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šablona\"\u003E\u003Cspan style=\"color:#e05600;\"\u003EAkcija sređivanja šablona\u003C/span\u003E\u003C/a\u003E. Pozivamo vas da joj se priključite.\u003C/td\u003E\u003C/tr\u003E\u003C/tbody\u003E\u003C/table\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E";}}());</script></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Sajt"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <h1 id="firstHeading" class="firstHeading mw-first-heading" lang="sh-Latn" dir="ltr"><span class="mw-page-title-main">Duljina luka</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" lang="sh-Latn" dir="ltr"> <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="Prijedi na druge jezične varijante članka. Dostupno je na 35 jezika" > <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-35" 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">35 jezika</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8B%A8%E1%8C%8E%E1%89%A3%E1%8C%A3_%E1%88%AD%E1%8B%9D%E1%88%98%E1%89%B5" title="የጎባጣ ርዝመት — Amharski" lang="am" hreflang="am" data-title="የጎባጣ ርዝመት" data-language-autonym="አማርኛ" data-language-local-name="Amharski" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B7%D9%88%D9%84_%D9%82%D9%88%D8%B3" title="طول قوس — Arapski" lang="ar" hreflang="ar" data-title="طول قوس" data-language-autonym="العربية" data-language-local-name="Arapski" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/%C6%8Fyrinin_uzunlu%C4%9Fu" title="Əyrinin uzunluğu — Azerbejdžanski" lang="az" hreflang="az" data-title="Əyrinin uzunluğu" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbejdžanski" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%94%D0%B0%D1%9E%D0%B6%D1%8B%D0%BD%D1%8F_%D0%BA%D1%80%D1%8B%D0%B2%D0%BE%D0%B9" title="Даўжыня крывой — Beloruski" lang="be" hreflang="be" data-title="Даўжыня крывой" data-language-autonym="Беларуская" data-language-local-name="Beloruski" 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%94%D0%B0%D1%9E%D0%B6%D1%8B%D0%BD%D1%8F_%D0%BA%D1%80%D1%8B%D0%B2%D0%BE%D0%B9" title="Даўжыня крывой — Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Даўжыня крывой" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Longitud_d%27arc" title="Longitud d'arc — Katalonski" lang="ca" hreflang="ca" data-title="Longitud d'arc" data-language-autonym="Català" data-language-local-name="Katalonski" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/D%C3%A9lka_k%C5%99ivky" title="Délka křivky — Češki" lang="cs" hreflang="cs" data-title="Délka křivky" data-language-autonym="Čeština" data-language-local-name="Češki" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Kurvel%C3%A6ngde" title="Kurvelængde — Danski" lang="da" hreflang="da" data-title="Kurvelængde" data-language-autonym="Dansk" data-language-local-name="Danski" 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/L%C3%A4nge_(Mathematik)" title="Länge (Mathematik) — Nemački" lang="de" hreflang="de" data-title="Länge (Mathematik)" data-language-autonym="Deutsch" data-language-local-name="Nemački" 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%9C%CE%AE%CE%BA%CE%BF%CF%82_%CF%84%CF%8C%CE%BE%CE%BF%CF%85" title="Μήκος τόξου — Grčki" lang="el" hreflang="el" data-title="Μήκος τόξου" data-language-autonym="Ελληνικά" data-language-local-name="Grčki" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Arc_length" title="Arc length — Engleski" lang="en" hreflang="en" data-title="Arc length" data-language-autonym="English" data-language-local-name="Engleski" 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/Longitud_de_arco" title="Longitud de arco — Španski" lang="es" hreflang="es" data-title="Longitud de arco" data-language-autonym="Español" data-language-local-name="Španski" 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/Pikkus_(matemaatika)" title="Pikkus (matemaatika) — Estonski" lang="et" hreflang="et" data-title="Pikkus (matemaatika)" data-language-autonym="Eesti" data-language-local-name="Estonski" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B7%D9%88%D9%84_%D9%82%D9%88%D8%B3" title="طول قوس — Persijski" lang="fa" hreflang="fa" data-title="طول قوس" data-language-autonym="فارسی" data-language-local-name="Persijski" 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/K%C3%A4yr%C3%A4n_pituus" title="Käyrän pituus — Finski" lang="fi" hreflang="fi" data-title="Käyrän pituus" data-language-autonym="Suomi" data-language-local-name="Finski" 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/Longueur_d%27un_arc" title="Longueur d'un arc — Francuski" lang="fr" hreflang="fr" data-title="Longueur d'un arc" data-language-autonym="Français" data-language-local-name="Francuski" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/%C3%8Dvhossz" title="Ívhossz — Mađarski" lang="hu" hreflang="hu" data-title="Ívhossz" data-language-autonym="Magyar" data-language-local-name="Mađarski" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Ferillengd" title="Ferillengd — Islandski" lang="is" hreflang="is" data-title="Ferillengd" data-language-autonym="Íslenska" data-language-local-name="Islandski" 