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Bezrozměrná veličina – Wikipedie

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class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">přesunout do postranního panelu</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">skrýt</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">(úvod)</div> </a> </li> <li id="toc-Jazyková_poznámka" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Jazyková_poznámka"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Jazyková poznámka</span> </div> </a> <ul id="toc-Jazyková_poznámka-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Reference" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Reference"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Reference</span> </div> </a> <ul id="toc-Reference-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Související_články" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Související_články"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Související články</span> </div> </a> <ul id="toc-Související_články-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="Obsah" 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="Přepnout obsah" > <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">Přepnout obsah</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">Bezrozměrná veličina</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="Přejděte k článku v jiném jazyce. Je dostupný v 40 jazycích" > <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-40" 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">40 jazyků</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/Dimensieloos" title="Dimensieloos – afrikánština" lang="af" hreflang="af" data-title="Dimensieloos" data-language-autonym="Afrikaans" data-language-local-name="afrikánština" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%83%D9%85%D9%8A%D8%A9_%D9%84%D8%A7_%D8%A8%D8%B9%D8%AF%D9%8A%D8%A9" title="كمية لا بعدية – arabština" lang="ar" hreflang="ar" data-title="كمية لا بعدية" data-language-autonym="العربية" data-language-local-name="arabština" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%91%D0%B5%D0%B7%D1%80%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%D0%BD%D0%B0%D1%8F_%D0%B2%D0%B5%D0%BB%D1%96%D1%87%D1%8B%D0%BD%D1%8F" title="Безразмерная велічыня – běloruština" lang="be" hreflang="be" data-title="Безразмерная велічыня" data-language-autonym="Беларуская" data-language-local-name="běloruština" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%91%D0%B5%D0%B7%D1%80%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%D0%BD%D0%B0_%D0%B2%D0%B5%D0%BB%D0%B8%D1%87%D0%B8%D0%BD%D0%B0" title="Безразмерна величина – bulharština" lang="bg" hreflang="bg" data-title="Безразмерна величина" data-language-autonym="Български" data-language-local-name="bulharština" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Bezdimenziona_veli%C4%8Dina" title="Bezdimenziona veličina – bosenština" lang="bs" hreflang="bs" data-title="Bezdimenziona veličina" data-language-autonym="Bosanski" data-language-local-name="bosenština" 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/Magnitud_adimensional" title="Magnitud adimensional – katalánština" lang="ca" hreflang="ca" data-title="Magnitud adimensional" data-language-autonym="Català" data-language-local-name="katalánština" 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/%D8%A8%DA%95%DB%8C_%D8%A8%DB%8E%DA%95%DB%95%DA%BE%DB%95%D9%86%D8%AF" title="بڕی بێڕەھەند – kurdština (sorání)" lang="ckb" hreflang="ckb" data-title="بڕی بێڕەھەند" data-language-autonym="کوردی" data-language-local-name="kurdština (sorání)" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A5%D0%B0%D0%BF%D0%B0%D1%81%C4%83%D1%80_%D0%BA%D0%B0%D0%BF" title="Хапасăр