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class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">mòu a la barra laterala</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">Escondre</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li 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">Començament</div> </a> </li> <li id="toc-Calcul_del_rai" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Calcul_del_rai"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Calcul del rai</span> </div> </a> <ul id="toc-Calcul_del_rai-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Aira_de_l'ellipsa" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Aira_de_l'ellipsa"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Aira de l'ellipsa</span> </div> </a> <ul id="toc-Aira_de_l'ellipsa-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lo_rai_terrèstre" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Lo_rai_terrèstre"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Lo rai terrèstre</span> </div> </a> <button aria-controls="toc-Lo_rai_terrèstre-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Commuta la subsecció Lo rai terrèstre</span> </button> <ul id="toc-Lo_rai_terrèstre-sublist" class="vector-toc-list"> <li id="toc-Sa_mesura" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Sa_mesura"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Sa mesura</span> </div> </a> <ul id="toc-Sa_mesura-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Son_utilizacion" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Son_utilizacion"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Son utilizacion</span> </div> </a> <ul id="toc-Son_utilizacion-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Bibliografia" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliografia"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Bibliografia</span> </div> </a> <ul id="toc-Bibliografia-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="Somari" 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="Commuta la taula de continguts." > <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">Commuta la taula de continguts.</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">Rai (geometria)</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="Vés a un article en una altra llengua. Disponible en 102 llengües" > <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-102" 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">102 lengas</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Radius" title="Radius - afrikaans" lang="af" hreflang="af" data-title="Radius" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Radius_(Kreis)" title="Radius (Kreis) - aleman de Soïssa" lang="gsw" hreflang="gsw" data-title="Radius (Kreis)" data-language-autonym="Alemannisch" data-language-local-name="aleman de Soïssa" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%88%AC%E1%8B%B5%E1%8B%A8%E1%88%B5" title="ሬድየስ - amaric" lang="am" hreflang="am" data-title="ሬድየስ" data-language-autonym="አማርኛ" data-language-local-name="amaric" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Radio_(cheometr%C3%ADa)" title="Radio (cheometría) - aragonés" lang="an" hreflang="an" data-title="Radio (cheometría)" data-language-autonym="Aragonés" data-language-local-name="aragonés" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%86%D8%B5%D9%81_%D8%A7%D9%84%D9%82%D8%B7%D8%B1" title="نصف القطر - arabi" lang="ar" hreflang="ar" data-title="نصف القطر" data-language-autonym="العربية" data-language-local-name="arabi" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Radiu_(xeometr%C3%ADa)" title="Radiu (xeometría) - asturian" lang="ast" hreflang="ast" data-title="Radiu (xeometría)" data-language-autonym="Asturianu" data-language-local-name="asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Radius" title="Radius - azerbaijani" lang="az" hreflang="az" data-title="Radius" data-language-autonym="Azərbaycanca" data-language-local-name="azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B4%D0%B8%D1%83%D1%81" title="Радиус - baixkir" lang="ba" hreflang="ba" data-title="Радиус" data-language-autonym="Башҡортса" data-language-local-name="baixkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B4%D1%8B%D1%83%D1%81" title="Радыус - belarús" lang="be" hreflang="be" data-title="Радыус" data-language-autonym="Беларуская" data-language-local-name="belarús" 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%A0%D0%B0%D0%B4%D1%8B%D1%8E%D1%81" title="Радыюс - Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Радыюс" 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-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B4%D0%B8%D1%83%D1%81" title="Радиус - bulgar" lang="bg" hreflang="bg" data-title="Радиус" data-language-autonym="Български" data-language-local-name="bulgar" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AC%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%B8%E0%A6%BE%E0%A6%B0%E0%A7%8D%E0%A6%A7" title="ব্যাসার্ধ - bengalin" lang="bn" hreflang="bn" data-title="ব্যাসার্ধ" data-language-autonym="বাংলা" data-language-local-name="bengalin" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Skin_(geometriezh)" title="Skin (geometriezh) - breton" lang="br" hreflang="br" data-title="Skin (geometriezh)" data-language-autonym="Brezhoneg" data-language-local-name="breton" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Polupre%C4%8Dnik" title="Poluprečnik - bosniac" lang="bs" hreflang="bs" data-title="Poluprečnik" data-language-autonym="Bosanski" data-language-local-name="bosniac" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Radi_(geometria)" title="Radi (geometria) - catalan" lang="ca" hreflang="ca" data-title="Radi (geometria)" data-language-autonym="Català" data-language-local-name="catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%86%DB%8C%D9%88%DB%95%D8%AA%DB%8C%D8%B1%DB%95" title="نیوەتیرە - kurd central" lang="ckb" hreflang="ckb" data-title="نیوەتیرە" data-language-autonym="کوردی" data-language-local-name="kurd central" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Polom%C4%9Br" title="Poloměr - chèc" lang="cs" hreflang="cs" data-title="Poloměr" data-language-autonym="Čeština" data-language-local-name="chèc" 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%A0%D0%B0%D0%B4%D0%B8%D1%83%D1%81" title="Радиус - chovash" lang="cv" hreflang="cv" data-title="Радиус" data-language-autonym="Чӑвашла" data-language-local-name="chovash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Radiws" title="Radiws - gal·lès" lang="cy" hreflang="cy" data-title="Radiws" data-language-autonym="Cymraeg" data-language-local-name="gal·lès" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Radius" title="Radius - danés" lang="da" hreflang="da" data-title="Radius" data-language-autonym="Dansk" data-language-local-name="danés" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Radius" title="Radius - alemand" lang="de" hreflang="de" data-title="Radius" data-language-autonym="Deutsch" data-language-local-name="alemand" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%91%CE%BA%CF%84%CE%AF%CE%BD%CE%B1_(%CE%B3%CE%B5%CF%89%CE%BC%CE%B5%CF%84%CF%81%CE%AF%CE%B1)" title="Ακτίνα (γεωμετρία) - grèc" lang="el" hreflang="el" data-title="Ακτίνα (γεωμετρία)" data-language-autonym="Ελληνικά" data-language-local-name="grèc" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-eml mw-list-item"><a href="https://eml.wikipedia.org/wiki/R%C3%A2%C7%B5_(giumetr%C3%ACa)" title="Râǵ (giumetrìa) - Emiliano-Romagnolo" lang="egl" hreflang="egl" data-title="Râǵ (giumetrìa)" data-language-autonym="Emiliàn e rumagnòl" data-language-local-name="Emiliano-Romagnolo" class="interlanguage-link-target"><span>Emiliàn e rumagnòl</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Radius" title="Radius - anglés" lang="en" hreflang="en" data-title="Radius" data-language-autonym="English" data-language-local-name="anglés" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Radiuso" title="Radiuso - esperanto" lang="eo" hreflang="eo" data-title="Radiuso" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Radio_(geometr%C3%ADa)" title="Radio (geometría) - espanhòl" lang="es" hreflang="es" data-title="Radio (geometría)" data-language-autonym="Español" data-language-local-name="espanhòl" 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/Raadius" title="Raadius - estonian" lang="et" hreflang="et" data-title="Raadius" data-language-autonym="Eesti" data-language-local-name="estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Erradio_(geometria)" title="Erradio (geometria) - basc" lang="eu" hreflang="eu" data-title="Erradio (geometria)" data-language-autonym="Euskara" data-language-local-name="basc" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B4%D8%B9%D8%A7%D8%B9" title="شعاع - perse" lang="fa" hreflang="fa" data-title="شعاع" data-language-autonym="فارسی" data-language-local-name="perse" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/S%C3%A4de_(geometria)" title="Säde (geometria) - finlandés" lang="fi" hreflang="fi" data-title="Säde (geometria)" data-language-autonym="Suomi" data-language-local-name="finlandés" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Rayon_(g%C3%A9om%C3%A9trie)" title="Rayon (géométrie) - francés" lang="fr" hreflang="fr" data-title="Rayon (géométrie)" data-language-autonym="Français" data-language-local-name="francés" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frr badge-Q70894304 mw-list-item" title=""><a href="https://frr.wikipedia.org/wiki/Raadius" title="Raadius - frisó septentrional" lang="frr" hreflang="frr" data-title="Raadius" data-language-autonym="Nordfriisk" data-language-local-name="frisó septentrional" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/Reidius" title="Reidius - gaelic escossés" lang="gd" hreflang="gd" data-title="Reidius" data-language-autonym="Gàidhlig" data-language-local-name="gaelic escossés" class="interlanguage-link-target"><span>Gàidhlig</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Raio_(xeometr%C3%ADa)" title="Raio (xeometría) - galician" lang="gl" hreflang="gl" data-title="Raio (xeometría)" data-language-autonym="Galego" data-language-local-name="galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%A4%E0%AB%8D%E0%AA%B0%E0%AA%BF%E0%AA%9C%E0%AB%8D%E0%AA%AF%E0%AA%BE" title="ત્રિજ્યા - gujarati" lang="gu" hreflang="gu" data-title="ત્રિજ્યા" data-language-autonym="ગુજરાતી" data-language-local-name="gujarati" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A8%D7%93%D7%99%D7%95%D7%A1" title="רדיוס - ebrèu" lang="he" hreflang="he" data-title="רדיוס" data-language-autonym="עברית" data-language-local-name="ebrèu" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%BF%E0%A4%9C%E0%A5%8D%E0%A4%AF%E0%A4%BE" title="त्रिज्या - Indi" lang="hi" hreflang="hi" data-title="त्रिज्या" data-language-autonym="हिन्दी" data-language-local-name="Indi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%87%D5%A1%D5%BC%D5%A1%D5%BE%D5%AB%D5%B2" title="Շառավիղ - armèni" lang="hy" hreflang="hy" data-title="Շառավիղ" data-language-autonym="Հայերեն" data-language-local-name="armèni" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Radio_(geometria)" title="Radio (geometria) - interlingua" lang="ia" hreflang="ia" data-title="Radio (geometria)" data-language-autonym="Interlingua" data-language-local-name="interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Jari-jari" title="Jari-jari - indonesian" lang="id" hreflang="id" data-title="Jari-jari" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-inh mw-list-item"><a href="https://inh.wikipedia.org/wiki/%D0%93%D3%80%D0%B0%D0%B9%D0%B8%D1%81%D1%82" title="ГӀайист - ingúix" lang="inh" hreflang="inh" data-title="ГӀайист" data-language-autonym="ГӀалгӀай" data-language-local-name="ingúix" class="interlanguage-link-target"><span>ГӀалгӀай</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Geisli_(r%C3%BAmfr%C3%A6%C3%B0i)" title="Geisli (rúmfræði) - islandés" lang="is" hreflang="is" data-title="Geisli (rúmfræði)" data-language-autonym="Íslenska" data-language-local-name="islandés" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Raggio_(geometria)" title="Raggio (geometria) - italian" lang="it" hreflang="it" data-title="Raggio (geometria)" data-language-autonym="Italiano" data-language-local-name="italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%8D%8A%E5%BE%84" title="半径 - japonés" lang="ja" hreflang="ja" data-title="半径" data-language-autonym="日本語" data-language-local-name="japonés" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A0%E1%83%90%E1%83%93%E1%83%98%E1%83%A3%E1%83%A1%E1%83%98" title="რადიუსი - georgian" lang="ka" hreflang="ka" data-title="რადიუსი" data-language-autonym="ქართული" data-language-local-name="georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Aqqa%E1%B9%9B" title="Aqqaṛ - cabil" lang="kab" hreflang="kab" data-title="Aqqaṛ" data-language-autonym="Taqbaylit" data-language-local-name="cabil" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B4%D0%B8%D1%83%D1%81" title="Радиус - cazac" lang="kk" hreflang="kk" data-title="Радиус" data-language-autonym="Қазақша" data-language-local-name="cazac" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%80%E1%9E%B6%E1%9F%86" title="កាំ - cambojian" lang="km" hreflang="km" data-title="កាំ" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="cambojian" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B0%98%EC%A7%80%EB%A6%84" title="반지름 - corean" lang="ko" hreflang="ko" data-title="반지름" data-language-autonym="한국어" data-language-local-name="corean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B4%D0%B8%D1%83%D1%81_(%D0%B0%D0%B9%D0%BB%D0%B0%D0%BD%D0%B0%D0%BD%D1%8B%D0%BD)" title="Радиус (айлананын) - kirguís" lang="ky" hreflang="ky" data-title="Радиус (айлананын)" data-language-autonym="Кыргызча" data-language-local-name="kirguís" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Radius" title="Radius - luxemborgés" lang="lb" hreflang="lb" data-title="Radius" data-language-autonym="Lëtzebuergesch" data-language-local-name="luxemborgés" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Apskritimo_spindulys" title="Apskritimo spindulys - lituan" lang="lt" hreflang="lt" data-title="Apskritimo spindulys" data-language-autonym="Lietuvių" data-language-local-name="lituan" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/R%C4%81diuss" title="Rādiuss - leton" lang="lv" hreflang="lv" data-title="Rādiuss" data-language-autonym="Latviešu" data-language-local-name="leton" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Tana_(je%C3%B4metria)" title="Tana (jeômetria) - malgash" lang="mg" hreflang="mg" data-title="Tana (jeômetria)" data-language-autonym="Malagasy" data-language-local-name="malgash" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9F%D0%BE%D0%BB%D1%83%D0%BF%D1%80%D0%B5%D1%87%D0%BD%D0%B8%D0%BA" title="Полупречник - macedonian" lang="mk" hreflang="mk" data-title="Полупречник" data-language-autonym="Македонски" data-language-local-name="macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%86%E0%B4%B0%E0%B4%82" title="ആരം - malaiàlam" lang="ml" hreflang="ml" data-title="ആരം" data-language-autonym="മലയാളം" data-language-local-name="malaiàlam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B4%D0%B8%D1%83%D1%81" title="Радиус - mongòl" lang="mn" hreflang="mn" data-title="Радиус" data-language-autonym="Монгол" data-language-local-name="mongòl" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%BF%E0%A4%9C%E0%A5%8D%E0%A4%AF%E0%A4%BE" title="त्रिज्या - marathi" lang="mr" hreflang="mr" data-title="त्रिज्या" data-language-autonym="मराठी" data-language-local-name="marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Jejari" title="Jejari - malai" lang="ms" hreflang="ms" data-title="Jejari" data-language-autonym="Bahasa Melayu" data-language-local-name="malai" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%A1%E1%80%81%E1%80%BB%E1%80%84%E1%80%BA%E1%80%B8%E1%80%9D%E1%80%80%E1%80%BA" title="အချင်းဝက် - birman" lang="my" hreflang="my" data-title="အချင်းဝက်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="birman" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%85%E0%A4%B0%E0%A5%8D%E0%A4%A7%E0%A4%B5%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%B8" title="अर्धव्यास - nepalés" lang="ne" hreflang="ne" data-title="अर्धव्यास" data-language-autonym="नेपाली" data-language-local-name="nepalés" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Straal_(wiskunde)" title="Straal (wiskunde) - neerlandés" lang="nl" hreflang="nl" data-title="Straal (wiskunde)" data-language-autonym="Nederlands" data-language-local-name="neerlandés" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Radius" title="Radius - norvegian nynorsk" lang="nn" hreflang="nn" data-title="Radius" data-language-autonym="Norsk nynorsk" data-language-local-name="norvegian nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Radius" title="Radius - norvegian bokmål" lang="nb" hreflang="nb" data-title="Radius" data-language-autonym="Norsk bokmål" data-language-local-name="norvegian bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Raadiyesii" title="Raadiyesii - oromo" lang="om" hreflang="om" data-title="Raadiyesii" data-language-autonym="Oromoo" data-language-local-name="oromo" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B0%E0%A9%87%E0%A8%A1%E0%A9%80%E0%A8%85%E0%A8%B8" title="ਰੇਡੀਅਸ - punjabi" lang="pa" hreflang="pa" data-title="ਰੇਡੀਅਸ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Promie%C5%84_(geometria)" title="Promień (geometria) - polonés" lang="pl" hreflang="pl" data-title="Promień (geometria)" data-language-autonym="Polski" data-language-local-name="polonés" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%B1%D8%AF%D8%A7%D8%B3" title="رداس - Western Punjabi" lang="pnb" hreflang="pnb" data-title="رداس" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Raio_(geometria)" title="Raio (geometria) - portugués" lang="pt" hreflang="pt" data-title="Raio (geometria)" data-language-autonym="Português" data-language-local-name="portugués" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Illwa" title="Illwa - quechua" lang="qu" hreflang="qu" data-title="Illwa" data-language-autonym="Runa Simi" data-language-local-name="quechua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Raz%C4%83" title="Rază - romanés" lang="ro" hreflang="ro" data-title="Rază" data-language-autonym="Română" data-language-local-name="romanés" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B4%D0%B8%D1%83%D1%81" title="Радиус - rus" lang="ru" hreflang="ru" data-title="Радиус" data-language-autonym="Русский" data-language-local-name="rus" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sc mw-list-item"><a href="https://sc.wikipedia.org/wiki/Raju_(geometria)" title="Raju (geometria) - sard" lang="sc" hreflang="sc" data-title="Raju (geometria)" data-language-autonym="Sardu" data-language-local-name="sard" class="interlanguage-link-target"><span>Sardu</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Radius" title="Radius - escossés" lang="sco" hreflang="sco" data-title="Radius" data-language-autonym="Scots" data-language-local-name="escossés" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Radijus" title="Radijus - serbocroat" lang="sh" hreflang="sh" data-title="Radijus" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbocroat" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%85%E0%B6%BB%E0%B6%BA" title="අරය - singalès" lang="si" hreflang="si" data-title="අරය" data-language-autonym="සිංහල" data-language-local-name="singalès" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Radius" title="Radius - Simple English" lang="en-simple" hreflang="en-simple" data-title="Radius" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Polomer_(kru%C5%BEnica)" title="Polomer (kružnica) - eslovac" lang="sk" hreflang="sk" data-title="Polomer (kružnica)" data-language-autonym="Slovenčina" data-language-local-name="eslovac" 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/Polmer" title="Polmer - eslovèn" lang="sl" hreflang="sl" data-title="Polmer" data-language-autonym="Slovenščina" data-language-local-name="eslovèn" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Taramunyongo" title="Taramunyongo - shona" lang="sn" hreflang="sn" data-title="Taramunyongo" data-language-autonym="ChiShona" data-language-local-name="shona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Gacan_(Joomitiri)" title="Gacan (Joomitiri) - somali" lang="so" hreflang="so" data-title="Gacan (Joomitiri)" data-language-autonym="Soomaaliga" data-language-local-name="somali" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Rrezja" title="Rrezja - albanés" lang="sq" hreflang="sq" data-title="Rrezja" data-language-autonym="Shqip" data-language-local-name="albanés" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9F%D0%BE%D0%BB%D1%83%D0%BF%D1%80%D0%B5%D1%87%D0%BD%D0%B8%D0%BA" title="Полупречник - serbi" lang="sr" hreflang="sr" data-title="Полупречник" data-language-autonym="Српски / srpski" data-language-local-name="serbi" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Radie" title="Radie - suedés" lang="sv" hreflang="sv" data-title="Radie" data-language-autonym="Svenska" data-language-local-name="suedés" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Nusukipenyo" title="Nusukipenyo - swahili" lang="sw" hreflang="sw" data-title="Nusukipenyo" data-language-autonym="Kiswahili" data-language-local-name="swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-szl mw-list-item"><a href="https://szl.wikipedia.org/wiki/Pr%C5%8Dmiy%C5%84_(geometryj%C5%8F)" title="Prōmiyń (geometryjŏ) - silesià" lang="szl" hreflang="szl" data-title="Prōmiyń (geometryjŏ)" data-language-autonym="Ślůnski" data-language-local-name="silesià" class="interlanguage-link-target"><span>Ślůnski</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%86%E0%AE%B0%E0%AE%AE%E0%AF%8D,_%E0%AE%B5%E0%AE%9F%E0%AE%BF%E0%AE%B5%E0%AE%BF%E0%AE%AF%E0%AE%B2%E0%AF%8D" title="ஆரம், வடிவியல் - tamol" lang="ta" hreflang="ta" data-title="ஆரம், வடிவியல்" data-language-autonym="தமிழ்" data-language-local-name="tamol" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%B5%E0%B1%8D%E0%B0%AF%E0%B0%BE%E0%B0%B8%E0%B0%BE%E0%B0%B0%E0%B1%8D%E0%B0%A5%E0%B0%AE%E0%B1%81" title="వ్యాసార్థము - telogó" lang="te" hreflang="te" data-title="వ్యాసార్థము" data-language-autonym="తెలుగు" data-language-local-name="telogó" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%A3%E0%B8%B1%E0%B8%A8%E0%B8%A1%E0%B8%B5" title="รัศมี - tai" lang="th" hreflang="th" data-title="รัศมี" data-language-autonym="ไทย" data-language-local-name="tai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Radius" title="Radius - tagal" lang="tl" hreflang="tl" data-title="Radius" data-language-autonym="Tagalog" data-language-local-name="tagal" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Yar%C4%B1%C3%A7ap" title="Yarıçap - turc" lang="tr" hreflang="tr" data-title="Yarıçap" data-language-autonym="Türkçe" data-language-local-name="turc" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B4%D0%B8%D1%83%D1%81" title="Радиус - tatar" lang="tt" hreflang="tt" data-title="Радиус" data-language-autonym="Татарча / tatarça" data-language-local-name="tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B4%D1%96%D1%83%D1%81" title="Радіус - ucrainés" lang="uk" hreflang="uk" data-title="Радіус" data-language-autonym="Українська" data-language-local-name="ucrainés" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%B1%D8%AF%D8%A7%D8%B3" title="رداس - ordó" lang="ur" hreflang="ur" data-title="رداس" data-language-autonym="اردو" data-language-local-name="ordó" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Radius" title="Radius - ozbèc" lang="uz" hreflang="uz" data-title="Radius" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="ozbèc" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/B%C3%A1n_k%C3%ADnh" title="Bán kính - vietnamian" lang="vi" hreflang="vi" data-title="Bán kính" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamian" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%8D%8A%E5%BE%84" title="半径 - xinès wu" lang="wuu" hreflang="wuu" data-title="半径" data-language-autonym="吴语" data-language-local-name="xinès wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A8%D7%90%D7%93%D7%99%D7%95%D7%A1" title="ראדיוס - 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id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="oc" dir="ltr"><figure class="mw-halign-right" typeof="mw:File"><a href="/wiki/Fichi%C3%A8r:CIRCLE_1.svg" class="mw-file-description" title="Rai, diamètre, circonferéncia, cercle"><img alt="Rai, diamètre, circonferéncia, cercle" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/CIRCLE_1.svg/220px-CIRCLE_1.svg.png" decoding="async" width="220" height="222" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/CIRCLE_1.svg/330px-CIRCLE_1.