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/Lunghezza_di_un_arco" title="Lunghezza di un arco — Italijanski" lang="it" hreflang="it" data-title="Lunghezza di un arco" data-language-autonym="Italiano" data-language-local-name="Italijanski" 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%BC%A7%E9%95%B7" title="弧長 — Japanski" lang="ja" hreflang="ja" data-title="弧長" data-language-autonym="日本語" data-language-local-name="Japanski" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B3%A1%EC%84%A0%EC%9D%98_%EA%B8%B8%EC%9D%B4" title="곡선의 길이 — Korejski" lang="ko" hreflang="ko" data-title="곡선의 길이" data-language-autonym="한국어" data-language-local-name="Korejski" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Booglengte" title="Booglengte — Holandski" lang="nl" hreflang="nl" data-title="Booglengte" data-language-autonym="Nederlands" data-language-local-name="Holandski" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Buelengde" title="Buelengde — Norveški bokmål" lang="nb" hreflang="nb" data-title="Buelengde" data-language-autonym="Norsk bokmål" data-language-local-name="Norveški bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/D%C5%82ugo%C5%9B%C4%87_krzywej" title="Długość krzywej — Poljski" lang="pl" hreflang="pl" data-title="Długość krzywej" data-language-autonym="Polski" data-language-local-name="Poljski" 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/Comprimento_do_arco" title="Comprimento do arco — Portugalski" lang="pt" hreflang="pt" data-title="Comprimento do arco" data-language-autonym="Português" data-language-local-name="Portugalski" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%94%D0%BB%D0%B8%D0%BD%D0%B0_%D0%BA%D1%80%D0%B8%D0%B2%D0%BE%D0%B9" title="Длина кривой — Ruski" lang="ru" hreflang="ru" data-title="Длина кривой" data-language-autonym="Русский" data-language-local-name="Ruski" 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/Arc_length" title="Arc length — Simple English" lang="en-simple" hreflang="en-simple" data-title="Arc length" 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-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Dol%C5%BEina_loka" title="Dolžina loka — Slovenački" lang="sl" hreflang="sl" data-title="Dolžina loka" data-language-autonym="Slovenščina" data-language-local-name="Slovenački" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Gjat%C3%ABsia_e_harkut" title="Gjatësia e harkut — Albanski" lang="sq" hreflang="sq" data-title="Gjatësia e harkut" data-language-autonym="Shqip" data-language-local-name="Albanski" 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%94%D1%83%D0%B6%D0%B8%D0%BD%D0%B0_%D0%BB%D1%83%D0%BA%D0%B0" title="Дужина лука — Srpski" lang="sr" hreflang="sr" data-title="Дужина лука" data-language-autonym="Српски / srpski" data-language-local-name="Srpski" 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/B%C3%A5gl%C3%A4ngd" title="Båglängd — Švedski" lang="sv" hreflang="sv" data-title="Båglängd" data-language-autonym="Svenska" data-language-local-name="Švedski" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%84%E0%B8%A7%E0%B8%B2%E0%B8%A1%E0%B8%A2%E0%B8%B2%E0%B8%A7%E0%B8%AA%E0%B9%88%E0%B8%A7%E0%B8%99%E0%B9%82%E0%B8%84%E0%B9%89%E0%B8%87" title="ความยาวส่วนโค้ง — Tajlandski" lang="th" hreflang="th" data-title="ความยาวส่วนโค้ง" data-language-autonym="ไทย" data-language-local-name="Tajlandski" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%94%D0%BE%D0%B2%D0%B6%D0%B8%D0%BD%D0%B0_%D0%BA%D1%80%D0%B8%D0%B2%D0%BE%D1%97" title="Довжина кривої — Ukrajinski" lang="uk" hreflang="uk" data-title="Довжина кривої" data-language-autonym="Українська" data-language-local-name="Ukrajinski" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%BC%A7%E9%95%BF" title="弧长 — Wu kineski" lang="wuu" hreflang="wuu" data-title="弧长" data-language-autonym="吴语" data-language-local-name="Wu kineski" 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/%E5%BC%A7%E9%95%BF" title="弧长 — Kineski" lang="zh" hreflang="zh" data-title="弧长" data-language-autonym="中文" data-language-local-name="Kineski" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q670036#sitelinks-wikipedia" title="Uredite jezičke veze" class="wbc-editpage">Uredi veze</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Imenski prostori"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" lang="sh-Latn" dir="ltr"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Duljina_luka" title="Vidi stranicu sadržaja [c]" accesskey="c"><span>Stranica</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Razgovor:Duljina_luka&action=edit&redlink=1" rel="discussion" class="new" title="Razgovarajte o sadržini ove stranice 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href="/w/index.php?title=Duljina_luka&action=edit" title="Uredite izvorni kod ove stranice [e]" accesskey="e"><span>Uredi kod</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Duljina_luka&action=history" title="Pogledajte prethodne verzije ove stranice [h]" accesskey="h"><span>Historija</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Pomagala"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" lang="sh-Latn" dir="ltr"> <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Alatke" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" 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href="/w/index.php?title=Duljina_luka&action=history"><span>Historija</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" lang="sh-Latn" dir="ltr"> <div class="vector-menu-heading"> Opšte </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Posebno:%C5%A0to_vodi_ovdje/Duljina_luka" title="Pogledajte listu svih stranica koje vode ovamo [j]" accesskey="j"><span>Šta vodi ovamo</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Posebno:Povezane_izmjene/Duljina_luka" rel="nofollow" title="Prelistajte nedavne izmjene stranica koje su povezane s ovom [k]" accesskey="k"><span>Povezane izmjene</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Duljina_luka&oldid=41462665" title="Nabavite trajnu vezu do ove verzije stranice"><span>Trajna veza</span></a></li><li id="t-info" class="mw-list-item"><a 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hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q670036" title="Pogledajte povezanu stavku u skladištu podataka [g]" accesskey="g"><span>Stavka na Wikipodacima</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Pomagala"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Izgled"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Izgled</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">premjesti na bočnu traku</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">sakrij</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Izvor: Wikipedija</div> </div> <div id="contentSub" lang="sh-Latn" dir="ltr"><div id="mw-content-subtitle" lang="sh-Latn" dir="ltr"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="sh-Latn" dir="ltr"><figure class="mw-halign-right" typeof="mw:File/Frame"><a href="/wiki/Datoteka:Arc_length.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/d/dc/Arc_length.gif" decoding="async" width="400" height="100" class="mw-file-element" data-file-width="400" data-file-height="100" /></a><figcaption>Nakon ispravljanja, krivulja daje pravocrtni segment iste duljine kao krivuljin luk</figcaption></figure> <p><b>Duljina luka</b> krivulje je <a href="/wiki/Grani%C4%8Dna_vrijednost" class="mw-redirect" title="Granična vrijednost">granična vrijednost</a> kojoj teži dužina u krivulji (u luk krivulje) upisanih izlomljenih <a href="/wiki/Linija" title="Linija">linija</a> kad se broj njihovih pravolinijskih segmenata neograničeno povećava tako da dužina najvećeg segmenta teži nuli. Opseg <a href="/wiki/Krug" title="Krug">kruga</a> (dužina <a href="/wiki/Kru%C5%BEnica" title="Kružnica">kružnice</a>) se može smatrati kao granična vrijednost opsega upisanih i opisanih konveksnih n-to kutova kada broj njihovih strana (n) neograničeno raste i duljina najveće strane teži nuli. <a href="/wiki/Opseg" title="Opseg">Opseg</a> kruga (kružnice) izračunava se po formuli <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=2\pi r\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>l</mi> <mo>=</mo> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l=2\pi r\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5b7b7b2e4bd4840f7c6768cc6755b2d63310a510" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.722ex; height:2.176ex;" alt="{\displaystyle l=2\pi r\,}" /></span>. Za <a href="/w/index.php?title=Neprekidnost&action=edit&redlink=1" class="new" title="Neprekidnost (stranica ne postoji)">neprekidne</a> krivulje spomenuta granična vrijednost uvijek postoji kao konačna ili <a href="/wiki/Beskona%C4%8Dnost" title="Beskonačnost">beskonačna</a>. Ako je ova granična vrijednost konačna, za krivulju (njen luk) se kaže da se može rektificirati (da je rektifikabilna). Uvjet <a href="/w/index.php?title=Rektifikabilnost&action=edit&redlink=1" class="new" title="Rektifikabilnost (stranica ne postoji)">rektifikabilnosti</a> je ustanovio <a href="/w/index.php?title=Camille_Jordan&action=edit&redlink=1" class="new" title="Camille Jordan (stranica ne postoji)">C. Jordan</a> (v. <a href="/w/index.php?title=Jordanova_krivulja&action=edit&redlink=1" class="new" title="Jordanova krivulja (stranica ne postoji)">Jordanova krivulja</a>). </p><p>Ako je krivulja u ravni data pravokutnim <a href="/wiki/Dekartov_koordinatni_sistem" class="mw-redirect" title="Dekartov koordinatni sistem">Dekartovim koordinatama</a>, jednadžbom <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 y=f(x),\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>,</mo> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y=f(x),\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7047c863f4170a9eab0f64f463c4260249a6a4b9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.705ex; height:2.843ex;" alt="{\displaystyle y=f(x),\,}" /></span> gde je <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\leq x\leq b\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>≤</mo> <mi>x</mi> <mo>≤</mo> <mi>b</mi> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\leq