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Прочитајте ги правилата и вклучете се!\n\u003C/p\u003E\u003C/div\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="Мрежно место"> <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="Содржина" 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">Содржина</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">премести во страничникот</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">скриј</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">Почеток</div> </a> </li> <li id="toc-Основни_формули" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Основни_формули"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Основни формули</span> </div> </a> <ul id="toc-Основни_формули-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Сферата_во_тридимензионален_простор" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Сферата_во_тридимензионален_простор"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Сферата во тридимензионален простор</span> </div> </a> <ul id="toc-Сферата_во_тридимензионален_простор-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Делови_на_сферата" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Делови_на_сферата"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Делови на сферата</span> </div> </a> <ul id="toc-Делови_на_сферата-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Воопштување_на_сферата" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Воопштување_на_сферата"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Воопштување на сферата</span> </div> </a> <ul id="toc-Воопштување_на_сферата-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Сферна_геометрија" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Сферна_геометрија"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Сферна геометрија</span> </div> </a> <ul id="toc-Сферна_геометрија-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Единаесет_својства_на_сферата" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Единаесет_својства_на_сферата"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Единаесет својства на сферата</span> </div> </a> <ul id="toc-Единаесет_својства_на_сферата-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Поврзано" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Поврзано"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Поврзано</span> </div> </a> <ul id="toc-Поврзано-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Наводи" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Наводи"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Наводи</span> </div> </a> <ul id="toc-Наводи-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Надворешни_врски" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Надворешни_врски"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Надворешни врски</span> </div> </a> <ul id="toc-Надворешни_врски-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="Содржина" 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="Прик./скр. содржина" > <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">Прик./скр. содржина</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">Сфера</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="Појдете на статија на друг јазик. Достапно на 106 јазици" > <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-106" 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">106 јазици</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/Sfeer" title="Sfeer — африканс" lang="af" hreflang="af" data-title="Sfeer" data-language-autonym="Afrikaans" data-language-local-name="африканс" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%88%89%E1%88%8D" title="ሉል — амхарски" lang="am" hreflang="am" data-title="ሉል" data-language-autonym="አማርኛ" data-language-local-name="амхарски" 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/%D9%83%D8%B1%D8%A9" title="كرة — арапски" lang="ar" hreflang="ar" data-title="كرة" data-language-autonym="العربية" data-language-local-name="арапски" 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/Esfera" title="Esfera — астурски" lang="ast" hreflang="ast" data-title="Esfera" data-language-autonym="Asturianu" data-language-local-name="астурски" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Sfera" title="Sfera — азербејџански" lang="az" hreflang="az" data-title="Sfera" data-language-autonym="Azərbaycanca" data-language-local-name="азербејџански" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%DA%A9%D9%88%D8%B1%D9%87_(%D9%87%D9%86%D8%AF%D8%B3%D9%87)" title="کوره (هندسه) — South Azerbaijani" lang="azb" hreflang="azb" data-title="کوره (هندسه)" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%97%E0%A7%8B%E0%A6%B2%E0%A6%95" title="গোলক — бенгалски" lang="bn" hreflang="bn" data-title="গোলক" data-language-autonym="বাংলা" data-language-local-name="бенгалски" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Ki%C3%BB-b%C4%ABn" title="Kiû-bīn — јужномински" lang="nan" hreflang="nan" data-title="Kiû-bīn" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="јужномински" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%A1%D1%84%D0%B5%D1%80%D0%B0" title="Сфера — башкирски" lang="ba" hreflang="ba" data-title="Сфера" data-language-autonym="Башҡортса" data-language-local-name="башкирски" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A1%D1%84%D0%B5%D1%80%D0%B0" title="Сфера — белоруски" lang="be" hreflang="be" data-title="Сфера" data-language-autonym="Беларуская" data-language-local-name="белоруски" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%97%E0%A5%8B%E0%A4%B2%E0%A4%BE" title="गोला — Bhojpuri" lang="bh" hreflang="bh" data-title="गोला" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target"><span>भोजपुरी</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A1%D1%84%D0%B5%D1%80%D0%B0" title="Сфера — бугарски" lang="bg" hreflang="bg" data-title="Сфера" data-language-autonym="Български" data-language-local-name="бугарски" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Sfera" title="Sfera — босански" lang="bs" hreflang="bs" data-title="Sfera" data-language-autonym="Bosanski" data-language-local-name="босански" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Esfera" title="Esfera — каталонски" lang="ca" hreflang="ca" data-title="Esfera" data-language-autonym="Català" data-language-local-name="каталонски" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A1%D1%84%D0%B5%D1%80%D0%B0" title="Сфера — чувашки" lang="cv" hreflang="cv" data-title="Сфера" data-language-autonym="Чӑвашла" data-language-local-name="чувашки" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Sf%C3%A9ra_(matematika)" title="Sféra (matematika) — чешки" lang="cs" hreflang="cs" data-title="Sféra (matematika)" data-language-autonym="Čeština" data-language-local-name="чешки" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Mburungwa" title="Mburungwa — шона" lang="sn" hreflang="sn" data-title="Mburungwa" data-language-autonym="ChiShona" data-language-local-name="шона" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Sff%C3%AAr" title="Sffêr — велшки" lang="cy" hreflang="cy" data-title="Sffêr" data-language-autonym="Cymraeg" data-language-local-name="велшки" 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/Kugle" title="Kugle — дански" lang="da" hreflang="da" data-title="Kugle" data-language-autonym="Dansk" data-language-local-name="дански" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D9%83%D9%88%D8%B1%D8%A9" title="كورة — марокански арапски" lang="ary" hreflang="ary" data-title="كورة" data-language-autonym="الدارجة" data-language-local-name="марокански арапски" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Kugel" title="Kugel — германски" lang="de" hreflang="de" data-title="Kugel" data-language-autonym="Deutsch" data-language-local-name="германски" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Sf%C3%A4%C3%A4r" title="Sfäär — естонски" lang="et" hreflang="et" data-title="Sfäär" data-language-autonym="Eesti" data-language-local-name="естонски" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A3%CF%86%CE%B1%CE%AF%CF%81%CE%B1" title="Σφαίρα — грчки" lang="el" hreflang="el" data-title="Σφαίρα" data-language-autonym="Ελληνικά" data-language-local-name="грчки" 