кап – čuvaština" lang="cv" hreflang="cv" data-title="Хапасăр кап" data-language-autonym="Чӑвашла" data-language-local-name="čuvaština" 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/Dimensionslose_Gr%C3%B6%C3%9Fe" title="Dimensionslose Größe – němčina" lang="de" hreflang="de" data-title="Dimensionslose Größe" data-language-autonym="Deutsch" data-language-local-name="němčina" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Dimensionless_quantity" title="Dimensionless quantity – angličtina" lang="en" hreflang="en" data-title="Dimensionless quantity" data-language-autonym="English" data-language-local-name="angličtina" 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/Magnitud_adimensional" title="Magnitud adimensional – španělština" lang="es" hreflang="es" data-title="Magnitud adimensional" data-language-autonym="Español" data-language-local-name="španělština" 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/Dimensioonita_suurus" title="Dimensioonita suurus – estonština" lang="et" hreflang="et" data-title="Dimensioonita suurus" data-language-autonym="Eesti" data-language-local-name="estonština" 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/%DA%A9%D9%85%DB%8C%D8%AA_%D8%A8%D8%AF%D9%88%D9%86_%D8%A8%D8%B9%D8%AF" title="کمیت بدون بعد – perština" lang="fa" hreflang="fa" data-title="کمیت بدون بعد" data-language-autonym="فارسی" data-language-local-name="perština" 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/Dimensioton_suure" title="Dimensioton suure – finština" lang="fi" hreflang="fi" data-title="Dimensioton suure" data-language-autonym="Suomi" data-language-local-name="finština" 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/Grandeur_sans_dimension" title="Grandeur sans dimension – francouzština" lang="fr" hreflang="fr" data-title="Grandeur sans dimension" data-language-autonym="Français" data-language-local-name="francouzština" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%92%D7%95%D7%93%D7%9C_%D7%97%D7%A1%D7%A8_%D7%9E%D7%9E%D7%93" title="גודל חסר ממד – hebrejština" lang="he" hreflang="he" data-title="גודל חסר ממד" data-language-autonym="עברית" data-language-local-name="hebrejština" 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%B5%E0%A4%BF%E0%A4%AE%E0%A4%BE%E0%A4%B9%E0%A5%80%E0%A4%A8_%E0%A4%B8%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE" title="विमाहीन संख्या – hindština" lang="hi" hreflang="hi" data-title="विमाहीन संख्या" data-language-autonym="हिन्दी" data-language-local-name="hindština" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Dimenzi%C3%B3mentes_mennyis%C3%A9g" title="Dimenziómentes mennyiség – maďarština" lang="hu" hreflang="hu" data-title="Dimenziómentes mennyiség" data-language-autonym="Magyar" data-language-local-name="maďarština" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Besaran_nirdimensi" title="Besaran nirdimensi – indonéština" lang="id" hreflang="id" data-title="Besaran nirdimensi" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonéština" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%84%A1%E6%AC%A1%E5%85%83%E9%87%8F" title="無次元量 – japonština" lang="ja" hreflang="ja" data-title="無次元量" data-language-autonym="日本語" data-language-local-name="japonština" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D3%A8%D0%BB%D1%88%D0%B5%D0%BC%D1%81%D1%96%D0%B7_%D1%88%D0%B0%D0%BC%D0%B0" title="Өлшемсіз шама – kazaština" lang="kk" hreflang="kk" data-title="Өлшемсіз шама" data-language-autonym="Қазақша" data-language-local-name="kazaština" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%AC%B4%EC%B0%A8%EC%9B%90%EB%9F%89" title="무차원량 – korejština" lang="ko" hreflang="ko" data-title="무차원량" data-language-autonym="한국어" data-language-local-name="korejština" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Bedimensis_dydis" title="Bedimensis