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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%D0%BE%D1%80%D0%B5%D1%88%D0%BD%D0%B8%D0%9F%D1%80%D0%BE%D0%BC%D0%B5%D0%BD%D0%B8&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="//login.wikimedia.org"> </head> <body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-Голема_кружница rootpage-Голема_кружница skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Прејди на содржината</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="Мрежно место"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="Главно мени" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-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-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">Главно мени</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">Главно мени</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">премести во страничникот</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">скриј</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Прегледник </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/%D0%93%D0%BB%D0%B0%D0%B2%D0%BD%D0%B0_%D1%81%D1%82%D1%80%D0%B0%D0%BD%D0%B8%D1%86%D0%B0" title="Посети главна страница [z]" accesskey="z"><span>Главна страница</span></a></li><li id="n-Што-е-Википедија?" class="mw-list-item"><a href="/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%92%D0%BE%D0%B2%D0%B5%D0%B4"><span>Што е Википедија?</span></a></li><li id="n-featuredcontent" class="mw-list-item"><a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:%D0%98%D0%B7%D0%B1%D1%80%D0%B0%D0%BD%D0%B8_%D1%81%D1%82%D0%B0%D1%82%D0%B8%D0%B8"><span>Избрана содржина</span></a></li><li id="n-randompage" 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%D1%87%D0%B0%D1%98%D0%BD%D0%B0" title="Вчитај случајна страница [x]" accesskey="x"><span>Случајна страница</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%9F%D0%BE%D1%80%D1%82%D0%B0%D0%BB" title="За проектот, што можете да направите, каде да најдете некои работи"><span>Портал</span></a></li> </ul> </div> </div> <div id="p-interaction" class="vector-menu mw-portlet mw-portlet-interaction" > <div class="vector-menu-heading"> технички </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-Тековни-настани" class="mw-list-item"><a href="/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%A2%D0%B5%D0%BA%D0%BE%D0%B2%D0%BD%D0%B8_%D0%BD%D0%B0%D1%81%D1%82%D0%B0%D0%BD%D0%B8"><span>Тековни настани</span></a></li><li id="n-recentchanges" 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%BA%D0%BE%D1%80%D0%B5%D1%88%D0%BD%D0%B8%D0%9F%D1%80%D0%BE%D0%BC%D0%B5%D0%BD%D0%B8" title="Список на скорешни промени на викито. [r]" accesskey="r"><span>Скорешни промени</span></a></li><li id="n-pump" class="mw-list-item"><a href="/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%A1%D0%B5%D0%BB%D1%81%D0%BA%D0%B0_%D1%87%D0%B5%D1%88%D0%BC%D0%B0"><span>Селска чешма</span></a></li><li id="n-Викисредби" class="mw-list-item"><a href="/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%92%D0%B8%D0%BA%D0%B8%D1%81%D1%80%D0%B5%D0%B4%D0%B1%D0%B0"><span>Викисредби</span></a></li><li id="n-help" class="mw-list-item"><a href="https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Contents" title="Место каде што може да се информирате."><span>Помош</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/%D0%93%D0%BB%D0%B0%D0%B2%D0%BD%D0%B0_%D1%81%D1%82%D1%80%D0%B0%D0%BD%D0%B8%D1%86%D0%B0" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Википедија" src="/static/images/mobile/copyright/wikipedia-wordmark-sr.svg" style="width: 7.8125em; height: 1.4375em;"> <img class="mw-logo-tagline" alt="Слободна енциклопедија" src="/static/images/mobile/copyright/wikipedia-tagline-mk.svg" width="114" height="11" style="width: 7.125em; height: 0.6875em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%91%D0%B0%D1%80%D0%B0%D1%98" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Пребарај низ Википедија [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Пребарај</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Пребарајте по Википедија" aria-label="Пребарајте по Википедија" autocapitalize="sentences" title="Пребарај низ Википедија [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Специјална:Барај"> </div> <button