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/Sphere" title="Sphere — англиски" lang="en" hreflang="en" data-title="Sphere" data-language-autonym="English" data-language-local-name="англиски" 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/Esfera" title="Esfera — шпански" lang="es" hreflang="es" data-title="Esfera" data-language-autonym="Español" data-language-local-name="шпански" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Sfero" title="Sfero — есперанто" lang="eo" hreflang="eo" data-title="Sfero" data-language-autonym="Esperanto" data-language-local-name="есперанто" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Esfera" title="Esfera — баскиски" lang="eu" hreflang="eu" data-title="Esfera" data-language-autonym="Euskara" data-language-local-name="баскиски" 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/%DA%A9%D8%B1%D9%87_(%D9%87%D9%86%D8%AF%D8%B3%D9%87)" title="کره (هندسه) — персиски" lang="fa" hreflang="fa" data-title="کره (هندسه)" data-language-autonym="فارسی" data-language-local-name="персиски" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Sph%C3%A8re" title="Sphère — француски" lang="fr" hreflang="fr" data-title="Sphère" data-language-autonym="Français" data-language-local-name="француски" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Sf%C3%A9ar" title="Sféar — ирски" lang="ga" hreflang="ga" data-title="Sféar" data-language-autonym="Gaeilge" data-language-local-name="ирски" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/Cruinne" title="Cruinne — шкотски гелски" lang="gd" hreflang="gd" data-title="Cruinne" data-language-autonym="Gàidhlig" data-language-local-name="шкотски гелски" class="interlanguage-link-target"><span>Gàidhlig</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Esfera" title="Esfera — галициски" lang="gl" hreflang="gl" data-title="Esfera" data-language-autonym="Galego" data-language-local-name="галициски" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E7%90%83%E9%9D%A2" title="球面 — ган" lang="gan" hreflang="gan" data-title="球面" data-language-autonym="贛語" data-language-local-name="ган" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%97%E0%AB%8B%E0%AA%B3%E0%AB%8B" title="ગોળો — гуџарати" lang="gu" hreflang="gu" data-title="ગોળો" data-language-autonym="ગુજરાતી" data-language-local-name="гуџарати" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B5%AC_(%EA%B8%B0%ED%95%98%ED%95%99)" title="구 (기하학) — корејски" lang="ko" hreflang="ko" data-title="구 (기하학)" data-language-autonym="한국어" data-language-local-name="корејски" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%97%E0%A5%8B%E0%A4%B2%E0%A4%BE" title="गोला — хинди" lang="hi" hreflang="hi" data-title="गोला" data-language-autonym="हिन्दी" data-language-local-name="хинди" 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/Sfera" title="Sfera — хрватски" lang="hr" hreflang="hr" data-title="Sfera" data-language-autonym="Hrvatski" data-language-local-name="хрватски" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Sfero" title="Sfero — идо" lang="io" hreflang="io" data-title="Sfero" data-language-autonym="Ido" data-language-local-name="идо" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Bola_(geometri)" title="Bola (geometri) — индонезиски" lang="id" hreflang="id" data-title="Bola (geometri)" data-language-autonym="Bahasa Indonesia" data-language-local-name="индонезиски" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Sphera" title="Sphera — интерлингва" lang="ia" hreflang="ia" data-title="Sphera" data-language-autonym="Interlingua" data-language-local-name="интерлингва" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/K%C3%BAla" title="Kúla — исландски" lang="is" hreflang="is" data-title="Kúla" data-language-autonym="Íslenska" data-language-local-name="исландски" 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/Sfera" title="Sfera — италијански" lang="it" hreflang="it" data-title="Sfera" data-language-autonym="Italiano" data-language-local-name="италијански" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A1%D7%A4%D7%99%D7%A8%D7%94_(%D7%92%D7%90%D7%95%D7%9E%D7%98%D7%A8%D7%99%D7%94)" title="ספירה (גאומטריה) — хебрејски" lang="he" hreflang="he" data-title="ספירה (גאומטריה)" data-language-autonym="עברית" data-language-local-name="хебрејски" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%97%E0%B3%8B%E0%B2%B3" title="ಗೋಳ — каннада" lang="kn" hreflang="kn" data-title="ಗೋಳ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="каннада" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A1%E1%83%A4%E1%83%94%E1%83%A0%E1%83%9D" title="სფერო — грузиски" lang="ka" hreflang="ka" data-title="სფერო" data-language-autonym="ქართული" data-language-local-name="грузиски" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A1%D1%84%D0%B5%D1%80%D0%B0" title="Сфера — казашки" lang="kk" hreflang="kk" data-title="Сфера" data-language-autonym="Қазақша" data-language-local-name="казашки" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Tufe" title="Tufe — свахили" lang="sw" hreflang="sw" data-title="Tufe" data-language-autonym="Kiswahili" data-language-local-name="свахили" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Esf%C3%A8" title="Esfè — хаитски" lang="ht" hreflang="ht" data-title="Esfè" data-language-autonym="Kreyòl ayisyen" data-language-local-name="хаитски" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Sf%C3%A8r" title="Sfèr — Guianan Creole" lang="gcr" hreflang="gcr" data-title="Sfèr" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Sphaera" title="Sphaera — латински" lang="la" hreflang="la" data-title="Sphaera" data-language-autonym="Latina" data-language-local-name="латински" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Sf%C4%93ra" title="Sfēra — латвиски" lang="lv" hreflang="lv" data-title="Sfēra" data-language-autonym="Latviešu" data-language-local-name="латвиски" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Sfera" title="Sfera — литвански" lang="lt" hreflang="lt" data-title="Sfera" data-language-autonym="Lietuvių" data-language-local-name="литвански" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/G%C3%B6mb" title="Gömb — унгарски" lang="hu" hreflang="hu" data-title="Gömb" data-language-autonym="Magyar" data-language-local-name="унгарски" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Bola_(je%C3%B4metria)" title="Bola (jeômetria) — малгашки" lang="mg" hreflang="mg" data-title="Bola (jeômetria)" data-language-autonym="Malagasy" data-language-local-name="малгашки" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%97%E0%B5%8B%E0%B4%B3%E0%B4%82" title="ഗോളം — малајалски" lang="ml" hreflang="ml" data-title="ഗോളം" data-language-autonym="മലയാളം" data-language-local-name="малајалски" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Sfera" title="Sfera — малајски" lang="ms" hreflang="ms" data-title="Sfera" data-language-autonym="Bahasa Melayu" data-language-local-name="малајски" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mdf mw-list-item"><a href="https://mdf.wikipedia.org/wiki/%D0%A1%D1%84%D0%B5%D1%80%D0%B0%D1%81%D1%8C" title="Сферась — мокшански" lang="mdf" hreflang="mdf" data-title="Сферась" data-language-autonym="Мокшень" data-language-local-name="мокшански" class="interlanguage-link-target"><span>Мокшень</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%91%D3%A9%D0%BC%D0%B1%D3%A9%D0%BB%D3%A9%D0%B3" title="Бөмбөлөг — монголски" lang="mn" hreflang="mn" data-title="Бөмбөлөг" data-language-autonym="Монгол" data-language-local-name="монголски" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%85%E1%80%80%E1%80%BA%E1%80%9C%E1%80%AF%E1%80%B6%E1%80%B8" title="စက်လုံး — бурмански" lang="my" hreflang="my" data-title="စက်လုံး" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="бурмански" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Vuravura_(Geometry)" title="Vuravura (Geometry) — фиџиски" lang="fj" hreflang="fj" data-title="Vuravura (Geometry)" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="фиџиски" class="interlanguage-link-target"><span>Na Vosa Vakaviti</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Sfeer_(wiskunde)" title="Sfeer (wiskunde) — холандски" lang="nl" hreflang="nl" data-title="Sfeer (wiskunde)" data-language-autonym="Nederlands" data-language-local-name="холандски" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%90%83%E9%9D%A2" title="球面 — јапонски" lang="ja" hreflang="ja" data-title="球面" data-language-autonym="日本語" data-language-local-name="јапонски" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Kuugel" title="Kuugel — севернофризиски" lang="frr" hreflang="frr" data-title="Kuugel" data-language-autonym="Nordfriisk" data-language-local-name="севернофризиски" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Kule" title="Kule — норвешки букмол" lang="nb" hreflang="nb" data-title="Kule" data-language-autonym="Norsk bokmål" data-language-local-name="норвешки букмол" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Kule" title="Kule — норвешки нинорск" lang="nn" hreflang="nn" data-title="Kule" data-language-autonym="Norsk nynorsk" data-language-local-name="норвешки нинорск" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Esf%C3%A8ra" title="Esfèra — окситански" lang="oc" hreflang="oc" data-title="Esfèra" data-language-autonym="Occitan" data-language-local-name="окситански" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Duqunqula" title="Duqunqula — оромо" lang="om" hreflang="om" data-title="Duqunqula" data-language-autonym="Oromoo" data-language-local-name="оромо" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Sfera" title="Sfera — узбечки" lang="uz" hreflang="uz" data-title="Sfera" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="узбечки" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%97%E0%A9%8B%E0%A8%B2%E0%A8%BC%E0%A8%BE" title="ਗੋਲ਼ਾ — пенџапски" lang="pa" hreflang="pa" data-title="ਗੋਲ਼ਾ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="пенџапски" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Sfier" title="Sfier — јамајски креолски" lang="jam" hreflang="jam" data-title="Sfier" data-language-autonym="Patois" data-language-local-name="јамајски креолски" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Sfera" title="Sfera — пиемонтски" lang="pms" hreflang="pms" data-title="Sfera" data-language-autonym="Piemontèis" data-language-local-name="пиемонтски" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Sfera" title="Sfera — полски" lang="pl" hreflang="pl" data-title="Sfera" data-language-autonym="Polski" data-language-local-name="полски" 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/Esfera" title="Esfera — португалски" lang="pt" hreflang="pt" data-title="Esfera" data-language-autonym="Português" data-language-local-name="португалски" 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/Sfer%C4%83" title="Sferă — романски" lang="ro" hreflang="ro" data-title="Sferă" data-language-autonym="Română" data-language-local-name="романски" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Lunq%27u" title="Lunq'u — кечуански" lang="qu" hreflang="qu" data-title="Lunq'u" data-language-autonym="Runa Simi" data-language-local-name="кечуански" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A1%D1%84%D0%B5%D1%80%D0%B0" title="Сфера — руски" lang="ru" hreflang="ru" data-title="Сфера" data-language-autonym="Русский" data-language-local-name="руски" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%A1%D1%84%D0%B5%D1%80%D0%B0" title="Сфера — јакутски" lang="sah" hreflang="sah" data-title="Сфера" data-language-autonym="Саха тыла" data-language-local-name="јакутски" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Sfera" title="Sfera — албански" lang="sq" hreflang="sq" data-title="Sfera" data-language-autonym="Shqip" data-language-local-name="албански" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Sfera" title="Sfera — сицилијански" lang="scn" hreflang="scn" data-title="Sfera" data-language-autonym="Sicilianu" data-language-local-name="сицилијански" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%9C%E0%B7%9D%E0%B6%BD%E0%B6%BA" title="ගෝලය — синхалски" lang="si" hreflang="si" data-title="ගෝලය" data-language-autonym="සිංහල" data-language-local-name="синхалски" 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/Sphere" title="Sphere — Simple English" lang="en-simple" hreflang="en-simple" data-title="Sphere" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Gu%C4%BEa_(matematika)" title="Guľa (matematika) — словачки" lang="sk" hreflang="sk" data-title="Guľa (matematika)" data-language-autonym="Slovenčina" data-language-local-name="словачки" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Sfera" title="Sfera — словенечки" lang="sl" hreflang="sl" data-title="Sfera" data-language-autonym="Slovenščina" data-language-local-name="словенечки" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Kubad" title="Kubad — сомалиски" lang="so" hreflang="so" data-title="Kubad" data-language-autonym="Soomaaliga" data-language-local-name="сомалиски" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DA%AF%DB%86" title="گۆ — централнокурдски" lang="ckb" hreflang="ckb" data-title="گۆ" data-language-autonym="کوردی" data-language-local-name="централнокурдски" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A1%D1%84%D0%B5%D1%80%D0%B0" title="Сфера — српски" lang="sr" hreflang="sr" data-title="Сфера" data-language-autonym="Српски / srpski" data-language-local-name="српски" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Sfera" title="Sfera — српскохрватски" lang="sh" hreflang="sh" data-title="Sfera" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="српскохрватски" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Buleudan" title="Buleudan — сундски" lang="su" hreflang="su" data-title="Buleudan" data-language-autonym="Sunda" data-language-local-name="сундски" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Pallo_(geometria)" title="Pallo (geometria) — фински" lang="fi" hreflang="fi" data-title="Pallo (geometria)" data-language-autonym="Suomi" data-language-local-name="фински" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Sf%C3%A4r" title="Sfär — шведски" lang="sv" hreflang="sv" data-title="Sfär" data-language-autonym="Svenska" data-language-local-name="шведски" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Espera" title="Espera — тагалог" lang="tl" hreflang="tl" data-title="Espera" data-language-autonym="Tagalog" data-language-local-name="тагалог" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%95%E0%AF%8B%E0%AE%B3%E0%AE%AE%E0%AF%8D" title="கோளம் — тамилски" lang="ta" hreflang="ta" data-title="கோளம்" data-language-autonym="தமிழ்" data-language-local-name="тамилски" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Tasegla" title="Tasegla — кабилски" lang="kab" hreflang="kab" data-title="Tasegla" data-language-autonym="Taqbaylit" data-language-local-name="кабилски" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%A1%D1%84%D0%B5%D1%80%D0%B0" title="Сфера — татарски" lang="tt" hreflang="tt" data-title="Сфера" data-language-autonym="Татарча / tatarça" data-language-local-name="татарски" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%97%E0%B1%8B%E0%B0%B3%E0%B0%82" title="గోళం — телугу" lang="te" hreflang="te" data-title="గోళం" data-language-autonym="తెలుగు" data-language-local-name="телугу" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%97%E0%B8%A3%E0%B8%87%E0%B8%81%E0%B8%A5%E0%B8%A1" title="ทรงกลม — тајландски" lang="th" hreflang="th" data-title="ทรงกลม" data-language-autonym="ไทย" data-language-local-name="тајландски" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-chr mw-list-item"><a href="https://chr.wikipedia.org/wiki/%E1%8E%A6%E1%8F%90%E1%8F%86%E1%8E%B8" title="ᎦᏐᏆᎸ — чероки" lang="chr" hreflang="chr" data-title="ᎦᏐᏆᎸ" data-language-autonym="ᏣᎳᎩ" data-language-local-name="чероки" class="interlanguage-link-target"><span>ᏣᎳᎩ</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/K%C3%BCre" title="Küre — турски" lang="tr" hreflang="tr" data-title="Küre" data-language-autonym="Türkçe" data-language-local-name="турски" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A1%D1%84%D0%B5%D1%80%D0%B0" title="Сфера — украински" lang="uk" hreflang="uk" data-title="Сфера" data-language-autonym="Українська" data-language-local-name="украински" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/M%E1%BA%B7t_c%E1%BA%A7u" title="Mặt cầu — виетнамски" lang="vi" hreflang="vi" data-title="Mặt cầu" data-language-autonym="Tiếng