dydis – litevština" lang="lt" hreflang="lt" data-title="Bedimensis dydis" data-language-autonym="Lietuvių" data-language-local-name="litevština" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%91%D0%B5%D0%B7%D0%B4%D0%B8%D0%BC%D0%B5%D0%BD%D0%B7%D0%B8%D0%BE%D0%BD%D0%B0%D0%BB%D0%BD%D0%B0_%D0%B2%D0%B5%D0%BB%D0%B8%D1%87%D0%B8%D0%BD%D0%B0" title="Бездимензионална величина – makedonština" lang="mk" hreflang="mk" data-title="Бездимензионална величина" data-language-autonym="Македонски" data-language-local-name="makedonština" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%B5%E0%A4%BF%E0%A4%AE%E0%A4%BE%E0%A4%B9%E0%A5%80%E0%A4%A8_%E0%A4%B8%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE" title="विमाहीन संख्या – nepálština" lang="ne" hreflang="ne" data-title="विमाहीन संख्या" data-language-autonym="नेपाली" data-language-local-name="nepálština" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Dimensjonslaus_storleik" title="Dimensjonslaus storleik – norština (nynorsk)" lang="nn" hreflang="nn" data-title="Dimensjonslaus storleik" data-language-autonym="Norsk nynorsk" data-language-local-name="norština (nynorsk)" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%AA%E0%A8%BE%E0%A8%B8%E0%A8%BE%E0%A8%B0%E0%A8%B0%E0%A8%B9%E0%A8%BF%E0%A8%A4_%E0%A8%AE%E0%A8%BE%E0%A8%A4%E0%A8%B0%E0%A8%BE" title="ਪਾਸਾਰਰਹਿਤ ਮਾਤਰਾ – paňdžábština" lang="pa" hreflang="pa" data-title="ਪਾਸਾਰਰਹਿਤ ਮਾਤਰਾ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="paňdžábština" 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/Wielko%C5%9B%C4%87_bezwymiarowa" title="Wielkość bezwymiarowa – polština" lang="pl" hreflang="pl" data-title="Wielkość bezwymiarowa" data-language-autonym="Polski" data-language-local-name="polština" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Magnitude_adimensional" title="Magnitude adimensional – portugalština" lang="pt" hreflang="pt" data-title="Magnitude adimensional" data-language-autonym="Português" data-language-local-name="portugalština" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/M%C4%83rime_adimensional%C4%83" title="Mărime adimensională – rumunština" lang="ro" hreflang="ro" data-title="Mărime adimensională" data-language-autonym="Română" data-language-local-name="rumunština" 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%91%D0%B5%D0%B7%D1%80%D0%B0%D0%B7%D0%BC%D0%B5%D1%80%D0%BD%D0%B0%D1%8F_%D0%B2%D0%B5%D0%BB%D0%B8%D1%87%D0%B8%D0%BD%D0%B0" title="Безразмерная величина – ruština" lang="ru" hreflang="ru" data-title="Безразмерная величина" data-language-autonym="Русский" data-language-local-name="ruština" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Dimensionless_quantity" title="Dimensionless quantity – Simple English" lang="en-simple" hreflang="en-simple" data-title="Dimensionless quantity" 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/Bezrozmern%C3%A1_veli%C4%8Dina" title="Bezrozmerná veličina – slovenština" lang="sk" hreflang="sk" data-title="Bezrozmerná veličina" data-language-autonym="Slovenčina" data-language-local-name="slovenština" 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/Brezrazse%C5%BEna_koli%C4%8Dina" title="Brezrazsežna količina – slovinština" lang="sl" hreflang="sl" data-title="Brezrazsežna količina" data-language-autonym="Slovenščina" data-language-local-name="slovinština" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Dimensionsl%C3%B6s_storhet" title="Dimensionslös storhet – švédština" lang="sv" hreflang="sv" data-title="Dimensionslös storhet" data-language-autonym="Svenska" data-language-local-name="švédština" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Boyutsuz_nicelik" title="Boyutsuz nicelik – turečtina" lang="tr" hreflang="tr" data-title="Boyutsuz