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1d/CIRCLE_1.svg/440px-CIRCLE_1.svg.png 2x" data-file-width="612" data-file-height="618" /></a><figcaption>Rai, diamètre, circonferéncia, cercle</figcaption></figure> <p>En <a href="/wiki/Geometria" title="Geometria">geometria</a>, lo <b>rai</b> d'un <a href="/wiki/Cercle" title="Cercle">cercle</a> o d'una <a href="/wiki/Esf%C3%A8ra" title="Esfèra">esfèra</a> es un <a href="/w/index.php?title=Segment_(matematicas)&action=edit&redlink=1" class="new" title="Segment (matematicas) (la pagina existís pas)">segment de drecha</a> quin que siá ligant son centre a sa <a href="/wiki/Circonfer%C3%A9ncia" title="Circonferéncia">circonferéncia</a>. Par extension, <b><i>lo</i> rai</b> d'un cercle o d'una esfèra es la <a href="/w/index.php?title=Longor&action=edit&redlink=1" class="new" title="Longor (la pagina existís pas)">longor</a> de cada d'aqueles segments. Lo rai es la mitat del <a href="/wiki/Diam%C3%A8tre" title="Diamètre">diamètre</a>. En sciéncias e en engenhariá, lo tèrme <a href="/w/index.php?title=Rai_de_corbadura&action=edit&redlink=1" class="new" title="Rai de corbadura (la pagina existís pas)">rai de corbadura</a> es sovent utilizat coma sinonim de rai. </p><p>Mai generalament — en <a href="/wiki/Geometria" title="Geometria">geometria</a>, <a href="/wiki/Engenhari%C3%A1" title="Engenhariá">engenhariá</a>, <a href="/w/index.php?title=Teoria_dels_grafes&action=edit&redlink=1" class="new" title="Teoria dels grafes (la pagina existís pas)">Teoria dels grafes</a>, e dins fòrça d'autres contèxtes — lo rai d'una causa (per exemple un <a href="/w/index.php?title=Cilindre&action=edit&redlink=1" class="new" title="Cilindre (la pagina existís pas)">cilindre</a>, un <a href="/wiki/Polig%C3%B2n" title="Poligòn">poligòn</a>, un <a href="/w/index.php?title=Teoria_dels_grafes&action=edit&redlink=1" class="new" title="Teoria dels grafes (la pagina existís pas)">graf</a>, o una pèça mecanica) es la <a href="/w/index.php?title=Dist%C3%A0ncia&action=edit&redlink=1" class="new" title="Distància (la pagina existís pas)">distància</a> de son <a href="/wiki/Centre" class="mw-disambig" title="Centre">centre</a> o axe de <a href="/wiki/Simetria" title="Simetria">simetria</a> a sos punts de superfícia mai alunhats. Dins aquel cas, lo rai pòt èsser pus grand que la mitat del diamètre. </p><p>La relacion entre lo rai <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/738e0cc81ec00b6037431a976a450a9499e90803" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.338ex; width:1ex; height:1.676ex;" alt="{\displaystyle r\!}"></span> e la <a href="/wiki/Circonfer%C3%A9ncia" title="Circonferéncia">circonferéncia</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62580b3a305faffbdacb0ea283dd1624bf9b37b2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.38ex; width:1ex; height:1.676ex;" alt="{\displaystyle c\!}"></span> d'un cercle es <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r={\frac {c}{2\pi }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>c</mi> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r={\frac {c}{2\pi }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d0629e741fc986f41a34efcbd5bb413a85a0bb81" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.478ex; height:4.676ex;" alt="{\displaystyle r={\frac {c}{2\pi }}}"></span>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Calcul_del_rai">Calcul del rai</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rai_(geometria)&veaction=edit&section=1" title="Modificar la seccion : Calcul del rai" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Rai_(geometria)&action=edit&section=1" title="Edita el codi de la secció: Calcul del rai"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File"><a href="/wiki/Fichi%C3%A8r:Cercle_circonscrit_%C3%A0_un_triangle.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Cercle_circonscrit_%C3%A0_un_triangle.svg/450px-Cercle_circonscrit_%C3%A0_un_triangle.svg.png" decoding="async" width="450" height="128" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Cercle_circonscrit_%C3%A0_un_triangle.svg/675px-Cercle_circonscrit_%C3%A0_un_triangle.