class="cdx-button cdx-search-input__end-button">Пребарај</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Лични алатки"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Изглед"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Сменете ги големината на фонтот, ширината и бојата" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Изглед" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-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-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Изглед</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_mk.wikipedia.org&uselang=mk" class=""><span>Дарување</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" 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%BE%D0%B7%D0%B4%D0%B0%D1%98%D0%9A%D0%BE%D1%80%D0%B8%D1%81%D0%BD%D0%B8%D1%87%D0%BA%D0%B0%D0%A1%D0%BC%D0%B5%D1%82%D0%BA%D0%B0&returnto=%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="Ви препорачуваме да направите сметка и да се најавите, иако тоа не е задолжително" class=""><span>Направи сметка</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" 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%D1%98%D0%B0%D0%B2%D1%83%D0%B2%D0%B0%D1%9A%D0%B5&returnto=%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="Ви препорачуваме да се најавите, иако тоа не е задолжително. [o]" accesskey="o" class=""><span>Најава</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Повеќе можности" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Лични алатки" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-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-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Лични алатки</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Корисничко мени" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_mk.wikipedia.org&uselang=mk"><span>Дарување</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item 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%BE%D0%B7%D0%B4%D0%B0%D1%98%D0%9A%D0%BE%D1%80%D0%B8%D1%81%D0%BD%D0%B8%D1%87%D0%BA%D0%B0%D0%A1%D0%BC%D0%B5%D1%82%D0%BA%D0%B0&returnto=%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="Ви препорачуваме да направите сметка и да се најавите, иако тоа не е задолжително"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Направи сметка</span></a></li><li id="pt-login" class="user-links-collapsible-item 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%D1%98%D0%B0%D0%B2%D1%83%D0%B2%D0%B0%D1%9A%D0%B5&returnto=%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="Ви препорачуваме да се најавите, иако тоа не е задолжително. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Најава</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Страници за одјавени уредници <a href="/wiki/%D0%9F%D0%BE%D0%BC%D0%BE%D1%88:%D0%92%D0%BE%D0%B2%D0%B5%D0%B4" aria-label="Дознајте повеќе за уредувањето"><span>дознајте повеќе</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" 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%9C%D0%BE%D0%B8%D0%9F%D1%80%D0%B8%D0%B4%D0%BE%D0%BD%D0%B5%D1%81%D0%B8" title="Список на уредувања направени од оваа IP-адреса [y]" accesskey="y"><span>Придонеси</span></a></li><li id="pt-anontalk" class="mw-list-item"><a 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/\u003E\u003C/a\u003E\u003Cfigcaption\u003EУредувачки викенд „Турска кујна“\u003C/figcaption\u003E\u003C/figure\u003E\n\u003Cp\u003EСе известуваат сите заинтересирани уредници на Википедија на македонски јазик дека во периодот 23-24 ноември 2024 година ќе се одржи \u003Ca href=\"/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%A3%D1%80%D0%B5%D0%B4%D1%83%D0%B2%D0%B0%D1%87%D0%BA%D0%B8_%D0%B2%D0%B8%D0%BA%D0%B5%D0%BD%D0%B4%D0%B8\" title=\"Википедија:Уредувачки викенди\"\u003Eуредувачки викенд\u003C/a\u003E на тема „\u003Cb\u003E\u003Ca href=\"/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%A3%D1%80%D0%B5%D0%B4%D1%83%D0%B2%D0%B0%D1%87%D0%BA%D0%B8_%D0%B2%D0%B8%D0%BA%D0%B5%D0%BD%D0%B4%D0%B8_2024#Турска_кујна\" title=\"Википедија:Уредувачки викенди 2024\"\u003EТурска кујна\u003C/a\u003E\u003C/b\u003E“.