100%}.mw-parser-output .tmbox .mbox-image{border:none;padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .tmbox .mbox-imageright{border:none;padding:2px 0.9em 2px 0;text-align:center}.mw-parser-output .tmbox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .tmbox .mbox-invalid-type{text-align:center}@media(min-width:720px){.mw-parser-output .tmbox{margin:4px 10%}.mw-parser-output .tmbox.mbox-small{clear:right;float:right;margin:4px 0 4px 1em;width:238px}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmbox{background-color:#2e2505}html.skin-theme-clientpref-night .mw-parser-output .tmbox-speedy{background-color:#310402}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmbox{background-color:#2e2505}html.skin-theme-clientpref-os .mw-parser-output .tmbox-speedy{background-color:#310402}}body.skin--responsive .mw-parser-output table.tmbox img{max-width:none!important}</style><table class="plainlinks metadata ambox ambox-move" role="presentation"><tbody><tr><td class="mbox-image"><div style="width:52px"><span typeof="mw:File"><a href="/wiki/Ficheiro:Mergefrom_2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Mergefrom_2.svg/50px-Mergefrom_2.svg.png" decoding="async" width="50" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Mergefrom_2.svg/75px-Mergefrom_2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Mergefrom_2.svg/100px-Mergefrom_2.svg.png 2x" data-file-width="50" data-file-height="20" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">O artigo ou secção <a href="/wiki/Transla%C3%A7%C3%A3o_(geometria)" title="Translação (geometria)">Translação (geometria)</a> deverá ser <a href="/wiki/Wikip%C3%A9dia:Fus%C3%A3o" title="Wikipédia:Fusão">fundido</a> aqui.<small> (desde novembro de 2021)</small><br />Se discorda, discuta sobre esta fusão na <a href="/wiki/Discuss%C3%A3o:Transla%C3%A7%C3%A3o" title="Discussão:Translação">página de discussão</a> deste artigo.</div></td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r68971778"><table class="plainlinks metadata ambox ambox-content" role="presentation"><tbody><tr><td class="mbox-image"><div style="width:52px"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Ambox_important.svg/40px-Ambox_important.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Ambox_important.svg/60px-Ambox_important.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Ambox_important.svg/80px-Ambox_important.svg.png 2x" data-file-width="40" data-file-height="40" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span"><div class="mw-collapsible" style="width:95%; margin: 0.2em 0;">Foram assinalados vários problemas nesta página ou se(c)ção:<span class="hide-when-compact"> <div class="mw-collapsible-content" style="margin-top: 0.3em;"> <ul><li>As fontes <b>não <a href="/wiki/Wikip%C3%A9dia:Livro_de_estilo/Cite_as_fontes" title="Wikipédia:Livro de estilo/Cite as fontes">cobrem todo o texto</a></b>.</li> <li>Contém <b><a href="/wiki/Wikip%C3%A9dia:Livro_de_estilo/Cite_as_fontes" title="Wikipédia:Livro de estilo/Cite as fontes">referências</a></b> que necessitam de formatação.</li></ul> </div></span></div></div></td></tr></tbody></table> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Ficheiro:Traslazione.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/49/Traslazione.gif/220px-Traslazione.gif" decoding="async" width="220" height="144" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/49/Traslazione.gif/330px-Traslazione.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/49/Traslazione.gif/440px-Traslazione.gif 2x" data-file-width="696" data-file-height="457" /></a><figcaption>Translação de três objectos</figcaption></figure> <p><b>Translação</b> é o <a href="/wiki/Movimento" title="Movimento">movimento</a> que um <a href="/wiki/Objeto" title="Objeto">objeto</a> realiza de um ponto a outro. É o deslocamento <a href="/wiki/Paralelo" title="Paralelo">paralelo</a>, em <a href="/wiki/Reta" title="Reta">linha reta</a> na mesma direção e no mesmo sentido, de um objeto ou figura, em função de um <a href="/wiki/Vetor_espacial" class="mw-redirect" title="Vetor espacial">vetor</a> percorrendo a mesma distância. </p><p>Uma translação é uma isometria que desloca a figura original segundo uma direção, um sentido e um comprimento (<a href="/wiki/Vetor_(matem%C3%A1tica)" title="Vetor (matemática)">vetor</a>). As translações conservam a direção