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href="/wiki/%D8%AE%D8%A7%D8%B5:Contribute"><span class="vector-icon mw-ui-icon-edit mw-ui-icon-wikimedia-edit"></span> <span>Contribute</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%D8%AE%D8%A7%D8%B5:CreateAccount&returnto=%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C+%D8%B3%D9%BE%DB%8C%D8%B3" title="ایہ تواڈے لئی چنگا اے جے تسیں کھاتہ کھولو تے لاگ ان ہوو؛ پر ایہ لازمی وی نئیں"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>کھاتہ بݨاؤ</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%D8%AE%D8%A7%D8%B5:UserLogin&returnto=%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C+%D8%B3%D9%BE%DB%8C%D8%B3" title="ایہ بہتر اے کہ لاگ ان ہو جاؤ، فیر وی ایہ لازمی نئیں۔ [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>لاگ‌ ان کرو</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Pages for logged out editors <a href="/wiki/%DB%81%D8%AA%DA%BE%D9%88%D9%86%DA%88%D8%A7%D8%A6%DB%8C:Introduction" aria-label="Learn more about editing"><span>learn more</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%D8%AE%D8%A7%D8%B5:MyTalk" title="ایس آئی پی پتے دیاں تبدیلیاں تے گل بات [n]" accesskey="n"><span>گل بات</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></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="Site"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Contents" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Contents</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">لُکاؤ</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">Beginning</div> </a> </li> <li id="toc-سہج_مختصر_خلاصہ" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#سہج_مختصر_خلاصہ"> <div class="vector-toc-text"> <span class="vector-toc-numb">۱</span> <span>سہج مختصر خلاصہ</span> </div> </a> <button aria-controls="toc-سہج_مختصر_خلاصہ-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>Toggle سہج مختصر خلاصہ subsection</span> </button> <ul id="toc-سہج_مختصر_خلاصہ-sublist" class="vector-toc-list"> <li id="toc-دوری" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#دوری"> <div class="vector-toc-text"> <span class="vector-toc-numb">۱.۱</span> <span>دوری</span> </div> </a> <ul id="toc-دوری-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-اینگل" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#اینگل"> <div class="vector-toc-text"> <span class="vector-toc-numb">۱.۲</span> <span>اینگل</span> </div> </a> <ul id="toc-اینگل-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-روٹیشناں_اتے_رفلیکشناں" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#روٹیشناں_اتے_رفلیکشناں"> <div class="vector-toc-text"> <span class="vector-toc-numb">۱.۳</span> <span>روٹیشناں اتے رفلیکشناں</span> </div> </a> <ul id="toc-روٹیشناں_اتے_رفلیکشناں-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-اقلیدسی_گروپ" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#اقلیدسی_گروپ"> <div class="vector-toc-text"> <span class="vector-toc-numb">۱.۴</span> <span>اقلیدسی گروپ</span> </div> </a> <ul id="toc-اقلیدسی_گروپ-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-غیر-کارٹیزیئن_ڈریکشنر" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#غیر-کارٹیزیئن_ڈریکشنر"> <div class="vector-toc-text"> <span class="vector-toc-numb">۲</span> <span>غیر-کارٹیزیئن ڈریکشنر</span> </div> </a> <ul id="toc-غیر-کارٹیزیئن_ڈریکشنر-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-جیؤمیٹریکل_شکلاں" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#جیؤمیٹریکل_شکلاں"> <div class="vector-toc-text"> <span class="vector-toc-numb">۳</span> <span>جیؤمیٹریکل شکلاں</span> </div> </a> <button aria-controls="toc-جیؤمیٹریکل_شکلاں-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>Toggle جیؤمیٹریکل شکلاں subsection</span> </button> <ul id="toc-جیؤمیٹریکل_شکلاں-sublist" class="vector-toc-list"> <li id="toc-ریکھاواں،_ستہاں،_اتے_ہور_سبسپیساں" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#ریکھاواں،_ستہاں،_اتے_ہور_سبسپیساں"> <div class="vector-toc-text"> <span class="vector-toc-numb">۳.۱</span> <span>ریکھاواں، ستہاں، اتے ہور سبسپیساں</span> </div> </a> <ul id="toc-ریکھاواں،_ستہاں،_اتے_ہور_سبسپیساں-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-لائن-ٹکڑے_اتے_تکوناں" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#لائن-ٹکڑے_اتے_تکوناں"> <div class="vector-toc-text"> <span class="vector-toc-numb">۳.۲</span> <span>لائن-ٹکڑے اتے تکوناں</span> </div> </a> <ul id="toc-لائن-ٹکڑے_اتے_تکوناں-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-پولیٹوپ_اتے_روٹ_سسٹم" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#پولیٹوپ_اتے_روٹ_سسٹم"> <div class="vector-toc-text"> <span class="vector-toc-numb">۳.۳</span> <span>پولیٹوپ اتے روٹ سسٹم</span> </div> </a> <ul id="toc-پولیٹوپ_اتے_روٹ_سسٹم-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-وکراں" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#وکراں"> <div class="vector-toc-text"> <span class="vector-toc-numb">۳.۴</span> <span>وکراں</span> </div> </a> <ul id="toc-وکراں-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-گیندا،_گولے،_اتے_ہائیپر-گولیر" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#گیندا،_گولے،_اتے_ہائیپر-گولیر"> <div class="vector-toc-text"> <span class="vector-toc-numb">۳.