x\leq b\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/adfde535eea3044843a6aa7a52d179345ab6df22" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:10.141ex; height:2.343ex;" alt="{\displaystyle a\leq x\leq b\,}" /></span>, i ako <a href="/wiki/Funkcija" class="mw-redirect" title="Funkcija">funkcija</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 y=f(x)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y=f(x)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ceab146b2e6d4d4a3580db2ba2d1d240edcbc080" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.059ex; height:2.843ex;" alt="{\displaystyle y=f(x)\,}" /></span> ima neprekidnu <a href="/wiki/Derivacija" class="mw-redirect" title="Derivacija">derivaciju</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 f'(x),\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>,</mo> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f'(x),\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e5e0448e7aeb28139d385ef898e65e2e90d4a07f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.178ex; height:3.009ex;" alt="{\displaystyle f'(x),\,}" /></span> njena duljina se izračunava po <a href="/wiki/Formula" title="Formula">formuli</a>: </p> <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 l=\int _{a}^{b}{\sqrt {1+[f'(x)]^{2}}}\,dx;}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>l</mi> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>1</mn> <mo>+</mo> <mo stretchy="false">[</mo> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <msup> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>x</mi> <mo>;</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l=\int _{a}^{b}{\sqrt {1+[f'(x)]^{2}}}\,dx;}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b0e20dc264b176db4216fd90dd15799f52546f57" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:24.979ex; height:6.343ex;" alt="{\displaystyle l=\int _{a}^{b}{\sqrt {1+[f'(x)]^{2}}}\,dx;}" /></span></dd></dl> <p>Ako je krivulja data parametarskim jednadžbama <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 x=x(t),\;y=y(t),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>=</mo> <mi>x</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>,</mo> <mspace width="thickmathspace"></mspace> <mi>y</mi> <mo>=</mo> <mi>y</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x=x(t),\;y=y(t),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bc721a4dee6887335a8f5fa3630fd5cb4d93d24c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.791ex; height:2.843ex;" alt="{\displaystyle x=x(t),\;y=y(t),}" /></span> gdje je <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\leq t\leq b,\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>≤</mo> <mi>t</mi> <mo>≤</mo> <mi>b</mi> <mo>,</mo> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\leq t\leq b,\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4a80b504e58052481cceb4dcd521b0d093c6b590" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.298ex; height:2.509ex;" alt="{\displaystyle a\leq t\leq b,\,}" /></span> njena duljina je: </p> <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 l=\int _{a}^{b}{\sqrt {[x'(t)]^{2}+[y'(t)]^{2}}}\,dt.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>l</mi> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo stretchy="false">[</mo> <msup> <mi>x</mi> <mo>′</mo> </msup> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <msup> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">[</mo> <msup> <mi>y</mi> <mo>′</mo> </msup> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <msup> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>t</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l=\int _{a}^{b}{\sqrt {[x'(t)]^{2}+[y'(t)]^{2}}}\,dt.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eae7538aff66e1d8c7af7f8f4dafb1d92b65e214" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:29.687ex; height:6.343ex;" alt="{\displaystyle l=\int _{a}^{b}{\sqrt {[x'(t)]^{2}+[y'(t)]^{2}}}\,dt.}" /></span></dd></dl> <p>Analogno ovome definira se i dužina krivulje u prostoru. </p>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="" lang="sh-Latn" dir="ltr">Izvor: <a dir="ltr" href="https://sh.wikipedia.org/w/index.php?title=Duljina_luka&oldid=41462665">https://sh.wikipedia.org/w/index.php?title=Duljina_luka&oldid=41462665</a></div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Posebno:Kategorije" title="Posebno:Kategorije">Kategorije</a>: <ul><li><a href="/wiki/Kategorija:Matemati%C4%8Dka_analiza" title="Kategorija:Matematička analiza">Matematička analiza</a></li><li><a href="/wiki/Kategorija:Geometrija" title="Kategorija:Geometrija">Geometrija</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" lang="sh-Latn" dir="ltr"> <ul id="footer-info"> <li id="footer-info-lastmod"> Ova stranica je posljednji put izmijenjena 20. augusta 2023. u 15:53.</li> <li id="footer-info-copyright">Tekst je dostupan pod licencom <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-ShareAlike</a>; 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