\n\u003Cbr style=\"clear:both;\" /\u003E\n\u003C/p\u003E\n\u003Cfigure class=\"mw-halign-left\" typeof=\"mw:File\"\u003E\u003Ca href=\"/wiki/%D0%9F%D0%BE%D0%B4%D0%B0%D1%82%D0%BE%D1%82%D0%B5%D0%BA%D0%B0:Wikipe-tan_mopping.png\" class=\"mw-file-description\"\u003E\u003Cimg src=\"//upload.wikimedia.org/wikipedia/commons/thumb/c/c0/Wikipe-tan_mopping.png/25px-Wikipe-tan_mopping.png\" decoding=\"async\" width=\"25\" height=\"30\" class=\"mw-file-element\" srcset=\"//upload.wikimedia.org/wikipedia/commons/thumb/c/c0/Wikipe-tan_mopping.png/38px-Wikipe-tan_mopping.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c0/Wikipe-tan_mopping.png/50px-Wikipe-tan_mopping.png 2x\" data-file-width=\"1800\" data-file-height=\"2149\" /\u003E\u003C/a\u003E\u003Cfigcaption\u003E\u003C/figcaption\u003E\u003C/figure\u003E\n\u003Cp\u003EСе известуваат сите заинтересирани уредници дека во периодот од 4 ноември до 3 декември 2024 година се одржува \u003Ca href=\"/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%A3%D1%80%D0%B5%D0%B4%D1%83%D0%B2%D0%B0%D1%87%D0%BA%D0%B8_%D0%BD%D0%B0%D1%82%D0%BF%D1%80%D0%B5%D0%B2%D0%B0%D1%80%D0%B8\" title=\"Википедија:Уредувачки натпревари\"\u003Eуредувачки натпревар\u003C/a\u003E за \u003Cb\u003E\u003Ca href=\"/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%A3%D1%80%D0%B5%D0%B4%D1%83%D0%B2%D0%B0%D1%87%D0%BA%D0%B8_%D0%BD%D0%B0%D1%82%D0%BF%D1%80%D0%B5%D0%B2%D0%B0%D1%80%D0%B8/%D0%A1%D1%80%D0%B5%D0%B4%D1%83%D0%B2%D0%B0%D1%9A%D0%B5_(2024)\" title=\"Википедија:Уредувачки натпревари/Средување (2024)\"\u003Eсредување на статии\u003C/a\u003E\u003C/b\u003E. 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-Геодезија" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Геодезија"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Геодезија</span> </div> </a> <ul id="toc-Геодезија-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Добивање_на_најкратки_патеки" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Добивање_на_најкратки_патеки"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Добивање на најкратки патеки</span> </div> </a> <ul id="toc-Добивање_на_најкратки_патеки-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">3</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">4</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">5</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">Голема кружница</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 63 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-63" 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">63 јазици</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%89%B3%E1%88%8B%E1%89%85_%E1%8A%AD%E1%89%A5" title="ታላቅ ክብ — амхарски" lang="am" hreflang="am" data-title="ታላቅ ክብ" 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/%D8%AF%D8%A7%D8%A6%D8%B1%D8%A9_%D8%B9%D8%B8%D9%85%D9%89" title="دائرة عظمى — арапски" lang="ar" hreflang="ar" data-title="دائرة عظمى" 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/Gran_c%C3%ADrculu" title="Gran círculu — астурски" lang="ast" hreflang="ast" data-title="Gran círculu" data-language-autonym="Asturianu" data-language-local-name="астурски" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AE%E0%A6%B9%E0%A6%BE%E0%A6%AC%E0%A7%83%E0%A6%A4%E0%A7%8D%E0%A6%A4" title="মহাবৃত্ত — бенгалски" lang="bn" hreflang="bn" data-title="মহাবৃত্ত" 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/T%C5%8Da-%C3%AE%E2%81%BF" title="Tōa-îⁿ — јужномински" lang="nan" hreflang="nan" data-title="Tōa-îⁿ" 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/%D2%98%D1%83%D1%80_%D1%82%D2%AF%D2%A3%D3%99%D1%80%D3%99%D0%BA" title="Ҙур түңәрәк — башкирски" lang="ba" hreflang="ba" data-title="Ҙур түңәрәк" data-language-autonym="Башҡортса" data-language-local-name="башкирски" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%93%D0%BE%D0%BB%D1%8F%D0%BC%D0%B0_%D0%BE%D0%BA%D1%80%D1%8A%D0%B6%D0%BD%D0%BE%D1%81%D1%82" title="Голяма окръжност — бугарски" lang="bg" hreflang="bg" data-title="Голяма окръжност" data-language-autonym="Български" data-language-local-name="бугарски" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Kelc%27h_bras" title="Kelc'h bras — бретонски" lang="br" hreflang="br" data-title="Kelc'h bras" data-language-autonym="Brezhoneg" data-language-local-name="бретонски" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Cercle_m%C3%A0xim" title="Cercle màxim — каталонски" lang="ca" hreflang="ca" data-title="Cercle