e o comprimento de segmentos de reta, e as amplitudes dos ângulos. </p><p>Na simetria de translação, a figura "desliza" sobre uma reta, mantendo-se inalterada. Podemos citar como exemplo de translação, <a href="/wiki/Elevador" title="Elevador">elevadores</a>, <a href="/wiki/Escada_rolante" title="Escada rolante">escadas rolantes</a> e até mesmo <a href="/wiki/Escorregador" title="Escorregador">escorregadores</a>. </p><p>Em todas as translações se observa que um mesmo elemento se desloca numa determinada direção e sempre paralelo a si próprio, isto é, sem nunca rodar. Num friso há um motivo que se repete periodicamente, numa determinada direção e sempre paralelo a si mesmo. </p><p>“Seja AB um segmento orientado, no plano π ou no espaço E. (Orientado significa que a ordem em que os extremos são citados é relevante: primeiro A, e depois B.) A translação determinada por AB é a transformação (correspondência biunívoca) τ : π → π, ou τ : E → E, definida por τ(X) = X’, de modo que (AB, XX’) e (AX, BX’) sejam os pares de lados opostos de um paralelogramo”. <sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span>[</span>1<span>]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Ver_também"><span id="Ver_tamb.C3.A9m"></span>Ver também</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Transla%C3%A7%C3%A3o&veaction=edit&section=1" title="Editar secção: Ver também" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Transla%C3%A7%C3%A3o&action=edit&section=1" title="Editar código-fonte da secção: Ver também"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Transla%C3%A7%C3%A3o_da_Terra" title="Translação da Terra">Translação da Terra</a></li></ul> <h2 id="Referências" style="cursor: help;" title="Esta seção foi configurada para não ser editável diretamente. Edite a página toda ou a seção anterior em vez disso."><span id="Refer.C3.AAncias"></span>Referências</h2> <div class="reflist" style="list-style-type: decimal;"><div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">LIMA, 2001</span> </li> </ol></div></div> <div role="navigation" class="navbox" aria-labelledby="Controle_de_autoridade" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th id="Controle_de_autoridade" scope="row" class="navbox-group" style="width:1%;width: 12%; text-align:center;"><a href="/wiki/Ajuda:Controle_de_autoridade" title="Ajuda:Controle de autoridade">Controle de autoridade</a></th><td class="navbox-list navbox-odd plainlinks" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><span style="white-space:nowrap;"><span typeof="mw:File"><a href="https://www.wikidata.org/wiki/Wikidata:Main_Page" title="Wikidata"><img alt="Wd" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/20px-Wikidata-logo.svg.png" decoding="async" width="20" height="11" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/30px-Wikidata-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/40px-Wikidata-logo.svg.png 2x" data-file-width="1050" data-file-height="590" /></a></span>: <span class="uid"><a href="https://www.wikidata.org/wiki/Q1129632" class="extiw" title="wikidata:Q1129632">Q1129632</a></span></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/Biblioteca_T%C3%A9cnica_Nacional_de_Praga" title="Biblioteca Técnica Nacional de Praga">PSH</a>: <span class="uid"><span class="plainlinks"><a rel="nofollow" class="external text" href="https://psh.techlib.cz/skos/PSH2937">2937</a></span></span></span></li></ul> </div></td></tr></tbody></table></div> <table class="noprint" style="border-top:none; border-bottom:none; background:transparent; color: inherit"><tbody><tr> <td style="text-align: center;"><span typeof="mw:File"><a href="/wiki/Ficheiro:E-to-the-i-pi.svg" class="mw-file-description"><img alt="Ícone de esboço" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/E-to-the-i-pi.svg/34px-E-to-the-i-pi.svg.png" decoding="async" width="34" height="30" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/E-to-the-i-pi.svg/51px-E-to-the-i-pi.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/35/E-to-the-i-pi.svg/68px-E-to-the-i-pi.svg.png 2x" data-file-width="512" data-file-height="453" /></a></span></td> <td><i>Este artigo sobre <a href="/wiki/Matem%C3%A1tica" title="Matemática">matemática</a> é um <a href="/wiki/Wikip%C3%A9dia:Esbo%C3%A7o" title="Wikipédia:Esboço">esboço</a>. 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