Việt" data-language-local-name="виетнамски" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E7%90%83" title="球 — книжевен кинески" lang="lzh" hreflang="lzh" data-title="球" data-language-autonym="文言" data-language-local-name="книжевен кинески" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Espira" title="Espira — варајски" lang="war" hreflang="war" data-title="Espira" data-language-autonym="Winaray" data-language-local-name="варајски" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E7%90%83%E9%9D%A2" title="球面 — ву" lang="wuu" hreflang="wuu" data-title="球面" data-language-autonym="吴语" data-language-local-name="ву" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%90%83%E9%AB%94" title="球體 — кантонски" lang="yue" hreflang="yue" data-title="球體" data-language-autonym="粵語" data-language-local-name="кантонски" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%90%83%E9%9D%A2" title="球面 — кинески" lang="zh" hreflang="zh" data-title="球面" data-language-autonym="中文" data-language-local-name="кинески" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-rsk mw-list-item"><a href="https://rsk.wikipedia.org/wiki/%D0%9B%D0%B0%D0%B1%D0%B4%D0%B0_(%D2%91%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F)" title="Лабда (ґеометрия) — Pannonian Rusyn" lang="rsk" hreflang="rsk" data-title="Лабда (ґеометрия)" data-language-autonym="Руски" data-language-local-name="Pannonian Rusyn" class="interlanguage-link-target"><span>Руски</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/Q12507#sitelinks-wikipedia" title="Уредување на меѓујазични врски" class="wbc-editpage">Уреди врски</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="Именски простори"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%D0%A1%D1%84%D0%B5%D1%80%D0%B0" title="Преглед на содржинската страница [c]" accesskey="c"><span>Страница</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/%D0%A0%D0%B0%D0%B7%D0%B3%D0%BE%D0%B2%D0%BE%D1%80:%D0%A1%D1%84%D0%B5%D1%80%D0%B0" rel="discussion" title="Разговор за содржинската страница [t]" accesskey="t"><span>Разговор</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Менување на јазичната варијанта" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">македонски</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Посети"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%D0%A1%D1%84%D0%B5%D1%80%D0%B0"><span>Читај</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%D0%A1%D1%84%D0%B5%D1%80%D0%B0&veaction=edit" title="Уредете ја страницава [v]" accesskey="v"><span>Уреди</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%D0%A1%D1%84%D0%B5%D1%80%D0%B0&action=edit" title="Уредување на изворниот код на страницава [e]" accesskey="e"><span>Уреди извор</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%D0%A1%D1%84%D0%B5%D1%80%D0%B0&action=history" title="Претходни верзии на оваа страница. [h]" accesskey="h"><span>Историја</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Алатки за страници"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <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="алатник" > <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" aria-hidden="true" ><span class="vector-dropdown-label-text">алатник</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header 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">Алатки</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">премести во страничникот</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">скриј</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Повеќе можности" > <div class="vector-menu-heading"> Дејства </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/%D0%A1%D1%84%D0%B5%D1%80%D0%B0"><span>Читај</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%A1%D1%84%D0%B5%D1%80%D0%B0&veaction=edit" title="Уредете ја страницава [v]" accesskey="v"><span>Уреди</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%A1%D1%84%D0%B5%D1%80%D0%B0&action=edit" title="Уредување на изворниот код на страницава [e]" accesskey="e"><span>Уреди извор</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%A1%D1%84%D0%B5%D1%80%D0%B0&action=history"><span>Историја</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Општо </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%A8%D1%82%D0%BE%D0%92%D0%BE%D0%B4%D0%B8%D0%9E%D0%B2%D0%B4%D0%B5/%D0%A1%D1%84%D0%B5%D1%80%D0%B0" title="Список на сите викистраници што водат овде [j]" accesskey="j"><span>Што води овде</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9F%D0%BE%D0%B2%D1%80%D0%B7%D0%B0%D0%BD%D0%B8%D0%9F%D1%80%D0%BE%D0%BC%D0%B5%D0%BD%D0%B8/%D0%A1%D1%84%D0%B5%D1%80%D0%B0" rel="nofollow" title="Скорешни промени на страници со врски на оваа страница [k]" accesskey="k"><span>Поврзани промени</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%A1%D0%BB%D1%83%D0%B6%D0%B1%D0%B5%D0%BD%D0%B8%D0%A1%D1%82%D1%80%D0%B0%D0%BD%D0%B8%D1%86%D0%B8" title="Список на сите службени страници [q]" accesskey="q"><span>Службени страници</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=%D0%A1%D1%84%D0%B5%D1%80%D0%B0&oldid=5176266" title="Постојана врска до оваа преработка на страницата"><span>Постојана врска</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=%D0%A1%D1%84%D0%B5%D1%80%D0%B0&action=info" title="Повеќе информации за страницата"><span>Информации за страницата</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9D%D0%B0%D0%B2%D0%BE%D0%B4&page=%D0%A1%D1%84%D0%B5%D1%80%D0%B0&id=5176266&wpFormIdentifier=titleform" title="Информации како да ја наведете оваа страница"><span>Наведи ја страницава</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%A1%D0%BA%D1%80%D0%B0%D1%82%D1%83%D0%B2%D0%B0%D1%87%D0%9D%D0%B0URL&url=https%3A%2F%2Fmk.wikipedia.org%2Fwiki%2F%25D0%25A1%25D1%2584%25D0%25B5%25D1%2580%25D0%25B0"><span>Дај скратена URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:QrCode&url=https%3A%2F%2Fmk.wikipedia.org%2Fwiki%2F%25D0%25A1%25D1%2584%25D0%25B5%25D1%2580%25D0%25B0"><span>Преземи QR-код</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"> Печати/извези </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=%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9A%D0%BD%D0%B8%D0%B3%D0%B0&bookcmd=book_creator&referer=%D0%A1%D1%84%D0%B5%D1%80%D0%B0"><span>Создај книга</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:DownloadAsPdf&page=%D0%A1%D1%84%D0%B5%D1%80%D0%B0&action=show-download-screen"><span>Преземи како PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=%D0%A1%D1%84%D0%B5%D1%80%D0%B0&printable=yes" title="Верзија за печатење на оваа страница [p]" accesskey="p"><span>Верзија за печатење</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"> На други проекти </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Sphere" hreflang="en"><span>Ризница</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/Q12507" title="Врска до поврзаниот предмет во складиштето за податоци [g]" accesskey="g"><span>Предмет на Википодатоци</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="Алатки за страници"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Изглед"> <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">Изглед</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">премести во страничникот</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">скриј</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">Од Википедија — слободната енциклопедија</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="mk" dir="ltr"><figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/%D0%9F%D0%BE%D0%B4%D0%B0%D1%82%D0%BE%D1%82%D0%B5%D0%BA%D0%B0:Sphere_wireframe_10deg_6r.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Sphere_wireframe_10deg_6r.svg/220px-Sphere_wireframe_10deg_6r.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Sphere_wireframe_10deg_6r.svg/330px-Sphere_wireframe_10deg_6r.