۵</span> <span>گیندا، گولے، اتے ہائیپر-گولیر</span> </div> </a> <ul id="toc-گیندا،_گولے،_اتے_ہائیپر-گولیر-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-ٹوپولوجی" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#ٹوپولوجی"> <div class="vector-toc-text"> <span class="vector-toc-numb">۴</span> <span>ٹوپولوجی</span> </div> </a> <ul id="toc-ٹوپولوجی-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-ورتوں" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#ورتوں"> <div class="vector-toc-text"> <span class="vector-toc-numb">۵</span> <span>ورتوں</span> </div> </a> <ul id="toc-ورتوں-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-بدل_اتے_جنرلائزیشناں" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#بدل_اتے_جنرلائزیشناں"> <div class="vector-toc-text"> <span class="vector-toc-numb">۶</span> <span>بدل اتے جنرلائزیشناں</span> </div> </a> <button aria-controls="toc-بدل_اتے_جنرلائزیشناں-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>Toggle بدل اتے جنرلائزیشناں subsection</span> </button> <ul id="toc-بدل_اتے_جنرلائزیشناں-sublist" class="vector-toc-list"> <li id="toc-وکرت_سپیساں" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#وکرت_سپیساں"> <div class="vector-toc-text"> <span class="vector-toc-numb">۶.۱</span> <span>وکرت سپیساں</span> </div> </a> <ul id="toc-وکرت_سپیساں-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-انشچت_دوگھاتی_اکار" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#انشچت_دوگھاتی_اکار"> <div class="vector-toc-text"> <span class="vector-toc-numb">۶.۲</span> <span>انشچت دوگھاتی اکار</span> </div> </a> <ul id="toc-انشچت_دوگھاتی_اکار-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-ہور_آبادی_فیلڈاں" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#ہور_آبادی_فیلڈاں"> <div class="vector-toc-text"> <span class="vector-toc-numb">۶.۳</span> <span>ہور آبادی فیلڈاں</span> </div> </a> <ul id="toc-ہور_آبادی_فیلڈاں-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-اننت_ایام" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#اننت_ایام"> <div class="vector-toc-text"> <span class="vector-toc-numb">۶.۴</span> <span>اننت ایام</span> </div> </a> <ul id="toc-اننت_ایام-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-ایہہ_وی_دیکھو" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#ایہہ_وی_دیکھو"> <div class="vector-toc-text"> <span class="vector-toc-numb">۷</span> <span>ایہہ وی دیکھو</span> </div> </a> <ul id="toc-ایہہ_وی_دیکھو-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-فٹنوٹس" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#فٹنوٹس"> <div class="vector-toc-text"> <span class="vector-toc-numb">۸</span> <span>فٹنوٹس</span> </div> </a> <ul id="toc-فٹنوٹس-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-حوالے" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#حوالے"> <div class="vector-toc-text"> <span class="vector-toc-numb">۹</span> <span>حوالے</span> </div> </a> <ul id="toc-حوالے-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-باہری_لنک" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#باہری_لنک"> <div class="vector-toc-text"> <span class="vector-toc-numb">۱۰</span> <span>باہری لنک</span> </div> </a> <ul id="toc-باہری_لنک-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="Contents" 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="Toggle the table of contents" > <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">Toggle the table of contents</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">اقلیدسی سپیس</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="Go to an article in another language. Available in ۶۴ languages" > <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-64" 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">۶۴ بولیاں</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/Euklidiese_ruimte" title="Euklidiese ruimte – Afrikaans" lang="af" hreflang="af" data-title="Euklidiese ruimte" 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/Euklidischer_Raum" title="Euklidischer Raum – Alemannic" lang="gsw" hreflang="gsw" data-title="Euklidischer Raum" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%81%D8%B6%D8%A7%D8%A1_%D8%A5%D9%82%D9%84%D9%8A%D8%AF%D9%8A" title="فضاء إقليدي – Arabic" lang="ar" hreflang="ar" data-title="فضاء إقليدي" data-language-autonym="العربية" data-language-local-name="Arabic" 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/Espaciu_euclideu" title="Espaciu euclideu – Asturian" lang="ast" hreflang="ast" data-title="Espaciu euclideu" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4_%D0%B0%D1%80%D0%B0%D1%83%D1%8B%D2%93%D1%8B" title="Евклид арауығы – Bashkir" lang="ba" hreflang="ba" data-title="Евклид арауығы" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4%D0%BE%D0%B2%D0%BE_%D0%BF%D1%80%D0%BE%D1%81%D1%82%D1%80%D0%B0%D0%BD%D1%81%D1%82%D0%B2%D0%BE" title="Евклидово пространство – Bulgarian" lang="bg" hreflang="bg" data-title="Евклидово пространство" data-language-autonym="Български" data-language-local-name="Bulgarian" 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%87%E0%A6%89%E0%A6%95%E0%A7%8D%E0%A6%B2%E0%A6%BF%E0%A6%A1%E0%A7%80%E0%A6%AF%E0%A6%BC_%E0%A6%B8%E0%A7%8D%E0%A6%A5%E0%A6%BE%E0%A6%A8" title="ইউক্লিডীয় স্থান – Bangla" lang="bn" hreflang="bn" data-title="ইউক্লিডীয় স্থান" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Espai_euclidi%C3%A0" title="Espai euclidià – Catalan" lang="ca" hreflang="ca" data-title="Espai euclidià" 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/%D8%A8%DB%86%D8%B4%D8%A7%DB%8C%DB%8C%DB%8C_%D8%A6%DB%8C%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C" title="بۆشاییی ئیقلیدسی – Central Kurdish" lang="ckb" hreflang="ckb" data-title="بۆشاییی ئیقلیدسی" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" 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/Eukleidovsk%C3%BD_prostor" title="Eukleidovský prostor – Czech" lang="cs" hreflang="cs" data-title="Eukleidovský prostor" data-language-autonym="Čeština" data-language-local-name="Czech" 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%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4_%D1%83%C3%A7%D0%BB%C4%83%D1%85%C4%95" title="Евклид уçлăхĕ – Chuvash" lang="cv" hreflang="cv" data-title="Евклид уçлăхĕ" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" 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/Gofod_Euclidaidd" title="Gofod Euclidaidd – Welsh" lang="cy" hreflang="cy" data-title="Gofod Euclidaidd" data-language-autonym="Cymraeg" data-language-local-name="Welsh" 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/Euklidisk_rum" title="Euklidisk rum – Danish" lang="da" hreflang="da" data-title="Euklidisk rum" data-language-autonym="Dansk" data-language-local-name="Danish" 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/Euklidischer_Raum" title="Euklidischer Raum – German" lang="de" hreflang="de" data-title="Euklidischer Raum" data-language-autonym="Deutsch" data-language-local-name="German" 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%95%CF%85%CE%BA%CE%BB%CE%B5%CE%AF%CE%B4%CE%B5%CE%B9%CE%BF%CF%82_%CF%87%CF%8E%CF%81%CE%BF%CF%82" title="Ευκλείδειος χώρος – Greek" lang="el" hreflang="el" data-title="Ευκλείδειος χώρος" data-language-autonym="Ελληνικά" data-language-local-name="Greek" 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/Euclidean_space" title="Euclidean space – English" lang="en" hreflang="en" data-title="Euclidean space" data-language-autonym="English" data-language-local-name="English" 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/E%C5%ADklida_spaco" title="Eŭklida spaco – Esperanto" lang="eo" hreflang="eo" data-title="Eŭklida spaco" 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/Espacio_eucl%C3%ADdeo" title="Espacio euclídeo – Spanish" lang="es" hreflang="es" data-title="Espacio euclídeo" data-language-autonym="Español" data-language-local-name="Spanish" 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/Eukleidiline_ruum" title="Eukleidiline ruum – Estonian" lang="et" hreflang="et" data-title="Eukleidiline ruum" 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/Euklidear_espazio" title="Euklidear espazio – Basque" lang="eu" hreflang="eu" data-title="Euklidear espazio" data-language-autonym="Euskara" data-language-local-name="Basque" 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/%D9%81%D8%B6%D8%A7%DB%8C_%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C" title="فضای اقلیدسی – Persian" lang="fa" hreflang="fa" data-title="فضای اقلیدسی" data-language-autonym="فارسی" data-language-local-name="Persian" 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/Euklidinen_avaruus" title="Euklidinen avaruus – Finnish" lang="fi" hreflang="fi" data-title="Euklidinen avaruus" data-language-autonym="Suomi" data-language-local-name="Finnish" 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/Espace_euclidien" title="Espace euclidien – French" lang="fr" hreflang="fr" data-title="Espace euclidien" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Espazo_euclidiano" title="Espazo euclidiano – Galician" lang="gl" hreflang="gl" data-title="Espazo euclidiano" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%90%D7%95%D7%A7%D7%9C%D7%99%D7%93%D7%99" title="מרחב אוקלידי – Hebrew" lang="he" hreflang="he" data-title="מרחב אוקלידי" data-language-autonym="עברית" data-language-local-name="Hebrew" 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%AF%E0%A5%82%E0%A4%95%E0%A5%8D%E0%A4%B2%E0%A4%BF%E0%A4%A1%E0%A5%80%E0%A4%A8_%E0%A4%B8%E0%A4%AE%E0%A4%B7%E0%A5%8D%E0%A4%9F%E0%A4%BF" title="यूक्लिडीन समष्टि – Hindi" lang="hi" hreflang="hi" data-title="यूक्लिडीन समष्टि" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Euklidski_prostor" title="Euklidski prostor – Croatian" lang="hr" hreflang="hr" data-title="Euklidski prostor" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Euklideszi_t%C3%A9r_(line%C3%A1ris_algebra)" title="Euklideszi tér (lineáris algebra) – Hungarian" lang="hu" hreflang="hu" data-title="Euklideszi tér (lineáris algebra)" data-language-autonym="Magyar" data-language-local-name="Hungarian" 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/Ruang_Euklides" title="Ruang Euklides – Indonesian" lang="id" hreflang="id" data-title="Ruang Euklides" 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-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Euklidana_spaco" title="Euklidana spaco – Ido" lang="io" hreflang="io" data-title="Euklidana spaco" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Spazio_euclideo" title="Spazio euclideo – Italian" lang="it" hreflang="it" data-title="Spazio euclideo" 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/%E3%83%A6%E3%83%BC%E3%82%AF%E3%83%AA%E3%83%83%E3%83%89%E7%A9%BA%E9%96%93" title="ユークリッド空間 – Japanese" lang="ja" hreflang="ja" data-title="ユークリッド空間" data-language-autonym="日本語" data-language-local-name="Japanese" 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/%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4_%D0%BA%D0%B5%D2%A3%D1%96%D1%81%D1%82%D1%96%D0%B3%D1%96" title="Евклид кеңістігі – Kazakh" lang="kk" hreflang="kk" data-title="Евклид кеңістігі" data-language-autonym="Қазақша" data-language-local-name="Kazakh" 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/%EC%9C%A0%ED%81%B4%EB%A6%AC%EB%93%9C_%EA%B3%B5%EA%B0%84" title="유클리드 공간 – Korean" lang="ko" hreflang="ko" data-title="유클리드 공간" data-language-autonym="한국어" data-language-local-name="Korean" 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/Euklidin%C4%97_erdv%C4%97" title="Euklidinė erdvė – Lithuanian" lang="lt" hreflang="lt" data-title="Euklidinė erdvė" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" 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%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4%D0%BE%D0%B2_%D0%BF%D1%80%D0%BE%D1%81%D1%82%D0%BE%D1%80" title="Евклидов