nicelik" data-language-autonym="Türkçe" data-language-local-name="turečtina" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%91%D0%B5%D0%B7%D1%80%D0%BE%D0%B7%D0%BC%D1%96%D1%80%D0%BD%D1%96%D1%81%D0%BD%D0%B0_%D1%84%D1%96%D0%B7%D0%B8%D1%87%D0%BD%D0%B0_%D0%B2%D0%B5%D0%BB%D0%B8%D1%87%D0%B8%D0%BD%D0%B0" title="Безрозмірнісна фізична величина – ukrajinština" lang="uk" hreflang="uk" data-title="Безрозмірнісна фізична величина" data-language-autonym="Українська" data-language-local-name="ukrajinština" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/%C4%90%E1%BA%A1i_l%C6%B0%E1%BB%A3ng_kh%C3%B4ng_th%E1%BB%A9_nguy%C3%AAn" title="Đại lượng không thứ nguyên – vietnamština" lang="vi" hreflang="vi" data-title="Đại lượng không thứ nguyên" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamština" 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/%E6%97%A0%E9%87%8F%E7%BA%B2%E9%87%8F" title="无量纲量 – čínština (dialekty Wu)" lang="wuu" hreflang="wuu" data-title="无量纲量" data-language-autonym="吴语" data-language-local-name="čínština (dialekty Wu)" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%97%A0%E9%87%8F%E7%BA%B2%E9%87%8F" title="无量纲量 – čínština" lang="zh" hreflang="zh" data-title="无量纲量" data-language-autonym="中文" data-language-local-name="čínština" 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data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Z Wikipedie, otevřené encyklopedie</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="cs" dir="ltr"><p><b>Bezrozměrová veličina</b><sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">&#91;</span>1<span class="cite-bracket">&#93;</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">&#91;</span>2<span class="cite-bracket">&#93;</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">&#91;</span>3<span class="cite-bracket">&#93;</span></a></sup> (často též <b>bezrozměrná veličina</b>, viz Jazyková poznámka) je taková <a href="/wiki/Veli%C4%8Dina" title="Veličina">veličina</a>, která má v dané <a href="/wiki/Fyzik%C3%A1ln%C3%AD_veli%C4%8Dina#Soustavy_fyzikálních_veličin_a_jednotek" title="Fyzikální veličina">soustavě jednotek</a> <a href="/wiki/Fyzik%C3%A1ln%C3%AD_rozm%C4%9Br_veli%C4%8Diny" title="Fyzikální rozměr veličiny">rozměr</a> "jedna" (v algebře rozměrů jde o neutrální prvek); tuto vlastnost vystihuje přednostní název <b>veličina s rozměrem jedna</b><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">&#91;</span>4<span class="cite-bracket">&#93;</span></a></sup>. Může však mít (i v rámci <a href="/wiki/Soustava_SI" title="Soustava SI">SI</a>) jednotku se zvláštním názvem a značkou<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">&#91;</span>5<span class="cite-bracket">&#93;</span></a></sup>; taková jednotka se pokládá za odvozenou a je <a href="/wiki/Bezrozm%C4%9Brn%C3%A1_jednotka" title="Bezrozměrná jednotka">bezrozměrová</a> (např. <a href="/wiki/Radi%C3%A1n" title="Radián">radián</a>, <a href="/wiki/Steradi%C3%A1n" title="Steradián">steradián</a>, <a href="/wiki/Decibel" title="Decibel">decibel</a>, <a href="/wiki/Neper" title="Neper">neper</a>, <a href="/wiki/Procento" title="Procento">procento</a>). </p><p>Bezrozměrová veličina je obvykle definována jako <a href="/wiki/N%C3%A1soben%C3%AD" title="Násobení">součin</a> či <a href="/wiki/D%C4%9Blen%C3%AD" title="Dělení">podíl</a> veličin, které sice mají rozměry, ale rozměrové koeficienty jednotlivých základních veličin se ve výsledku vzájemně vykrátí. Jindy může být definována jako součin, podíl či funkce jiných bezrozměrových veličin. Obsahují-li vztahy popisující fyzikální zákony či definiční rovnice technických veličin <a href="/wiki/Exponenci%C3%A1ln%C3%AD_funkce" title="Exponenciální funkce">exponenciální</a>, <a href="/wiki/Logaritmus" title="Logaritmus">logaritmické</a> nebo <a