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Sphere_wireframe_10deg_6r.svg/440px-Sphere_wireframe_10deg_6r.svg.png 2x" data-file-width="800" data-file-height="800" /></a><figcaption>Перспективна проекција на сфера во две димензии</figcaption></figure> <p><b>Сфера</b> (<a href="/wiki/%D0%93%D1%80%D1%87%D0%BA%D0%B8_%D1%98%D0%B0%D0%B7%D0%B8%D0%BA" title="Грчки јазик">грчки</a>: <span lang="el"><i>σφαῖρα</i></span> — „топка“)<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> — совршено тркалезно <a href="/wiki/%D0%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%81%D0%BA%D0%BE_%D1%82%D0%B5%D0%BB%D0%BE" class="mw-redirect" title="Геометриско тело">геометриско тело</a>. Како и кај <a href="/wiki/%D0%9A%D1%80%D1%83%D0%B6%D0%BD%D0%B8%D1%86%D0%B0" title="Кружница">кружницата</a> (во две димензии), сферата претставува множество точки, сите подеднакво оддалечени (<i>r</i>) од дадена точка во просторот. Растојанието <i>r</i> е <a href="/wiki/%D0%9F%D0%BE%D0%BB%D1%83%D0%BF%D1%80%D0%B5%D1%87%D0%BD%D0%B8%D0%BA" title="Полупречник">полупречник</a> на кружницата, а дадената точка е нејзиниот <a href="/w/index.php?title=%D0%A6%D0%B5%D0%BD%D1%82%D0%B0%D1%80_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0)&action=edit&redlink=1" class="new" title="Центар (геометрија) (страницата не постои)">центар</a>. Најголемото растојание помеѓу две точки на сферата се нарекува <a href="/wiki/%D0%9F%D1%80%D0%B5%D1%87%D0%BD%D0%B8%D0%BA" title="Пречник">пречник</a>. Тој минува низ центарот, и така е еднаков на два полупречника. </p><p>Геометријата прави разлика помеѓу <b>сфера</b> (која е впрочем дводимензионална затворена <a href="/wiki/%D0%9F%D0%BE%D0%B2%D1%80%D1%88%D0%B8%D0%BD%D0%B0" class="mw-redirect" title="Површина">површина</a> вметната во тридимензионален <a href="/wiki/%D0%9F%D1%80%D0%BE%D1%81%D1%82%D0%BE%D1%80" title="Простор">простор</a>) и <b><a href="/wiki/%D0%A2%D0%BE%D0%BF%D0%BA%D0%B0_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0)" title="Топка (геометрија)">топка</a></b>, која е вистинско тридимензионално тело бидејќи го вклучува и внатрешниот простор на сферата. </p><p>Сферата е ротациона површина, т.е. се добива со ротација на полукружница околу дијаметарот. Растојанието од центарот на сферата до дадената рамнина <i>Σ</i> се вика <i>централно растојание</i> на рамнината и сферата. Ако тоа растојание е еднакво на радисуот на сферата, тогаш сферата и рамнината имаат една заедничка точка, па рамнината ја допира сферата и се вика <i>тангентна рамнина</i>. Ако растојанието, пак, е помало од радиусот на сферата, тогаш рамнината ја сече сферата, а пресекот на сферата со рамнина е кружница. Ако рамнината минува низ центарот на сферата, тогаш пресекот е најголемата кружница и тогаш сферата е поделена на две полусфери. Ако, пак, рамнината <i>Σ</i> ја сече сферата, но не минува низ центарот, тогаш сферата е поделена на два нееднакви дела при што секој од нив се вика <i>калота</i>. Вообичаено, како калота се смета помалиот дел од сферата. Делот од сферата што е зафатен меѓу два паралелни пресеци се вика <i>појас</i> или <i>зона</i>. Растојаниеот меѓу двата паралелни пресеци е <i>висина</i> на појасот.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Основни_формули"><span id=".D0.9E.D1.81.D0.BD.D0.BE.D0.B2.D0.BD.D0.B8_.D1.84.D0.BE.D1.80.D0.BC.D1.83.D0.BB.D0.B8"></span>Основни формули</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%A1%D1%84%D0%B5%D1%80%D0%B0&veaction=edit&section=1" title="Уреди го одделот „Основни формули“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%A1%D1%84%D0%B5%D1%80%D0%B0&action=edit&section=1" title="Уреди изворен код на одделот: Основни формули"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Плоштина на сфера се пресметува со следнава формула:<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </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 S=\ 4\pi r^{2}=\pi d^{2}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <mtext> </mtext> <mn>4</mn> <mi>π</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mi>π</mi> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S=\ 4\pi r^{2}=\pi d^{2}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3f0e495288fc227813f4088ebc9cc54968247324" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:17.125ex; height:2.676ex;" alt="{\displaystyle S=\ 4\pi r^{2}=\pi d^{2}.}"></span></dd></dl> <p>Плоштина на појасот на сфера се пресметува со следнава формула:<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </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 S=\ 2\pi rH.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <mtext> </mtext> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mi>H</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S=\ 2\pi rH.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba471fa18846fe27ae1455faf352f512c0cf6a32" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.432ex; height:2.176ex;" alt="{\displaystyle S=\ 2\pi rH.}"></span></dd></dl> <p>Волуменот на сфераata (топка) се пресметува според формулата: </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 V={\frac {4}{3}}\pi r^{3}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>4</mn> <mn>3</mn> </mfrac> </mrow> <mi>π</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V={\frac {4}{3}}\pi r^{3}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c143ddb445538122a38612d2f43fe82eed286a97" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:10.966ex; height:5.176ex;" alt="{\displaystyle V={\frac {4}{3}}\pi r^{3}.}"></span></dd></dl> <p>Површината на отсечокот на сферата се пресметува според формулата: </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 s=\ 2\pi rH=2\pi r^{2}(1-\cos(\alpha ))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> <mo>=</mo> <mtext> </mtext> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mi>H</mi> <mo>=</mo> <mn>2</mn> <mi>π</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s=\ 2\pi rH=2\pi r^{2}(1-\cos(\alpha ))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/acd2ca9f262c4be9b6aab88469860088436835aa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:30.292ex; height:3.176ex;" alt="{\displaystyle s=\ 2\pi rH=2\pi r^{2}(1-\cos(\alpha ))}"></span> , каде H е висината на отсечокот, а <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 \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span> е зенитниот агол</dd></dl> <div class="mw-heading mw-heading2"><h2 id="Сферата_во_тридимензионален_простор"><span id=".D0.A1.D1.84.D0.B5.D1.80.D0.B0.D1.82.D0.B0_.D0.B2.D0.BE_.D1.82.D1.80.D0.B8.D0.B4.D0.B8.D0.BC.D0.B5.D0.BD.D0.B7.D0.B8.D0.BE.D0.BD.D0.B0.D0.BB.D0.B5.D0.BD_.D0.BF.D1.80.D0.BE.D1.81.D1.82.D0.BE.D1.80"></span>Сферата во тридимензионален простор</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%A1%D1%84%D0%B5%D1%80%D0%B0&veaction=edit&section=2" title="Уреди го одделот „Сферата во тридимензионален простор“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%A1%D1%84%D0%B5%D1%80%D0%B0&action=edit&section=2" title="Уреди изворен код на одделот: Сферата во тридимензионален простор"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Равенката </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 (x-x_{0})^{2}+(y-y_{0})^{2}+(z-z_{0})^{2}=R^{2},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>x</mi> <mo>−</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <mi>y</mi> <mo>−</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <mi>z</mi> <mo>−</mo> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x-x_{0})^{2}+(y-y_{0})^{2}+(z-z_{0})^{2}=R^{2},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87ef11c21371fa11e188dab0a11573d93effbbcc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:39.642ex; height:3.176ex;" alt="{\displaystyle (x-x_{0})^{2}+(y-y_{0})^{2}+(z-z_{0})^{2}=R^{2},}"></span></dd></dl> <p>каде <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_{0},y_{0},z_{0})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x_{0},y_{0},z_{0})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/39177ddeeb9f9a393b664e522bc8e3bf0face153" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.59ex; height:2.843ex;" alt="{\displaystyle (x_{0},y_{0},z_{0})}"></span> се координатите на центарот на сферата, а <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"></span> е полупречникот. </p><p>Параметарска равенка на сфера со центар во точката <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_{0},y_{0},z_{0})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x_{0},y_{0},z_{0})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/39177ddeeb9f9a393b664e522bc8e3bf0face153" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.59ex; height:2.843ex;" alt="{\displaystyle (x_{0},y_{0},z_{0})}"></span>: </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 {\begin{cases}x=x_{0}+R\cdot \sin \theta \cdot \cos \phi ,\\y=y_{0}+R\cdot \sin \theta \cdot \sin \phi ,\\z=z_{0}+R\cdot \cos \theta ,\\\end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <mi>x</mi> <mo>=</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mi>R</mi> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mi>θ</mi> <mo>⋅</mo> <mi>cos</mi> <mo>⁡</mo> <mi>ϕ</mi> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>y</mi> <mo>=</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mi>R</mi> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mi>θ</mi> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mi>ϕ</mi> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>z</mi> <mo>=</mo> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mi>R</mi> <mo>⋅</mo> <mi>cos</mi> <mo>⁡</mo> <mi>θ</mi> <mo>,</mo> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{cases}x=x_{0}+R\cdot \sin \theta \cdot \cos \phi ,\\y=y_{0}+R\cdot \sin \theta \cdot \sin \phi ,\\z=z_{0}+R\cdot \cos \theta ,\\\end{cases}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5faeafd1360a2e34f4553e98aa89dccfb3019c45" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.671ex; width:27.456ex; height:8.509ex;" alt="{\displaystyle {\begin{cases}x=x_{0}+R\cdot \sin \theta \cdot \cos \phi ,\\y=y_{0}+R\cdot \sin \theta \cdot \sin \phi ,\\z=z_{0}+R\cdot \cos \theta ,\\\end{cases}}}"></span></dd></dl> <p>каде <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta \in [-\pi /2,\pi /2]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> <mo>∈</mo> <mo stretchy="false">[</mo> <mo>−</mo> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <mo>,</mo> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta \in [-\pi /2,\pi /2]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8a4ff4294591965f0a3fb526758ceefd1ba45e5f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.381ex; height:2.843ex;" alt="{\displaystyle \theta \in [-\pi /2,\pi /2]}"></span> и <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 \phi \in [0,2\pi ).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> <mo>∈</mo> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mn>2</mn> <mi>π</mi> <mo stretchy="false">)</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi \in [0,2\pi ).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0cea866d786c6002067ec5df43a3e65d2380fe3f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.115ex; height:2.843ex;" alt="{\displaystyle \phi \in [0,2\pi ).}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="Делови_на_сферата"><span id=".D0.94.D0.B5.D0.BB.D0.BE.D0.B2.D0.B8_.D0.BD.D0.B0_.D1.81.D1.84.D0.B5.D1.80.D0.B0.D1.82.D0.B0"></span>Делови на сферата</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%A1%D1%84%D0%B5%D1%80%D0%B0&veaction=edit&section=3" title="Уреди го одделот „Делови на сферата“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%A1%D1%84%D0%B5%D1%80%D0%B0&action=edit&section=3" title="Уреди изворен код на одделот: Делови на сферата"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Сферата се дели на две подеднакви „полусфери“ кога низ нејзиниот центар минува рамнина. Доколку низ центарот се сечат две рамнини, тогаш тие ја делат на два двоаголника (а топката на два „сферни клина“). Ако потсечеме една топка, добиваме одвоен дел наречен „калота“ (капа). Ако сферата ја сечат две рамнини, делот меѓу нив ќе биде „појас“, а во случај на топка, ќе биде „слој“. </p><p>Отсечката чии крајни точки се центарот на сферата и која било точка од сферата се вика <i>радиус</i> на сферата. Отсечката, пак, чии крајни точки се кои било две точки од сферата се вика <i>тетива</i>. Тетивата што минува низ центарот на сферата се вика <i>дијаметар</i>.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Воопштување_на_сферата"><span id=".D0.92.D0.BE.D0.BE.D0.BF.D1.88.D1.82.D1.83.D0.B2.D0.B0.D1.9A.D0.B5_.D0.BD.D0.B0_.D1.81.D1.84.D0.B5.D1.80.D0.B0.D1.82.D0.B0"></span>Воопштување на сферата</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%A1%D1%84%D0%B5%D1%80%D0%B0&veaction=edit&section=4" title="Уреди го одделот „Воопштување на сферата“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%A1%D1%84%D0%B5%D1%80%D0%B0&action=edit&section=4" title="Уреди изворен код на одделот: Воопштување на сферата"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r4650192">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}</style><div role="note" class="hatnote navigation-not-searchable">Главна статија: <a href="/wiki/N-%D1%81%D1%84%D0%B5%D1%80%D0%B0" class="mw-redirect" title="N-сфера">n-сфера</a></div> <p>Сферата може да се воопшти на колку било <a href="/wiki/%D0%94%D0%B8%D0%BC%D0%B5%D0%BD%D0%B7%D0%B8%D1%98%D0%B0" title="Димензија">димензии</a>. За секој <a href="/wiki/%D0%9F%D1%80%D0%B8%D1%80%D0%BE%D0%B4%D0%B5%D0%BD_%D0%B1%D1%80%D0%BE%D1%98" title="Природен број">природен број</a> <i>n</i> постои „<i>n</i>-сфера“, (се запишува <i>S<sup>n</sup></i>), која е множество од точки во (<span class="nowrap"><i>n</i> + 1</span>)-димензионален простор на подеднакво растојание <i>r</i> од централната точка во просторот, каде <i>r</i> е, како и претходно, позитивен <a href="/wiki/%D0%A0%D0%B5%D0%B0%D0%BB%D0%B5%D0%BD_%D0%B1%D1%80%D0%BE%D1%98" title="Реален број">реален број</a>. Поконкретно: </p> <ul><li>0-сферата е пар од крајни точки на интервал (−<i>r</i>, <i>r</i>) на реалната бројна оска</li> <li>1-сферата е <a href="/wiki/%D0%9A%D1%80%D1%83%D0%B6%D0%BD%D0%B8%D1%86%D0%B0" title="Кружница">кружница</a> со полупречник <i>r</i></li> <li>2-сферата е обична сфера</li> <li>3-сферата е сфера во четиридимензионален Евклидов простор.</li></ul> <p>Сферата каде <i>n</i> > 2 се нарекува и <a href="/wiki/%D0%A5%D0%B8%D0%BF%D0%B5%D1%80%D1%81%D1%84%D0%B5%D1%80%D0%B0" title="Хиперсфера">хиперсфера</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Сферна_геометрија"><span id=".D0.A1.D1.84.D0.B5.D1.80.D0.BD.D0.B0_.D0.B3.D0.B5.D0.BE.D0.BC.D0.B5.D1.82.D1.80.D0.B8.D1.98.D0.B0"></span>Сферна геометрија</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%A1%D1%84%D0%B5%D1%80%D0%B0&veaction=edit&section=5" title="Уреди го одделот „Сферна геометрија“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%A1%D1%84%D0%B5%D1%80%D0%B0&action=edit&section=5" title="Уреди изворен код на одделот: Сферна геометрија"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/%D0%9F%D0%BE%D0%B4%D0%B0%D1%82%D0%BE%D1%82%D0%B5%D0%BA%D0%B0:Sphere_halve.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Sphere_halve.png/220px-Sphere_halve.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Sphere_halve.png/330px-Sphere_halve.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Sphere_halve.png/440px-Sphere_halve.png 2x" data-file-width="960" data-file-height="960" /></a><figcaption><a href="/wiki/%D0%93%D0%BE%D0%BB%D0%B5%D0%BC%D0%B0_%D0%BA%D1%80%D1%83%D0%B6%D0%BD%D0%B8%D1%86%D0%B0" title="Голема кружница">Голема кружница</a> на сфера</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4650192"><div role="note" class="hatnote navigation-not-searchable">Главна статија: <a href="/w/index.php?title=%D0%A1%D1%84%D0%B5%D1%80%D0%BD%D0%B0_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0&action=edit&redlink=1" class="new" title="Сферна геометрија (страницата не постои)">Сферна геометрија</a></div> <p>Основните елементи на <a href="/wiki/%D0%9F%D0%BB%D0%B0%D0%BD%D0%B8%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0" title="Планиметрија">планиметријата</a> се <a href="/wiki/%D0%A2%D0%BE%D1%87%D0%BA%D0%B0_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0)" title="Точка (геометрија)">точката</a> и <a href="/wiki/%D0%9B%D0%B8%D0%BD%D0%B8%D1%98%D0%B0_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" class="mw-redirect mw-disambig" title="Линија (математика)">линијата</a>. Кај сферата, точките се дефинираат исто, но линиите се поинакви. Ако мериме по лачна должина, најкраткиот пат што поврзува две точки што лежат на сферата е дел од <a href="/wiki/%D0%93%D0%BE%D0%BB%D0%B5%D0%BC%D0%B0_%D0%BA%D1%80%D1%83%D0%B6%D0%BD%D0%B8%D1%86%D0%B0" title="Голема кружница">голема кружница</a> што ги содржи тие две точки. За сферата важат многу теореми од класичната