простор – Macedonian" lang="mk" hreflang="mk" data-title="Евклидов простор" 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%AF%E0%B5%82%E0%B4%95%E0%B5%8D%E0%B4%B2%E0%B4%BF%E0%B4%A1%E0%B4%BF%E0%B4%AF%E0%B5%BB_%E0%B4%B8%E0%B5%8D%E0%B4%AA%E0%B5%86%E0%B4%AF%E0%B5%8D%E0%B4%B8%E0%B5%8D" title="യൂക്ലിഡിയൻ സ്പെയ്സ് – Malayalam" lang="ml" hreflang="ml" data-title="യൂക്ലിഡിയൻ സ്പെയ്സ്" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" 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%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4%D0%B8%D0%B9%D0%BD_%D0%BE%D1%80%D0%BE%D0%BD_%D0%B7%D0%B0%D0%B9" title="Евклидийн орон зай – Mongolian" lang="mn" hreflang="mn" data-title="Евклидийн орон зай" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Ruang_Euclides" title="Ruang Euclides – Malay" lang="ms" hreflang="ms" data-title="Ruang Euclides" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" 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%9A%E1%80%B0%E1%80%80%E1%80%9C%E1%80%85%E1%80%BA%E1%80%92%E1%80%BA_%E1%80%85%E1%80%95%E1%80%B1%E1%80%B7%E1%80%85%E1%80%BA" title="ယူကလစ်ဒ် စပေ့စ် – Burmese" lang="my" hreflang="my" data-title="ယူကလစ်ဒ် စပေ့စ်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Euclidische_ruimte" title="Euclidische ruimte – Dutch" lang="nl" hreflang="nl" data-title="Euclidische ruimte" data-language-autonym="Nederlands" data-language-local-name="Dutch" 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/Euklidsk_rom" title="Euklidsk rom – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Euklidsk rom" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%AF%E0%A9%81%E0%A8%95%E0%A8%B2%E0%A8%BF%E0%A8%A1%E0%A9%80%E0%A8%85%E0%A8%A8_%E0%A8%B8%E0%A8%AA%E0%A9%87%E0%A8%B8" title="ਯੁਕਲਿਡੀਅਨ ਸਪੇਸ – Punjabi" lang="pa" hreflang="pa" data-title="ਯੁਕਲਿਡੀਅਨ ਸਪੇਸ" 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/Przestrze%C5%84_euklidesowa" title="Przestrzeń euklidesowa – Polish" lang="pl" hreflang="pl" data-title="Przestrzeń euklidesowa" data-language-autonym="Polski" data-language-local-name="Polish" 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/Espa%C3%A7o_euclidiano" title="Espaço euclidiano – Portuguese" lang="pt" hreflang="pt" data-title="Espaço euclidiano" data-language-autonym="Português" data-language-local-name="Portuguese" 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/Spa%C8%9Biu_euclidian" title="Spațiu euclidian – Romanian" lang="ro" hreflang="ro" data-title="Spațiu euclidian" data-language-autonym="Română" data-language-local-name="Romanian" 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%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4%D0%BE%D0%B2%D0%BE_%D0%BF%D1%80%D0%BE%D1%81%D1%82%D1%80%D0%B0%D0%BD%D1%81%D1%82%D0%B2%D0%BE" title="Евклидово пространство – Russian" lang="ru" hreflang="ru" data-title="Евклидово пространство" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Euklidski_prostor" title="Euklidski prostor – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Euklidski prostor" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" 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%BA%E0%B7%94%E0%B6%9A%E0%B7%8A%E0%B6%BD%E0%B7%92%E0%B6%A9%E0%B7%92%E0%B6%BA%E0%B7%8F%E0%B6%B1%E0%B7%94_%E0%B6%85%E0%B7%80%E0%B6%9A%E0%B7%8F%E0%B7%81%E0%B6%BA" title="යුක්ලිඩියානු අවකාශය – Sinhala" lang="si" hreflang="si" data-title="යුක්ලිඩියානු අවකාශය" data-language-autonym="සිංහල" data-language-local-name="Sinhala" 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/Euclidean_space" title="Euclidean space – Simple English" lang="en-simple" hreflang="en-simple" data-title="Euclidean space" 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/Evklidski_prostor" title="Evklidski prostor – Slovenian" lang="sl" hreflang="sl" data-title="Evklidski prostor" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" 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/Hap%C3%ABsira_Euklidiane" title="Hapësira Euklidiane – Albanian" lang="sq" hreflang="sq" data-title="Hapësira Euklidiane" data-language-autonym="Shqip" data-language-local-name="Albanian" 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%95%D1%83%D0%BA%D0%BB%D0%B8%D0%B4%D0%BE%D0%B2_%D0%BF%D1%80%D0%BE%D1%81%D1%82%D0%BE%D1%80" title="Еуклидов простор – Serbian" lang="sr" hreflang="sr" data-title="Еуклидов простор" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" 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/Euklidiskt_rum" title="Euklidiskt rum – Swedish" lang="sv" hreflang="sv" data-title="Euklidiskt rum" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AF%E0%AF%82%E0%AE%95%E0%AF%8D%E0%AE%B3%E0%AE%BF%E0%AE%9F%E0%AE%BF%E0%AE%AF_%E0%AE%B5%E0%AF%86%E0%AE%B3%E0%AE%BF" title="யூக்ளிடிய வெளி – Tamil" lang="ta" hreflang="ta" data-title="யூக்ளிடிய வெளி" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Espasyong_Euclides" title="Espasyong Euclides – Tagalog" lang="tl" hreflang="tl" data-title="Espasyong Euclides" data-language-autonym="Tagalog" data-language-local-name="Tagalog" 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/%C3%96klid_uzay%C4%B1" title="Öklid uzayı – Turkish" lang="tr" hreflang="tr" data-title="Öklid uzayı" data-language-autonym="Türkçe" data-language-local-name="Turkish" 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%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4_%D1%84%D3%99%D0%B7%D0%B0%D1%81%D1%8B" title="Евклид фәзасы – Tatar" lang="tt" hreflang="tt" data-title="Евклид фәзасы" 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%95%D0%B2%D0%BA%D0%BB%D1%96%D0%B4%D1%96%D0%B2_%D0%BF%D1%80%D0%BE%D1%81%D1%82%D1%96%D1%80" title="Евклідів простір – Ukrainian" lang="uk" hreflang="uk" data-title="Евклідів