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Cercle_circonscrit_%C3%A0_un_triangle.svg/900px-Cercle_circonscrit_%C3%A0_un_triangle.svg.png 2x" data-file-width="1769" data-file-height="504" /></a><figcaption></figcaption></figure> <p>Per calcular lo rai d'un cercle passant per tres punts <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{1},P_{2},P_{3}\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{1},P_{2},P_{3}\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5b621fdc184820d940a42371fd93a7f8fe5cc8e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:9.707ex; height:2.509ex;" alt="{\displaystyle P_{1},P_{2},P_{3}\!}"></span>, se pòt utilizar la formula seguenta: </p> <div style="text-align: center;"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r={\frac {|P_{1}-P_{3}|}{2\sin(\theta )}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mrow> <mrow> <mn>2</mn> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>θ</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r={\frac {|P_{1}-P_{3}|}{2\sin(\theta )}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b9229aa93f72dd6c04d808edcfed4ef53ada536" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:14.21ex; height:6.509ex;" alt="{\displaystyle r={\frac {|P_{1}-P_{3}|}{2\sin(\theta )}}}"></span> </p> </div> <p>ont <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta \!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta \!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f4648910623b113399a15dc3065ab747ea127b5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.371ex; width:1.074ex; height:2.176ex;" alt="{\displaystyle \theta \!}"></span> es l'<a href="/wiki/Angle" title="Angle">angle</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \angle P_{1}P_{2}P_{3}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∠</mi> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \angle P_{1}P_{2}P_{3}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/454a8723db8c3f7ce5988ab35a0a8484024a98cb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.964ex; height:2.509ex;" alt="{\displaystyle \angle P_{1}P_{2}P_{3}.}"></span> </p> <div style="clear:both;"></div> <div class="mw-heading mw-heading2"><h2 id="Aira_de_l'ellipsa"><span id="Aira_de_l.27ellipsa"></span>Aira de l'ellipsa</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rai_(geometria)&veaction=edit&section=2" title="Modificar la seccion : Aira de l'ellipsa" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Rai_(geometria)&action=edit&section=2" title="Edita el codi de la secció: Aira de l'ellipsa"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File"><a href="/wiki/Fichi%C3%A8r:Ellipse_affinite2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Ellipse_affinite2.png/200px-Ellipse_affinite2.png" decoding="async" width="200" height="174" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Ellipse_affinite2.png/300px-Ellipse_affinite2.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Ellipse_affinite2.png/400px-Ellipse_affinite2.png 2x" data-file-width="440" data-file-height="382" /></a><figcaption></figcaption></figure> <ul><li>Calcul de l'aira interiora a una ellipsa:</li></ul> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A=\pi ab\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mi>π</mi> <mi>a</mi> <mi>b</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=\pi ab\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/054e5e946a7a106ca68c7ca0f3cae845621b678f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:8.788ex; height:2.176ex;" alt="{\displaystyle A=\pi ab\,\!}"></span></dd></dl> <p><br /> ont <i>a</i> e <i>b</i> son los semiaxes de l'<a href="/wiki/Ellipsa" title="Ellipsa">ellipsa</a> (se ditz, rarament, que son los rais de l'ellipsa). </p> <div class="mw-heading mw-heading2"><h2 id="Lo_rai_terrèstre"><span id="Lo_rai_terr.C3.A8stre"></span>Lo rai terrèstre</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rai_(geometria)&veaction=edit&section=3" title="Modificar la seccion : Lo rai terrèstre" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Rai_(geometria)&action=edit&section=3" title="Edita el codi de la secció: Lo rai terrèstre"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Sa_mesura">Sa mesura</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rai_(geometria)&veaction=edit&section=4" title="Modificar la seccion : Sa mesura" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Rai_(geometria)&action=edit&section=4" title="Edita el codi de la secció: Sa mesura"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La primièra mesura del rai terrèstre en astronomia foguèt concebuda per <a href="/w/index.php?title=Eratost%C3%A8nes&action=edit&redlink=1" class="new" title="Eratostènes (la pagina existís pas)">Eratostènes</a>. Son calcul es lo seguent: lo <a href="/wiki/Solelh" class="mw-redirect" title="Solelh">Solelh</a> es tan alunhat que sos <a href="/w/index.php?title=Rai_(lutz)&action=edit&redlink=1" class="new" title="Rai (lutz) (la pagina existís pas)">rais</a> arriban parallelament en tot punt de la <a href="/wiki/T%C3%A8rra" title="Tèrra">Tèrra</a>. Aviá legit qu'a Siene (<a href="/wiki/Assoan" title="Assoan">Assoan</a>), los