геометрија, но има многу што не важат (погл. <a href="/w/index.php?title=%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4%D0%BE%D0%B2%D0%B0_%D0%B0%D0%BA%D1%81%D0%B8%D0%BE%D0%BC%D0%B0_%D0%B7%D0%B0_%D0%BF%D0%B0%D1%80%D0%B0%D0%BB%D0%B5%D0%BB%D0%BD%D0%BE%D1%81%D1%82%D0%B0&action=edit&redlink=1" class="new" title="Евклидова аксиома за паралелноста (страницата не постои)">аксиома за паралелноста</a>). Во <a href="/w/index.php?title=%D0%A1%D1%84%D0%B5%D1%80%D0%BD%D0%B0_%D1%82%D1%80%D0%B8%D0%B3%D0%BE%D0%BD%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0&action=edit&redlink=1" class="new" title="Сферна тригонометрија (страницата не постои)">сферната тригонометрија</a>, <a href="/wiki/%D0%90%D0%B3%D0%BE%D0%BB" title="Агол">аглите</a> се сместени помеѓу големи кружници, па затоа по многу нешта се разликува од обичната <a href="/wiki/%D0%A2%D1%80%D0%B8%D0%B3%D0%BE%D0%BD%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0" title="Тригонометрија">тригонометрија</a>. На пример, збирот од внатрешните агли на сферниот триаголник е поголем од 180 степени. Исто така, секои два <a href="/w/index.php?title=%D0%A1%D0%BB%D0%B8%D1%87%D0%BD%D0%BE%D1%81%D1%82_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0)&action=edit&redlink=1" class="new" title="Сличност (геометрија) (страницата не постои)">слични</a> сферни триаголника се <a href="/wiki/%D0%A1%D0%BA%D0%BB%D0%B0%D0%B4%D0%BD%D0%BE%D1%81%D1%82_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0)" title="Складност (геометрија)">складни</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Единаесет_својства_на_сферата"><span id=".D0.95.D0.B4.D0.B8.D0.BD.D0.B0.D0.B5.D1.81.D0.B5.D1.82_.D1.81.D0.B2.D0.BE.D1.98.D1.81.D1.82.D0.B2.D0.B0_.D0.BD.D0.B0_.D1.81.D1.84.D0.B5.D1.80.D0.B0.D1.82.D0.B0"></span>Единаесет својства на сферата</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%A1%D1%84%D0%B5%D1%80%D0%B0&veaction=edit&section=6" title="Уреди го одделот „Единаесет својства на сферата“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%A1%D1%84%D0%B5%D1%80%D0%B0&action=edit&section=6" title="Уреди изворен код на одделот: Единаесет својства на сферата"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Во делото „Геометријата и вообразбата“<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> <a href="/wiki/%D0%94%D0%B0%D0%B2%D0%B8%D0%B4_%D0%A5%D0%B8%D0%BB%D0%B1%D0%B5%D1%80%D1%82" title="Давид Хилберт">Давид Хилберт</a> и Стефан Кон-Фосен даваат единаесет својства. Неколку од нив важат и за <a href="/wiki/%D0%A0%D0%B0%D0%BC%D0%BD%D0%B8%D0%BD%D0%B0" class="mw-redirect mw-disambig" title="Рамнина">рамнина</a>, која може да се замисли како сфера со бесконечен полупречник. Својствата се следниве: </p> <ol><li><i>Точките не сферата се подеднакво оддалечени од дадената точка. Воедно, соодносот на оддалеченоста на точките од две дадени точки е непроменлив.</i></li> <li><i>Контурите и рамнинските пресеци на сферата се кружници.</i></li> <li><i>Сферата има постојана широчина и обем.</i></li> <li><i>Сите точки на сферата се точки на заокруженост.</i></li> <li><i>Сферата нема жаришни површини.</i></li> <li><i>Сите геодетски линии на сферата се затворени криви.</i></li> <li><i>Од сите тела при даден волумен, сферата има најмала плоштина; од сите тела при дадена плоштина, сферата има најголем волумен.</i></li> <li><i>Сферата има најмала вкупна средна закривеност од сите конвексни тела при дадена плоштина.</i></li> <li><i>Сферата има постојана средна закривеност.</i></li> <li><i>Сферата има постојана позитивна Гаусова закривеност.</i></li> <li><i>Сферата се трансформира сама во себе со трипараметарски несвитливи движења.</i></li></ol> <div class="mw-heading mw-heading2"><h2 id="Поврзано"><span id=".D0.9F.D0.BE.D0.B2.D1.80.D0.B7.D0.B0.D0.BD.D0.BE"></span>Поврзано</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%A1%D1%84%D0%B5%D1%80%D0%B0&veaction=edit&section=7" title="Уреди го одделот „Поврзано“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%A1%D1%84%D0%B5%D1%80%D0%B0&action=edit&section=7" title="Уреди изворен код на одделот: Поврзано"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%D0%A2%D0%BE%D0%BF%D0%BA%D0%B0_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0)" title="Топка (геометрија)">Топка (геометрија)</a></li> <li><a href="/wiki/%D0%A1%D1%84%D0%B5%D1%80%D0%BE%D0%B8%D0%B4" title="Сфероид">Сфероид</a></li> <li><a href="/wiki/%D0%9A%D0%BE%D1%86%D0%BA%D0%B0" title="Коцка">Коцка</a></li> <li><a href="/wiki/%D0%9A%D0%B2%D0%B0%D0%B4%D0%B0%D1%80" title="Квадар">Квадар</a></li> <li><a href="/wiki/%D0%97%D0%B0%D0%BA%D1%80%D0%B8%D0%B2%D0%B5%D0%BD%D0%BE%D1%81%D1%82" title="Закривеност">Закривеност</a></li> <li><a href="/w/index.php?title=%D0%A1%D1%84%D0%B5%D1%80%D0%BD%D0%B8_%D0%BA%D0%BE%D0%BE%D1%80%D0%B4%D0%B8%D0%BD%D0%B0%D1%82%D0%B8&action=edit&redlink=1" class="new" title="Сферни координати (страницата не постои)">Сферни координати</a></li> <li><a href="/wiki/N-%D1%81%D1%84%D0%B5%D1%80%D0%B0" class="mw-redirect" title="N-сфера"><i>n</i>-сфера</a></li> <li><a href="/wiki/%D0%A5%D0%B8%D0%BF%D0%B5%D1%80%D1%81%D1%84%D0%B5%D1%80%D0%B0" title="Хиперсфера">Хиперсфера</a></li> <li><a href="/w/index.php?title=%D0%94%D0%B0%D1%98%D1%81%D0%BE%D0%BD%D0%BE%D0%B2%D0%B0_%D1%81%D1%84%D0%B5%D1%80%D0%B0&action=edit&redlink=1" class="new" title="Дајсонова сфера (страницата не постои)">Дајсонова сфера</a></li> <li><a href="/w/index.php?title=%D0%A0%D0%B8%D0%BC%D0%B0%D0%BD%D0%BE%D0%B2%D0%B0_%D1%81%D1%84%D0%B5%D1%80%D0%B0&action=edit&redlink=1" class="new" title="Риманова сфера (страницата не постои)">Риманова сфера</a></li> <li><a href="/w/index.php?title=%D0%9F%D1%80%D0%BE%D1%81%D1%82%D0%BE%D1%80%D0%B5%D0%BD_%D0%B0%D0%B3%D0%BE%D0%BB&action=edit&redlink=1" class="new" title="Просторен агол (страницата не постои)">Просторен агол</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Наводи"><span id=".D0.9D.D0.B0.D0.B2.D0.BE.D0.B4.D0.B8"></span>Наводи</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%A1%D1%84%D0%B5%D1%80%D0%B0&veaction=edit&section=8" title="Уреди го одделот „Наводи“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%A1%D1%84%D0%B5%D1%80%D0%B0&action=edit&section=8" title="Уреди изворен код на одделот: Наводи"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist" style="list-style-type: decimal;"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><span class="наведување на лексикон на македонскиот јазик" id="асфера"><a rel="nofollow" class="external text" href="https://recnik.off.net.mk/recnik/makedonski-leksikon/сфера">„сфера“</a> — Лексикон на македонскиот јазик</span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text">Боривоје Миладиновиќ, Трајче Ѓорѓијевски и Никола Петрески, <i>Математика за II година гимназиско образование</i>. Скопје: Алби, 2009, стр. 181.</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text">Боривоје Миладиновиќ, Трајче Ѓорѓијевски и Никола Петрески, <i>Математика за II година гимназиско образование</i>. Скопје: Алби, 2009, стр. 183.</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text">Боривоје Миладиновиќ, Трајче Ѓорѓијевски и Никола Петрески, <i>Математика за II година гимназиско образование</i>. Скопје: Алби, 2009, стр. 183.</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text">Боривоје Миладиновиќ, Трајче Ѓорѓијевски и Никола Петрески, <i>Математика за II година гимназиско образование</i>. Скопје: Алби, 2009, стр. 180.</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><a href="#cite_ref-6">↑</a></span> <span class="reference-text"><cite id="CITEREFHilbert,_David;_Cohn-Vossen,_Stephan1952" class="citation book"><a href="/wiki/%D0%94%D0%B0%D0%B2%D0%B8%D0%B4_%D0%A5%D0%B8%D0%BB%D0%B1%D0%B5%D1%80%D1%82" title="Давид Хилберт">Hilbert, David</a>; Cohn-Vossen, Stephan (1952). <i>Geometry and the Imagination</i> (II. изд.). Chelsea. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9F%D0%B5%D1%87%D0%B0%D1%82%D0%B5%D0%BD%D0%98%D0%B7%D0%B2%D0%BE%D1%80/0-8284-1087-9" title="Специјална:ПечатенИзвор/0-8284-1087-9"><bdi>0-8284-1087-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Geometry+and+the+Imagination&rft.edition=II&rft.pub=Chelsea&rft.date=1952&rft.isbn=0-8284-1087-9&rft.au=Hilbert%2C+David%3B+Cohn-Vossen%2C+Stephan&rfr_id=info%3Asid%2Fmk.wikipedia.org%3A%D0%A1%D1%84%D0%B5%D1%80%D0%B0" class="Z3988"></span><span class="cs1-maint citation-comment">CS1-одржување: повеќе имиња: список на автори (<a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:CS1-%D0%BE%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%9A%D0%B5:_%D0%BF%D0%BE%D0%B2%D0%B5%D1%9C%D0%B5_%D0%B8%D0%BC%D0%B8%D1%9A%D0%B0:_%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA_%D0%BD%D0%B0_%D0%B0%D0%B2%D1%82%D0%BE%D1%80%D0%B8" title="Категорија:CS1-одржување: повеќе имиња: список на автори">link</a>)</span><style data-mw-deduplicate="TemplateStyles:r5289462">.mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background-image:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png");background-image:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg");background-repeat:no-repeat;background-size:9px;background-position:right .1em center}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background-image:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png");background-image:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg");background-repeat:no-repeat;background-size:9px;background-position:right .1em center}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background-image:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png");background-image:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg");background-repeat:no-repeat;background-size:9px;background-position:right .1em center}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:var(--color-subtle,#54595d)}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background-image:url("//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png");background-image:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg");background-repeat:no-repeat;background-size:12px;background-position:right .1em center}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:inherit;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}</style></span> </li> </ol></div></div> <ul><li>William Dunham. стр. 28, 226, <i>The Mathematical Universe: An Alphabetical Journey Through the Great Proofs, Problems and Personalities</i>, <a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9F%D0%B5%D1%87%D0%B0%D1%82%D0%B5%D0%BD%D0%98%D0%B7%D0%B2%D0%BE%D1%80/0471176613" class="internal mw-magiclink-isbn">ISBN 0-471-17661-3</a>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Надворешни_врски"><span id=".D0.9D.D0.B0.D0.B4.D0.B2.D0.BE.D1.80.D0.B5.D1.88.D0.BD.D0.B8_.D0.B2.D1.80.D1.81.D0.BA.D0.B8"></span>Надворешни врски</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%A1%D1%84%D0%B5%D1%80%D0%B0&veaction=edit&section=9" title="Уреди го одделот „Надворешни врски“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%A1%D1%84%D0%B5%D1%80%D0%B0&action=edit&section=9" title="Уреди изворен код на одделот: Надворешни врски"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <table role="presentation" class="mbox-small plainlinks sistersitebox" style="background-color:var(--background-color-neutral-subtle, #f8f9fa);border:1px solid var(--border-color-base, #a2a9b1);color:inherit"> <tbody><tr> <td class="mbox-image"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></td> <td class="mbox-text plainlist">„<span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Spheres?uselang=mk">Сфери</a>“ на Ризницата <sup><a href="/wiki/%D0%A0%D0%B8%D0%B7%D0%BD%D0%B8%D1%86%D0%B0_(%D0%92%D0%B8%D0%BA%D0%B8%D0%BC%D0%B5%D0%B4%D0%B8%D1%98%D0%B0)" title="Ризница (Викимедија)">?</a></sup></span></td></tr></tbody></table> <ul><li><a rel="nofollow" class="external text" href="http://www.abe.msstate.edu/~fto/tools/vol/sphere.html">Пресметајте волумен на сфера</a> <small><a rel="nofollow" class="external text" href="https://web.archive.org/web/20110929164107/http://www.abe.msstate.edu/~fto/tools/vol/sphere.html">Архивирано</a> на 29 септември 2011 г.</small> <span class="languageicon" style="font-size:0.95em; font-weight:bold; color:#808080ff;">(англиски)</span></li> <li><a href="https://planetmath.org/alphabetical.html" class="extiw" title="planetmath:186">Сфера</a> - PlanetMath <span class="languageicon" style="font-size:0.95em; font-weight:bold; color:#808080ff;">(англиски)</span></li> <li>„<span class="plainlinks"><a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/{{{urlname}}}.html">Сфера</a></span>“ од Ерик В. Вајсштајн — <a href="/wiki/MathWorld" title="MathWorld">MathWorld</a> <span class="languageicon" style="font-size:0.95em; font-weight:bold; color:#808080ff;">(англиски)</span></li></ul> <p><br /> </p> <table class="navbox" style="border-spacing:0"><tbody><tr><td style="padding:2px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group"><a href="/wiki/%D0%9D%D0%BE%D1%80%D0%BC%D0%B0%D1%82%D0%B8%D0%B2%D0%BD%D0%B0_%D0%BA%D0%BE%D0%BD%D1%82%D1%80%D0%BE%D0%BB%D0%B0" title="Нормативна контрола">Нормативна контрола</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a rel="nofollow" class="external text" href="//www.worldcat.org/identities/lccn-sh85-126590">WorldCat</a></li> <li><a href="/wiki/%D0%9A%D0%BE%D0%BD%D1%82%D1%80%D0%BE%D0%BB%D0%B5%D0%BD_%D0%B1%D1%80%D0%BE%D1%98_%D0%BD%D0%B0_%D0%9A%D0%BE%D0%BD%D0%B3%D1%80%D0%B5%D1%81%D0%BD%D0%B0%D1%82%D0%B0_%D0%B1%D0%B8%D0%B1%D0%BB%D0%B8%D0%BE%D1%82%D0%B5%D0%BA%D0%B0" title="Контролен број на Конгресната библиотека">LCCN</a>: <span class="uid"><a rel="nofollow" class="external text" href="http://id.loc.gov/authorities/subjects/sh85126590">sh85126590</a></span></li> <li><a href="/wiki/%D0%9E%D0%B1%D0%B5%D0%B4%D0%B8%D0%BD%D0%B5%D1%82%D0%B0_%D0%BD%D0%BE%D1%80%D0%BC%D0%B0%D1%82%D0%B8%D0%B2%D0%BD%D0%B0_%D0%BF%D0%BE%D0%B4%D0%B0%D1%82%D0%BE%D1%82%D0%B5%D0%BA%D0%B0" title="Обединета нормативна податотека">GND</a>: <span class="uid"><a rel="nofollow" class="external text" href="http://d-nb.info/gnd/4165914-4">4165914-4</a></span></li> <li><a href="/wiki/%D0%9D%D0%B0%D1%86%D0%B8%D0%BE%D0%BD%D0%B0%D0%BB%D0%BD%D0%B0_%D0%B1%D0%B8%D0%B1%D0%BB%D0%B8%D0%BE%D1%82%D0%B5%D0%BA%D0%B0_%D0%BD%D0%B0_%D0%A4%D1%80%D0%B0%D0%BD%D1%86%D0%B8%D1%98%D0%B0" title="Национална библиотека на Франција">BNF</a>: <span class="uid"><a rel="nofollow" class="external text" href="http://catalogue.bnf.fr/ark:/12148/cb119812876">cb119812876</a> <a rel="nofollow" class="external text" href="http://data.bnf.fr/ark:/12148/cb119812876">(податоци)</a></span></li></ul> </div></td></tr></tbody></table></td></tr></tbody></table></div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Преземено од „<a dir="ltr" href="https://mk.wikipedia.org/w/index.php?title=Сфера&oldid=5176266">https://mk.wikipedia.org/w/index.php?title=Сфера&oldid=5176266</a>“</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D0%B8" title="Специјална:Категории">Категории</a>: <ul><li><a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:%D0%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%81%D0%BA%D0%B8_%D1%84%D0%B8%D0%B3%D1%83%D1%80%D0%B8" title="Категорија:Геометриски фигури">Геометриски фигури</a></li><li><a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:%D0%A1%D1%84%D0%B5%D1%80%D0%B8" title="Категорија:Сфери">Сфери</a></li><li><a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:%D0%9F%D0%BE%D0%B2%D1%80%D1%88%D0%B8%D0%BD%D0%B8" title="Категорија:Површини">Површини</a></li><li><a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:%D0%A2%D0%BE%D0%BF%D0%BE%D0%BB%D0%BE%D0%B3%D0%B8%D1%98%D0%B0" title="Категорија:Топологија">Топологија</a></li><li><a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:%D0%94%D0%B8%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0" title="Категорија:Диференцијална геометрија">Диференцијална геометрија</a></li><li><a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:%D0%94%D0%B8%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0_%D1%82%D0%BE%D0%BF%D0%BE%D0%BB%D0%BE%D0%B3%D0%B8%D1%98%D0%B0" title="Категорија:Диференцијална топологија">Диференцијална топологија</a></li><li><a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:%D0%95%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%D0%B0%D1%80%D0%BD%D0%B0_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0" title="Категорија:Елементарна геометрија">Елементарна геометрија</a></li></ul></div><div id="mw-hidden-catlinks" 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