простір" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Yevklid_fazosi" title="Yevklid fazosi – Uzbek" lang="uz" hreflang="uz" data-title="Yevklid fazosi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" 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/Kh%C3%B4ng_gian_Euclid" title="Không gian Euclid – Vietnamese" lang="vi" hreflang="vi" data-title="Không gian Euclid" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" 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%AC%A7%E5%87%A0%E9%87%8C%E5%BE%97%E7%A9%BA%E9%97%B4" title="欧几里得空间 – Wu" lang="wuu" hreflang="wuu" data-title="欧几里得空间" data-language-autonym="吴语" data-language-local-name="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%AC%A7%E5%87%A0%E9%87%8C%E5%BE%97%E7%A9%BA%E9%97%B4" title="欧几里得空间 – Chinese" lang="zh" hreflang="zh" data-title="欧几里得空间" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%AD%90%E5%B9%BE%E9%87%8C%E5%BE%97%E7%A9%BA%E9%96%93" title="歐幾里得空間 – Cantonese" lang="yue" hreflang="yue" data-title="歐幾里得空間" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div 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vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">سند</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">لُکاؤ</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="More options" > <div class="vector-menu-heading"> Actions </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%B3%D9%BE%DB%8C%D8%B3"><span>پڑھو</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%B3%D9%BE%DB%8C%D8%B3&action=edit" title="Edit the source code of this page [e]" accesskey="e"><span>سودھو</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%B3%D9%BE%DB%8C%D8%B3&action=history"><span>تریخ دیکھو</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> عام </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/%D8%AE%D8%A7%D8%B5:WhatLinksHere/%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%B3%D9%BE%DB%8C%D8%B3" title="اس نال جڑے سارے وکی صفحے۔ [j]" accesskey="j"><span>ایتھے کیہہ جڑدا</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/%D8%AE%D8%A7%D8%B5:RecentChangesLinked/%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%B3%D9%BE%DB%8C%D8%B3" rel="nofollow" title="اس صفحے نال جڑے صفحیاں وچ نویاں تبدیلیاں [k]" accesskey="k"><span>رلدیاں ملدیاں تبدیلیاں</span></a></li><li id="t-upload" class="mw-list-item"><a href="//commons.wikimedia.org/wiki/Special:UploadWizard?uselang=pnb" title="فائل چڑھاؤ [u]" accesskey="u"><span>فائل چڑھاؤ</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/%D8%AE%D8%A7%D8%B5:SpecialPages" title="سارے خاص صفحیاں دی اک لسٹ [q]" accesskey="q"><span>خاص صفحے</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%B3%D9%BE%DB%8C%D8%B3&oldid=489339" title="اس صفحے دے اس ورژن نال پکا جوڑ"><span>پکا جوڑ</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%B3%D9%BE%DB%8C%D8%B3&action=info" title="More information about this page"><span>صفحے بارے جاݨکاری</span></a></li><li id="n-اج-دے-رُجحان" class="mw-list-item"><a href="http://tools.wmflabs.org/wikitrends/punjabi-most-visited-today.html"><span>اج دے رُجحان</span></a></li><li id="n-ہفتے-دے-رُجحان" class="mw-list-item"><a href="http://tools.wmflabs.org/wikitrends/punjabi-most-visited-this-week.html"><span>ہفتے دے رُجحان</span></a></li><li id="n-مہینے-دے-رُجحان" class="mw-list-item"><a href="http://tools.wmflabs.org/wikitrends/punjabi-most-visited-this-month.html"><span>مہینے دے رُجحان</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=%D8%AE%D8%A7%D8%B5:CiteThisPage&page=%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%B3%D9%BE%DB%8C%D8%B3&id=489339&wpFormIdentifier=titleform" title="اس صفحے دے حوالہ دے طریقہ دے بارے وچ معلومات"><span>ایس صفحے دا حوالہ دیو</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=%D8%AE%D8%A7%D8%B5:UrlShortener&url=https%3A%2F%2Fpnb.wikipedia.org%2Fwiki%2F%25D8%25A7%25D9%2582%25D9%2584%25DB%258C%25D8%25AF%25D8%25B3%25DB%258C_%25D8%25B3%25D9%25BE%25DB%258C%25D8%25B3"><span>Get shortened URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=%D8%AE%D8%A7%D8%B5:QrCode&url=https%3A%2F%2Fpnb.wikipedia.org%2Fwiki%2F%25D8%25A7%25D9%2582%25D9%2584%25DB%258C%25D8%25AF%25D8%25B3%25DB%258C_%25D8%25B3%25D9%25BE%25DB%258C%25D8%25B3"><span>Download QR code</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> چھاپو یا باہر لو </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=%D8%AE%D8%A7%D8%B5:%DA%A9%D8%AA%D8%A7%D8%A8&bookcmd=book_creator&referer=%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C+%D8%B3%D9%BE%DB%8C%D8%B3"><span>کتاب بناؤ</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=%D8%AE%D8%A7%D8%B5:DownloadAsPdf&page=%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%B3%D9%BE%DB%8C%D8%B3&action=show-download-screen"><span>PDF وجوں ڈاؤن لوڈ کرو</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%B3%D9%BE%DB%8C%D8%B3&printable=yes" title="اس صفحے دا چھپن والا ورژن ویکھو [p]" accesskey="p"><span>چھاپݨ والا صفحہ</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> ہور منصوبےآں وچ </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q17295" title="ریپوزیٹری آئیٹم نال جوڑ [g]" accesskey="g"><span>وِکیڈیٹا تے مد</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="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <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">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">لُکاؤ</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">آزاد انسائیکلوپیڈیا، وکیپیڈیا توں</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-rtl mw-parser-output" lang="pnb" dir="rtl"><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/%D9%81%D8%A7%D8%A6%D9%84:Sphere_wireframe.