rais tombavan verticalament dins un <a href="/wiki/Potz" title="Potz">potz</a> lo jorn del <a href="/wiki/Solstici" title="Solstici">solstici</a> d'<a href="/wiki/Estiu" title="Estiu">estiu</a>. Aquò vòl dire que lo Solelh passa pel <a href="/wiki/Zenit_(astronomia)" title="Zenit (astronomia)">zenit</a>, alara i a pas d'ombra. Mai al nòrd, al meteis moment, los rais atenhián <a href="/wiki/Alex%C3%A0ndria" title="Alexàndria">Alexàndria</a> jos un angle non nul, que mesurèt. L'angle mesurat es d'un cinquanten de cercle. Aquò significa que la circonferéncia de la Tèrra es cinquanta còps pus granda que la distància de Siene cap a Alexàndria. Aviá tanben legit que las caravanas de camels partent de Siene comptavan cinquanta jorns per aténher Alexàndria percorrent cent estadis cada jorn. Calculèt que la distància entre ambedoas vilas de la val de Nil èra de <span class="nowrap">5 000 estadis</span>. L'estadi equival a <span class="nowrap">158 m</span>. </p><p>Per mesura de l'ombre portada amb d'objèctes de nautor coneguda situats en dos punts de latitud diferenta, trobèt la valor de <span class="nowrap">250 000 estadis</span> per la longor del meridian, es a dire la <a href="/wiki/Circonfer%C3%A9ncia" title="Circonferéncia">circonferéncia</a> terrèstra. Aquela mesura es exacta a 2% prèp. Ne deduguèt lo rai de la Tèrra. </p> <div class="mw-heading mw-heading3"><h3 id="Son_utilizacion">Son utilizacion</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rai_(geometria)&veaction=edit&section=5" title="Modificar la seccion : Son utilizacion" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Rai_(geometria)&action=edit&section=5" title="Edita el codi de la secció: Son utilizacion"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Lo rai terrèstre es utilizat per fòrça calculs <a href="/wiki/Astronomia" title="Astronomia">astronomics</a> coma: </p> <ul><li>Lo calcul de la <a href="/w/index.php?title=Parallaxa&action=edit&redlink=1" class="new" title="Parallaxa (la pagina existís pas)">parallaxa</a> diurna d'un astre:</li></ul> <dl><dd>Parallaxa diurna: dos observators se plaçant en dos punts A e B de la Tèrre mai alunhats possible e nòtan la configuracion de las estelas a l'entorn de l'astre observat. Pòdon atal calcular los angles BAP e ABP, puèi ne deduire la parallaxa que permetrà d'obtenir la distància TP.</dd></dl> <p><span typeof="mw:File"><a href="/wiki/Fichi%C3%A8r:Parallaxe_diurne.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/50/Parallaxe_diurne.png/600px-Parallaxe_diurne.png" decoding="async" width="600" height="138" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/50/Parallaxe_diurne.png/900px-Parallaxe_diurne.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/50/Parallaxe_diurne.png/1200px-Parallaxe_diurne.png 2x" data-file-width="1300" data-file-height="300" /></a></span> </p> <div class="mw-heading mw-heading2"><h2 id="Bibliografia">Bibliografia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rai_(geometria)&veaction=edit&section=6" title="Modificar la seccion : Bibliografia" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Rai_(geometria)&action=edit&section=6" title="Edita el codi de la secció: Bibliografia"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><i>Los elements de geometria d'Euclides</i>, tradusits literalament en <span style="font-size:0.95em; font-weight:bold; color:var(--color-subtle, #54595d);" title="En francés">(<abbr title="">fr</abbr>)</span>, e seguits d'un tractat del cercle, del cilindre, d'un còn e de l'esfèra, de la mesura de las superfícias e dels solids, amb de nòtas; Euclides, F Peyrard ; París, F. Louis, 1809.</li> <li><i>Geometria 4: las relacions dins lo cercle.</i> ; Michel Morin, Alain Roy ; Mont-Royal, Quebèc: Modulo, 1995.</li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Recuperada de « <a dir="ltr" href="https://oc.wikipedia.org/w/index.php?title=Rai_(geometria)&oldid=1876857">https://oc.wikipedia.org/w/index.php?title=Rai_(geometria)&oldid=1876857</a> »</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Especial:Categorias" title="Especial:Categorias">Categorias de la pagina</a> : <ul><li><a href="/wiki/Categoria:Mod%C3%A8l_infobox" title="Categoria:Modèl infobox">Modèl infobox</a></li><li><a href="/wiki/Categoria:Geometria" title="Categoria:Geometria">Geometria</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Aquela pagina es estada modificada pel darrièr còp lo 24 mai de 2013 a 21.46.</li> <li id="footer-info-copyright"><span style="white-space: normal"><a href="/wiki/Wikip%C3%A8dia:Drech_d%27autor" title="Wikipèdia:Drech d'autor">Drech d'autor</a> : Los tèxtes son disponibles jos <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/deed.fr">licéncia Creative Commons paternitat pertatge a l’identic</a> ; d’autras condicions se pòdon aplicar. 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