href="/wiki/Goniometrick%C3%A1_funkce" title="Goniometrická funkce">goniometrické</a> funkce, jsou jejich argumenty také bezrozměrovými veličinami. </p><p>Příkladem bezrozměrových veličin jsou <a href="/wiki/Podobnostn%C3%AD_%C4%8D%C3%ADslo" title="Podobnostní číslo">podobnostní čísla</a>, <a href="/wiki/Bezrozm%C4%9Brn%C3%A1_rychlost" title="Bezrozměrná rychlost">bezrozměrová rychlost</a>, <a href="/wiki/T%C5%99en%C3%AD#Součinitel_smykového_tření" title="Tření">součinitel smykového tření</a>, <a href="/wiki/Index_lomu" title="Index lomu">index lomu</a>, <a href="/wiki/Koncentrace_(chemie)#Molární_zlomek" title="Koncentrace (chemie)">molární zlomek</a>, <a href="/wiki/Konstanta_jemn%C3%A9_struktury" title="Konstanta jemné struktury">konstanta jemné struktury</a>, <a href="/wiki/Lorentz%C5%AFv_faktor" title="Lorentzův faktor">Lorentzův faktor</a> nebo <a href="/wiki/Boltzmann%C5%AFv_faktor" title="Boltzmannův faktor">Boltzmannův faktor</a>. Počtem a metodou sestrojení bezrozměrných veličin ve fyzikálních zákonech se zabývá <a href="/wiki/Buckingham%C5%AFv_p%C3%AD_teor%C3%A9m" class="mw-redirect" title="Buckinghamův pí teorém">Buckinghamův pí teorém.</a> </p><p>Podobně jako u všech veličin neznamená rovnost rozměru stejný charakter veličiny (například <a href="/wiki/Teplo" title="Teplo">teplo</a> a&#160;<a href="/wiki/Moment_s%C3%ADly" title="Moment síly">moment síly</a>). S bezrozměrovými veličinami nelze zacházet jako s pouhými <a href="/wiki/%C4%8C%C3%ADslo" title="Číslo">čísly</a>, ale je třeba mít na zřeteli jejich skutečný charakter, daný definicí veličiny, nikoli jednotkou (např. <a href="/wiki/%C3%9Ahel" title="Úhel">úhel</a> není totéž co <a href="/wiki/F%C3%A1ze_(vlna)" title="Fáze (vlna)">fáze</a>, a proto radián nelze volně zaměňovat za 1 - viz např. článek <a href="/wiki/%C3%9Ahlov%C3%A1_frekvence" title="Úhlová frekvence">úhlová frekvence</a>). Někdy se pro snazší a korektní zacházení doplňují v praxi jednotky bezrozměrových veličin různými přívlastky či vyjadřují se jako podíly takto "upřesněných" stejných jednotek (<i>cykl</i> za sekundu namísto reciproké sekundy; <i>gramy složky na 100 gramů roztoku</i> nebo <i>hmotnostní</i> procento namísto procenta u objemového zlomku apod.), zpravidla to však neodpovídá pravidlům pro veličiny a jednotky (např. příručce SI). Kvůli nespecifičnosti bezrozměrových jednotek bývá někdy kritizována i současná podoba <a href="/wiki/Soustava_SI" title="Soustava SI">soustavy SI</a>.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">&#91;</span>6<span class="cite-bracket">&#93;</span></a></sup> </p><p>Zavedeme-li koherentní soustavu jednotek, tj. odvozené jednotky budou definovány pomocí jednotek základních <a href="/wiki/Fyzik%C3%A1ln%C3%AD_veli%C4%8Dina#Jednotkové_rovnice" title="Fyzikální veličina">jednotkovými rovnicemi</a> bez dodatečných číselných koeficientů, můžeme se všemi veličinami dané soustavy zacházet jako s bezrozměrovými. Není to však obvyklé, protože se tím ztrácí informace o kvalitativní stránce veličin. </p> <div class="mw-heading mw-heading2"><h2 id="Jazyková_poznámka"><span id="Jazykov.C3.A1_pozn.C3.A1mka"></span>Jazyková poznámka</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bezrozm%C4%9Brn%C3%A1_veli%C4%8Dina&amp;veaction=edit&amp;section=1" title="Editace sekce: Jazyková poznámka" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bezrozm%C4%9Brn%C3%A1_veli%C4%8Dina&amp;action=edit&amp;section=1" title="Editovat zdrojový kód sekce Jazyková poznámka"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Fyzikální rozměr</b><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">&#91;</span>7<span class="cite-bracket">&#93;</span></a></sup> je vlastností veličiny (tedy také jednotky), nikoli objektu. Příklady: rozměr objemu <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 =L^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle =L^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/23b796b0f34f91030bd7816b4b39da64b1b14f5d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.09ex; height:2.676ex;" alt="{\displaystyle =L^{3}}"></span>; rozměr úhlu <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 =L/L=L^{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>L</mi> <mo>=</mo> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle =L/L=L^{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/95ee83394e10ef25d6cc7896937f4a3842017830" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.517ex; height:3.176ex;" alt="{\displaystyle =L/L=L^{0}}"></span>. Norma se zde přiklonila k adjektivu <b>rozměrový</b>, např. rozměrový exponent<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">&#91;</span>8<span class="cite-bracket">&#93;</span></a></sup>; <b>bezrozměrová veličina</b><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">&#91;</span>9<span class="cite-bracket">&#93;</span></a></sup> má rozměr 1. Podobně se běžně užívá rozměrová analýza, rozměrová zkouška. </p><p>Naproti tomu <b>rozměr v geometrii</b> je vlastností objektu (nikoli veličiny): rozměr balíku je 20 cm <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 \times }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>&#x00D7;<!-- × --></mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \times }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ffafff1ad26cbe49045f19a67ce532116a32703" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.019ex; margin-bottom: -0.19ex; width:1.808ex; height:1.509ex;" alt="{\displaystyle \times }"></span> 30 cm <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 \times }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>&#x00D7;<!-- × --></mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \times }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ffafff1ad26cbe49045f19a67ce532116a32703" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.019ex; margin-bottom: -0.19ex; width:1.808ex; height:1.509ex;" alt="{\displaystyle \times }"></span> 50 cm. Jako adjektivum se zde užívá tvar <b>rozměrný</b> - rozměrné zavazadlo, případně v matematice s číslovkou: <b>bezrozměrný bod</b> má 0 rozměrů; časoprostor je čtyřrozměrný. Jako termín by byla "bezrozměrná veličina" proti tomuto pojetí; nové normy i učebnice<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">&#91;</span>10<span class="cite-bracket">&#93;</span></a></sup><sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">&#91;</span>11<span class="cite-bracket">&#93;</span></a></sup> užívají "bezrozměrová veličina". </p> <div class="mw-heading mw-heading2"><h2 id="Reference">Reference</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bezrozm%C4%9Brn%C3%A1_veli%C4%8Dina&amp;veaction=edit&amp;section=2" title="Editace sekce: Reference" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bezrozm%C4%9Brn%C3%A1_veli%C4%8Dina&amp;action=edit&amp;section=2" title="Editovat zdrojový kód sekce Reference"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">Šindelář V., Tůma Z.: Metrologie, její vývoj a současnost;ČMS Praha, 2002</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text">Norma ČSN <a href="/w/index.php?title=ISO_80000&amp;action=edit&amp;redlink=1" class="new" title="ISO 80000 (stránka neexistuje)">ISO 80000</a>-1:2011 Veličiny a jednotky - Část 1: Obecně, položka 3.8: veličina s rozměrem jedna; bezrozměrová veličina</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text">Norma ČSN IEC 60050-112:2013 Mezinárodní elektrotechnický slovník - Část 112: Veličiny a jednotky, položka 112-01-13: veličina s rozměrem jedna; bezrozměrová veličina</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text">Viz výše ČSN ISO 80000-1:2011, též v předchozí normě <a href="/w/index.php?title=ISO_31&amp;action=edit&amp;redlink=1" class="new" title="ISO 31 (stránka neexistuje)">ISO 31</a>).