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/08/Sphere_wireframe.svg/220px-Sphere_wireframe.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/08/Sphere_wireframe.svg/330px-Sphere_wireframe.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/08/Sphere_wireframe.svg/440px-Sphere_wireframe.svg.png 2x" data-file-width="400" data-file-height="400" /></a><figcaption>اک گولہ (سفیئر)، <a href="/wiki/%D9%81%DB%8C%D8%AB%D8%A7%D8%BA%D9%88%D8%B1%D8%AB" class="mw-redirect" title="فیثاغورث">فیثاغورث</a> مطابق سبھ توں زیادہ مکمل سپیشیئل (مقامی) اکار، جو اقلیدسی سپیساں دی اجوکی سمجھ لئی اک اہم نظریہ وی اے۔</figcaption></figure> <p>جیؤمیٹری (جیؤمیٹری) وچّ، <b>اقلیدسی سپیس</b> دو-ڈمینشنل اقلیدسی سطح ، تنّ-ڈمینشنل اقلیدسی جیؤمیٹری دی سپیس، اتے کجھ ہور سپیساں رکھدی اے۔ اس دا نام <a href="/wiki/%D9%BE%D8%B1%D8%A7%D9%86%D8%A7_%DB%8C%D9%88%D9%86%D8%A7%D9%86" title="پرانا یونان">پرانے یونان</a> دے ریاضی دان <a href="/wiki/%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3" title="اقلیدس">اقلیدس</a> توں بعد رکھیا گیا اے۔ شبد “اقلیدسی” ایہناں سپیساں نوں ماڈرن جیؤمیٹری (جیؤمیٹری) وچّ وچاریاں جان والیاں ہور سپیساں توں الگّ کردا اے۔ اقلیدسی سپیساں دا اچّ-ڈمینشلاں تکّ اعلیٰ سدھارن کرن وی ہندا اے۔ </p><p>کلاسیکل <a href="/wiki/%DB%8C%D9%88%D9%86%D8%A7%D9%86%DB%8C" class="mw-redirect" title="یونانی">یونانی</a> جیؤمیٹری (جیؤمیٹری) کجھ سدھ نشان ورت کے اقلیدسی سپیس اتے اقلیدسی تنّ-ڈمینشنل سپیس متاثر کردی سی۔، جدوں کہ ایہناں سپیساں دیاں ہور خاصیتاں دا تھیورماں دے طور تے پتہ کیتا جاندا سی۔ جیؤمیٹریکل بنتراں ریشنل نمبراں نوں متاثر کرن لئی وی ورتیاں جاندیاں ہن۔ جدوں <a href="/wiki/%D8%A7%D9%84%D8%AC%D8%A8%D8%B1%D8%A7" title="الجبرا">الجبرا</a> اتے ریاضیاتی تجزیہ کافی ترقی یافتہ ہو گئے، ایہہ تعلق الٹے ہو گئے اتے ہن کارٹیزیئن نردیشانکاں اتے تچزیاتی جیؤمیٹری (جیؤمیٹری) دے وچار ورت کے اقلیدسی سپیس نوں متاثر کرنا عامَ گلّ ہو گئی اے۔ اس دا مطلب اے کہ سپیس دے نقطے حقیقی نمبراں دے گروہاں نال درسائے جاندے ہن، اتے جیؤمیٹریکل سائزاں نوں سمیکرناں اتے غیر یکسانیت دے روپ وچّ متاثر کیتا جان لگا اے۔ اس پہنچ نے الجبرے اتے <a href="/wiki/%DA%A9%DB%8C%D9%84%DA%A9%D9%88%D9%84%D8%B3" title="کیلکولس">کیلکلس</a> دے اؤزاراں نوں جیؤمیٹری دے سوالاں نوں سہن لئی لیاندا اے اتے اس دا ایہہ فائدہ اے کہ ایہہ تنّ ڈمینشلاں توں زیادہ والیاں اقلیدسی سپیساں تکّ اسانی نال جنرلائیز ہو جاندے ہن۔ </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="سہج_مختصر_خلاصہ"><span id=".D8.B3.DB.81.D8.AC_.D9.85.D8.AE.D8.AA.D8.B5.D8.B1_.D8.AE.D9.84.D8.A7.D8.B5.DB.81"></span>سہج مختصر خلاصہ</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%B3%D9%BE%DB%8C%D8%B3&action=edit&section=1" title="حصہ لکھو: سہج مختصر خلاصہ"><span>سودھو</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="دوری"><span id=".D8.AF.D9.88.D8.B1.DB.8C"></span>دوری</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%B3%D9%BE%DB%8C%D8%B3&action=edit&section=2" title="حصہ لکھو: دوری"><span>سودھو</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="اینگل"><span id=".D8.A7.DB.8C.D9.86.DA.AF.D9.84"></span>اینگل</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%B3%D9%BE%DB%8C%D8%B3&action=edit&section=3" title="حصہ لکھو: اینگل"><span>سودھو</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="روٹیشناں_اتے_رفلیکشناں"><span id=".D8.B1.D9.88.D9.B9.DB.8C.D8.B4.D9.86.D8.A7.DA.BA_.D8.A7.D8.AA.DB.92_.D8.B1.D9.81.D9.84.DB.8C.DA.A9.D8.B4.D9.86.D8.A7.DA.BA"></span>روٹیشناں اتے رفلیکشناں</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%B3%D9%BE%DB%8C%D8%B3&action=edit&section=4" title="حصہ لکھو: روٹیشناں اتے رفلیکشناں"><span>سودھو</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="اقلیدسی_گروپ"><span id=".D8.A7.D9.82.D9.84.DB.8C.D8.AF.D8.B3.DB.8C_.DA.AF.D8.B1.D9.88.D9.BE"></span>اقلیدسی گروپ</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%B3%D9%BE%DB%8C%D8%B3&action=edit&section=5" title="حصہ لکھو: اقلیدسی گروپ"><span>سودھو</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading2"><h2 id="غیر-کارٹیزیئن_ڈریکشنر"><span id=".D8.BA.DB.8C.D8.B1-.DA.A9.D8.A7.D8.B1.D9.B9.DB.8C.D8.B2.DB.8C.D8.A6.D9.86_.DA.88.D8.B1.DB.8C.DA.A9.D8.B4.D9.86.D8.B1"></span>غیر-کارٹیزیئن ڈریکشنر</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%B3%D9%BE%DB%8C%D8%B3&action=edit&section=6" title="حصہ لکھو: غیر-کارٹیزیئن ڈریکشنر"><span>سودھو</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading2"><h2 id="جیؤمیٹریکل_شکلاں"><span id=".D8.AC.DB.8C.D8.A4.D9.85.DB.8C.D9.B9.D8.B1.DB.8C.DA.A9.D9.84_.D8.B4.DA.A9.D9.84.D8.A7.DA.BA"></span>جیؤمیٹریکل شکلاں</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%B3%D9%BE%DB%8C%D8%B3&action=edit&section=7" title="حصہ لکھو: جیؤمیٹریکل شکلاں"><span>سودھو</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="ریکھاواں،_ستہاں،_اتے_ہور_سبسپیساں"><span id=".D8.B1.DB.8C.DA.A9.DA.BE.D8.A7.D9.88.D8.A7.DA.BA.D8.8C_.D8.B3.D8.AA.DB.81.D8.A7.DA.BA.D8.8C_.D8.A7.D8.AA.DB.92_.DB.81.D9.88.D8.B1_.D8.B3.D8.A8.D8.B3.D9.BE.DB.8C.D8.B3.D8.A7.DA.BA"></span>ریکھاواں، ستہاں، اتے ہور سبسپیساں</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%B3%D9%BE%DB%8C%D8%B3&action=edit&section=8" title="حصہ لکھو: ریکھاواں، ستہاں، اتے ہور سبسپیساں"><span>سودھو</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="لائن-ٹکڑے_اتے_تکوناں"><span id=".D9.84.D8.A7.D8.A6.D9.86-.D9.B9.DA.A9.DA.91.DB.92_.D8.A7.D8.AA.DB.92_.D8.AA.DA.A9.D9.88.D9.86.D8.A7.DA.BA"></span>لائن-ٹکڑے اتے تکوناں</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%B3%D9%BE%DB%8C%D8%B3&action=edit&section=9" title="حصہ لکھو: لائن-ٹکڑے اتے تکوناں"><span>سودھو</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="پولیٹوپ_اتے_روٹ_سسٹم"><span id=".D9.BE.D9.88.D9.84.DB.8C.D9.B9.D9.88.D9.BE_.D8.A7.D8.AA.DB.92_.D8.B1.D9.88.D9.B9_.D8.B3.D8.B3.D9.B9.D9.85"></span>پولیٹوپ اتے روٹ سسٹم</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%B3%D9%BE%DB%8C%D8%B3&action=edit&section=10" title="حصہ لکھو: پولیٹوپ اتے روٹ سسٹم"><span>سودھو</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="وکراں"><span id=".D9.88.DA.A9.D8.B1.D8.A7.DA.BA"></span>وکراں</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%B3%D9%BE%DB%8C%D8%B3&action=edit&section=11" title="حصہ لکھو: وکراں"><span>سودھو</span></a><span class="mw-editsection-bracket">]</span></span></div> <div lang="ur" class="UrduText"> <div role="note" class="hatnote navigation-not-searchable relarticle mainarticle">اصل مضمون: <a href="/w/index.php?title=%D9%88%DA%A9%D8%B1%D8%A7%DA%BA_%D8%AF%DB%8C_%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%AC%DB%8C%D8%A4%D9%85%DB%8C%D9%B9%D8%B1%DB%8C&action=edit&redlink=1" class="new" title="وکراں دی اقلیدسی جیؤمیٹری (صفحہ مَوجود نہیں اے)">وکراں دی اقلیدسی جیؤمیٹری</a></div> <div class="boilerplate">ہور دیکھو: <a href="/w/index.php?title=%D9%88%DA%A9%D8%B1%D8%A7%DA%BA_%D8%AF%DB%8C_%D9%84%D8%B3%D9%B9&action=edit&redlink=1" class="new" title="وکراں دی لسٹ (صفحہ مَوجود نہیں اے)">وکراں دی لسٹ</a></div> <p><a href="/w/index.php?title=%D8%B3%D8%A7%D9%86%DA%86%DB%81:Expand_section&action=edit&redlink=1" class="new" title="سانچہ:Expand section (صفحہ مَوجود نہیں اے)">سانچہ:Expand section</a> </p> <div class="mw-heading mw-heading3"><h3 id="گیندا،_گولے،_اتے_ہائیپر-گولیر"><span id=".DA.AF.DB.8C.D9.86.D8.AF.D8.A7.D8.8C_.DA.AF.D9.88.D9.84.DB.92.D8.8C_.D8.A7.D8.AA.DB.92_.DB.81.D8.A7.D8.A6.DB.8C.D9.BE.D8.B1-.DA.AF.D9.88.D9.84.DB.8C.D8.B1"></span>گیندا، گولے، اتے ہائیپر-گولیر</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%B3%D9%BE%DB%8C%D8%B3&action=edit&section=12" title="حصہ لکھو: گیندا، گولے، اتے ہائیپر-گولیر"><span>سودھو</span></a><span class="mw-editsection-bracket">]</span></span></div> <div lang="ur" class="UrduText"> <div role="note" class="hatnote navigation-not-searchable relarticle mainarticle">اصل مضمون: <a href="/w/index.php?title=%DA%AF%DB%8C%D9%86%D8%AF_(%DA%AF%D9%86%D8%AA)&action=edit&redlink=1" class="new" title="گیند (گنت) (صفحہ مَوجود نہیں اے)">گیند (گنت)</a> تے <a href="/w/index.php?title=%DB%81%D8%A7%D8%A6%DB%8C%D9%BE%D8%B1%D8%B3%D8%B7%D8%AD%DB%8C&action=edit&redlink=1" class="new" title="ہائیپرسطحی (صفحہ مَوجود نہیں اے)">ہائیپرسطحی</a></div> <div class="boilerplate">ہور دیکھو: <a href="/w/index.php?title=N-%DA%AF%D9%88%D9%84%DB%81&action=edit&redlink=1" class="new" title="N-گولہ (صفحہ مَوجود نہیں اے)">n-گولہ</a> تے <a href="/w/index.php?title=%D8%B3%D8%B7%D8%AD%D8%A7%DA%BA_%D8%AF%DB%8C_%D9%84%D8%B3%D9%B9&action=edit&redlink=1" class="new" title="سطحاں دی لسٹ (صفحہ مَوجود نہیں اے)">سطحاں دی لسٹ</a></div> <p><a href="/w/index.php?title=%D8%B3%D8%A7%D9%86%DA%86%DB%81:Expand_section&action=edit&redlink=1" class="new" title="سانچہ:Expand section (صفحہ مَوجود نہیں اے)">سانچہ:Expand section</a> </p> <div class="mw-heading mw-heading2"><h2 id="ٹوپولوجی"><span id=".D9.B9.D9.88.D9.BE.D9.88.D9.84.D9.88.D8.AC.DB.8C"></span><a href="/wiki/%D9%B9%D9%88%D9%BE%D9%88%D9%84%D9%88%D8%AC%DB%8C" title="ٹوپولوجی">ٹوپولوجی</a></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%B3%D9%BE%DB%8C%D8%B3&action=edit&section=13" title="حصہ لکھو: ٹوپولوجی"><span>سودھو</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading2"><h2 id="ورتوں"><span id=".D9.88.D8.B1.D8.AA.D9.88.DA.BA"></span>ورتوں</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%B3%D9%BE%DB%8C%D8%B3&action=edit&section=14" title="حصہ لکھو: ورتوں"><span>سودھو</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading2"><h2 id="بدل_اتے_جنرلائزیشناں"><span id=".D8.A8.D8.AF.D9.84_.D8.A7.D8.AA.DB.92_.D8.AC.D9.86.D8.B1.D9.84.D8.A7.D8.A6.D8.B2.DB.8C.D8.B4.D9.86.D8.A7.DA.BA"></span>بدل اتے جنرلائزیشناں</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%B3%D9%BE%DB%8C%D8%B3&action=edit&section=15" title="حصہ لکھو: بدل اتے جنرلائزیشناں"><span>سودھو</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="وکرت_سپیساں"><span id=".D9.88.DA.A9.D8.B1.D8.AA_.D8.B3.D9.BE.DB.8C.D8.B3.D8.A7.DA.BA"></span>وکرت سپیساں</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%B3%D9%BE%DB%8C%D8%B3&action=edit&section=16" title="حصہ لکھو: وکرت سپیساں"><span>سودھو</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="انشچت_دوگھاتی_اکار"><span id=".D8.A7.D9.86.D8.B4.DA.86.D8.AA_.D8.AF.D9.88.DA.AF.DA.BE.D8.A7.D8.AA.DB.8C_.D8.A7.DA.A9.D8.A7.D8.B1"></span>انشچت دوگھاتی اکار</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%B3%D9%BE%DB%8C%D8%B3&action=edit&section=17" title="حصہ لکھو: انشچت دوگھاتی اکار"><span>سودھو</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="ہور_آبادی_فیلڈاں"><span id=".DB.81.D9.88.D8.B1_.D8.A2.D8.A8.D8.A7.D8.AF.DB.8C_.D9.81.DB.8C.D9.84.DA.88.D8.A7.DA.BA"></span>ہور آبادی فیلڈاں</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%B3%D9%BE%DB%8C%D8%B3&action=edit&section=18" title="حصہ لکھو: ہور آبادی فیلڈاں"><span>سودھو</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="اننت_ایام"><span id=".D8.A7.D9.86.D9.86.D8.AA_.D8.A7.DB.8C.D8.A7.D9.85"></span>اننت ایام</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%B3%D9%BE%DB%8C%D8%B3&action=edit&section=19" title="حصہ لکھو: اننت ایام"><span>سودھو</span></a><span class="mw-editsection-bracket">]</span></span></div> <div lang="ur" class="UrduText"> <div role="note" class="hatnote navigation-not-searchable relarticle mainarticle">اصل مضمون: <a href="/w/index.php?title=%D8%A7%D9%86%D8%AF%D8%B1%D9%88%D9%86%DB%8C_%D9%BE%D8%B1%D9%88%DA%88%DA%A9%D9%B9_%D8%B3%D9%BE%DB%8C%D8%B3&action=edit&redlink=1" class="new" title="اندرونی پروڈکٹ سپیس (صفحہ مَوجود نہیں اے)">اندرونی پروڈکٹ سپیس</a> تے <a href="/wiki/%DB%81%D9%84%D8%A8%D8%B1%D9%B9_%D8%B3%D9%BE%DB%8C%D8%B3" title="ہلبرٹ سپیس">ہلبرٹ سپیس</a></div> <p><a href="/w/index.php?title=%D8%B3%D8%A7%D9%86%DA%86%DB%81:Expand_section&action=edit&redlink=1" class="new" title="سانچہ:Expand section (صفحہ مَوجود نہیں اے)">سانچہ:Expand section</a> </p> <div class="mw-heading mw-heading2"><h2 id="ایہہ_وی_دیکھو"><span id=".D8.A7.DB.8C.DB.81.DB.81_.D9.88.DB.8C_.D8.AF.DB.8C.DA.A9.DA.BE.D9.88"></span>ایہہ وی دیکھو</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%B3%D9%BE%DB%8C%D8%B3&action=edit&section=20" title="حصہ لکھو: ایہہ وی دیکھو"><span>سودھو</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/w/index.php?title=%D8%AD%D9%82%DB%8C%D9%82%DB%8C_%DA%88%D8%B1%DB%8C%DA%A9%D8%B4%D9%86%D8%B1_%D8%B3%D9%BE%DB%8C%D8%B3&action=edit&redlink=1" class="new" title="حقیقی ڈریکشنر سپیس (صفحہ مَوجود نہیں اے)">حقیقی ڈریکشنر سپیس</a>، اقلیدسی سپیس دی اک اکثر ورتی جاندی حالت</li> <li><a href="/w/index.php?title=%DA%A9%D8%A6%DB%8C_%D8%AD%D9%82%DB%8C%D9%82%D8%AA%DB%8C_%D8%A7%D8%B3%D8%AA%DA%BE%D8%B1%D8%A7%D9%86%DA%A9%D8%A7%DA%BA_%D8%AF%DB%92_%D9%81%D9%86%DA%A9%D8%B4%D9%86&action=edit&redlink=1" class="new" title="کئی حقیقتی استھرانکاں دے فنکشن (صفحہ مَوجود نہیں اے)">کئی حقیقتی استھرانکاں دے فنکشن</a>، کسے اقلیدسی سپیس اتے اک فنکشن دی اک ڈریکشنر -حالت</li> <li><a href="/w/index.php?title=%D8%B1%DB%8C%DA%A9%DA%BE%DA%AF%D9%86%D8%AA%DA%A9_%D8%A7%D9%84%D8%AC%D8%A8%D8%B1%D8%A7&action=edit&redlink=1" class="new" title="ریکھگنتک الجبرا (صفحہ مَوجود نہیں اے)">ریکھگنتک الجبرا</a>، اک بدلویں الجبرک فارمولا ویونتبندی</li> <li><a href="/w/index.php?title=%D9%88%DB%8C%DA%A9%D9%B9%D8%B1_%DA%A9%DB%8C%D9%84%DA%A9%D9%84%D8%B3&action=edit&redlink=1" class="new" title="ویکٹر کیلکلس (صفحہ مَوجود نہیں اے)">ویکٹر کیلکلس</a>، اک معیاری الجبرک فارمولا ویونتبندی</li> <li><a href="/wiki/%D9%88%DB%8C%DA%A9%D9%B9%D8%B1_%D8%B3%D9%BE%DB%8C%D8%B3" title="ویکٹر سپیس">ویکٹر سپیس</a></li> <li><a href="/w/index.php?title=%D8%A7%DA%86%D9%91-%DA%88%D9%85%DB%8C%D9%86%D8%B4%D9%86%D9%84_%D8%B3%D9%BE%DB%8C%D8%B3&action=edit&redlink=1" class="new" title="اچّ-ڈمینشنل سپیس (صفحہ مَوجود نہیں اے)">اچّ-ڈمینشنل سپیس</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="فٹنوٹس"><span id=".D9.81.D9.B9.D9.86.D9.88.D9.B9.D8.B3"></span>فٹنوٹس</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%B3%D9%BE%DB%8C%D8%B3&action=edit&section=21" title="حصہ لکھو: فٹنوٹس"><span>سودھو</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist references-small" style="{{# گزینه: | small= font-size:small; | below= font-size:smaller; }}"> </div> <div class="mw-heading mw-heading2"><h2 id="حوالے"><span id=".D8.AD.D9.88.D8.A7.D9.84.DB.92"></span>حوالے</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%B3%D9%BE%DB%8C%D8%B3&action=edit&section=22" title="حصہ لکھو: حوالے"><span>سودھو</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist references-small" style="{{# گزینه: | small= font-size:small; | below= font-size:smaller; }}"> </div> <div class="mw-heading mw-heading2"><h2 id="باہری_لنک"><span id=".D8.A8.D8.A7.DB.81.D8.B1.DB.8C_.D9.84.D9.86.DA.A9"></span>باہری لنک</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D8%A7%D9%82%D9%84%DB%8C%D8%AF%D8%B3%DB%8C_%D8%B3%D9%BE%DB%8C%D8%B3&action=edit&section=23" title="حصہ لکھو: باہری لنک"><span>سودھو</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><strong class="error"><span class="scribunto-error mw-scribunto-error-91b6e29d">Lua error in package.lua at line 80: module 'Module:Citation/CS1/COinS' not found.</span></strong></li></ul> <p><a href="/w/index.php?title=%D8%B3%D8%A7%D9%86%DA%86%DB%81:%D9%81%D9%86%DA%A9%D8%B4%D9%86%D9%84_%D8%AA%D8%AC%D8%B2%DB%8C%DB%81&action=edit&redlink=1" class="new" title="سانچہ:فنکشنل تجزیہ (صفحہ مَوجود نہیں اے)">سانچہ:فنکشنل تجزیہ</a> </p> <span lang="ur"><table class="navbox" style="border-spacing:0"><tbody><tr><td style="padding:1px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group"><a href="/w/index.php?title=%D9%85%D8%B9%D8%A7%D9%88%D9%86%D8%AA:%D9%85%D8%B9%D9%84%D9%88%D9%85%D8%A7%D8%AA_%DA%A9%D8%AA%D8%A8_%D8%AE%D8%A7%D9%86%DB%81&action=edit&redlink=1" class="new" title="معاونت:معلومات کتب خانہ (صفحہ مَوجود نہیں اے)">معلومات کتب خانہ</a></th><td class="navbox-list navbox-odd" style="text-align:right;border-right-width:2px;border-right-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><span style="white-space:nowrap;"><a href="/w/index.php?title=%D9%85%D8%B1%D8%A8%D9%88%D8%B7_%D9%81%D8%A7%D8%A6%D9%84_%D9%85%D9%82%D8%AA%D8%AF%D8%B1%DB%81&action=edit&redlink=1" class="new" title="مربوط فائل مقتدرہ (صفحہ مَوجود نہیں اے)">جی این ڈی</a>: <span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4309127-1">4309127-1</a></span></span></li> <li><span style="white-space:nowrap;"><a href="/w/index.php?title=Biblioth%C3%A8que_nationale_de_France&action=edit&redlink=1" class="new" title="Bibliothèque nationale de France (صفحہ مَوجود نہیں اے)">بی این ایف</a>: <span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb122864798">cb122864798</a> <a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb122864798">(data)</a></span></span></li> <li><span style="white-space:nowrap;"><a href="/w/index.php?title=National_Diet_Library&action=edit&redlink=1" class="new" title="National Diet Library (صفحہ مَوجود نہیں اے)">این ڈی ایل</a>: <span class="uid"><a rel="nofollow" class="external text" href="https://id.ndl.go.jp/auth/ndlna/00562065">00562065</a></span></span></li> <li><span style="white-space:nowrap;"><a href="/w/index.php?title=National_Library_of_the_Czech_Republic&action=edit&redlink=1" class="new" title="National Library of the Czech Republic (صفحہ مَوجود نہیں اے)">این 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