</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text">ČSN ISO 80000-1:2011 Veličiny a jednotky - Část 1: Obecně, tabulka 2</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><a href="#cite_ref-6">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external free" href="http://iopscience.iop.org/0026-1394/52/1/40/pdf/0026-1394_52_1_40.pdf">http://iopscience.iop.org/0026-1394/52/1/40/pdf/0026-1394_52_1_40.pdf</a> - Dimensionless units in the SI</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><a href="#cite_ref-7">↑</a></span> <span class="reference-text">ČSN IEC 60050-112:2013, položka 112-01-11 rozměr veličiny; rozměr</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><a href="#cite_ref-8">↑</a></span> <span class="reference-text">ČSN IEC 60050-112:2013, položka 112-01-12 rozměrový exponent</span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><a href="#cite_ref-9">↑</a></span> <span class="reference-text">ČSN IEC 60050-112:2013, položka 112-01-13 veličina s rozměrem jedna; bezrozměrová veličina</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><a href="#cite_ref-10">↑</a></span> <span class="reference-text"><b>Metrologie, její vývoj a současnost</b>, Šindelář V., Tůma Z., ČMS, Praha, 2002</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><a href="#cite_ref-11">↑</a></span> <span class="reference-text"><b>Fyzika</b>, Halliday D., Resnick R., Walker J., překlad VUT Brno. Nové vydání: VUTIUM Brno, 2013, 2 díly</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Související_články"><span id="Souvisej.C3.ADc.C3.AD_.C4.8Dl.C3.A1nky"></span>Související články</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bezrozm%C4%9Brn%C3%A1_veli%C4%8Dina&amp;veaction=edit&amp;section=3" title="Editace sekce: Související články" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bezrozm%C4%9Brn%C3%A1_veli%C4%8Dina&amp;action=edit&amp;section=3" title="Editovat zdrojový kód sekce Související články"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Fyzik%C3%A1ln%C3%AD_veli%C4%8Dina" title="Fyzikální veličina">Fyzikální veličina</a></li> <li><a href="/wiki/Fyzik%C3%A1ln%C3%AD_rozm%C4%9Br_veli%C4%8Diny" title="Fyzikální rozměr veličiny">Fyzikální rozměr veličiny</a></li> <li><a href="/wiki/Rozm%C4%9Brov%C3%A1_zkou%C5%A1ka" class="mw-redirect" title="Rozměrová zkouška">Rozměrová zkouška</a></li> <li><a href="/wiki/Rozm%C4%9Br" class="mw-disambig" title="Rozměr">Rozměr</a></li> <li><a href="/wiki/Buckingham%C5%AFv_p%C3%AD_teor%C3%A9m" class="mw-redirect" title="Buckinghamův pí teorém">Buckinghamův pí teorém</a></li></ul> <table class="plainlinks metadata noprint pahyl" cellpadding="2" style="background: transparent;"> <tbody><tr> <td><figure class="mw-halign-left" typeof="mw:File"><a href="/wiki/Soubor:Wiki_letter_w.svg" class="mw-file-description" title="Pahýl"><img alt="Pahýl" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/40px-Wiki_letter_w.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/60px-Wiki_letter_w.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/80px-Wiki_letter_w.svg.png 2x" data-file-width="44" data-file-height="44" /></a><figcaption>Pahýl</figcaption></figure> </td> <td><i>Tento článek je příliš stručný nebo <a href="/wiki/Wikipedie:Pah%C3%BDl" title="Wikipedie:Pahýl">postrádá důležité informace</a>.<br />Pomozte Wikipedii tím, že jej vhodně <a class="external text" href="https://cs.wikipedia.org/w/index.php?title=Bezrozm%C4%9Brn%C3%A1_veli%C4%8Dina&amp;action=edit">rozšíříte</a>. 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