màxim" data-language-autonym="Català" data-language-local-name="каталонски" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Hlavn%C3%AD_kru%C5%BEnice" title="Hlavní kružnice — чешки" lang="cs" hreflang="cs" data-title="Hlavní kružnice" data-language-autonym="Čeština" data-language-local-name="чешки" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Storcirkel" title="Storcirkel — дански" lang="da" hreflang="da" data-title="Storcirkel" data-language-autonym="Dansk" data-language-local-name="дански" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Gro%C3%9Fkreis" title="Großkreis — германски" lang="de" hreflang="de" data-title="Großkreis" data-language-autonym="Deutsch" data-language-local-name="германски" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-dsb mw-list-item"><a href="https://dsb.wikipedia.org/wiki/Wjeliki_krejz" title="Wjeliki krejz — долнолужички" lang="dsb" hreflang="dsb" data-title="Wjeliki krejz" data-language-autonym="Dolnoserbski" data-language-local-name="долнолужички" class="interlanguage-link-target"><span>Dolnoserbski</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Suurring" title="Suurring — естонски" lang="et" hreflang="et" data-title="Suurring" data-language-autonym="Eesti" data-language-local-name="естонски" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Great_circle" title="Great circle — англиски" lang="en" hreflang="en" data-title="Great circle" 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/Gran_c%C3%ADrculo" title="Gran círculo — шпански" lang="es" hreflang="es" data-title="Gran círculo" 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/%C4%88efcirklo" title="Ĉefcirklo — есперанто" lang="eo" hreflang="eo" data-title="Ĉefcirklo" 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/Zirkulu_nagusi" title="Zirkulu nagusi — баскиски" lang="eu" hreflang="eu" data-title="Zirkulu nagusi" 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/%D8%AF%D8%A7%DB%8C%D8%B1%D9%87_%D8%A8%D8%B2%D8%B1%DA%AF" title="دایره بزرگ — персиски" lang="fa" hreflang="fa" data-title="دایره بزرگ" 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/Grand_cercle" title="Grand cercle — француски" lang="fr" hreflang="fr" data-title="Grand cercle" data-language-autonym="Français" data-language-local-name="француски" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-fy mw-list-item"><a href="https://fy.wikipedia.org/wiki/Grutsirkel" title="Grutsirkel — западнофризиски" lang="fy" hreflang="fy" data-title="Grutsirkel" data-language-autonym="Frysk" data-language-local-name="западнофризиски" class="interlanguage-link-target"><span>Frysk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/M%C3%B3rchiorcal" title="Mórchiorcal — ирски" lang="ga" hreflang="ga" data-title="Mórchiorcal" data-language-autonym="Gaeilge" data-language-local-name="ирски" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/C%C3%ADrculo_m%C3%A1ximo" title="Círculo máximo — галициски" lang="gl" hreflang="gl" data-title="Círculo máximo" data-language-autonym="Galego" data-language-local-name="галициски" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%8C%80%EC%9B%90" title="대원 — корејски" lang="ko" hreflang="ko" data-title="대원" data-language-autonym="한국어" data-language-local-name="корејски" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%84%D5%A5%D5%AE_%D5%B7%D6%80%D5%BB%D5%A1%D5%B6" title="Մեծ շրջան — ерменски" lang="hy" hreflang="hy" data-title="Մեծ շրջան" data-language-autonym="Հայերեն" data-language-local-name="ерменски" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AC%E0%A5%83%E0%A4%B9%E0%A4%A4%E0%A5%8D_%E0%A4%B5%E0%A5%83%E0%A4%A4%E0%A5%8D%E0%A4%A4" title="बृहत् वृत्त — хинди" lang="hi" hreflang="hi" data-title="बृहत् वृत्त" data-language-autonym="हिन्दी" data-language-local-name="хинди" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hsb mw-list-item"><a href="https://hsb.wikipedia.org/wiki/Wulki_kruh" title="Wulki kruh — горнолужички" lang="hsb" hreflang="hsb" data-title="Wulki kruh" data-language-autonym="Hornjoserbsce" data-language-local-name="горнолужички" class="interlanguage-link-target"><span>Hornjoserbsce</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Ortodroma" title="Ortodroma — хрватски" lang="hr" hreflang="hr" data-title="Ortodroma" data-language-autonym="Hrvatski" data-language-local-name="хрватски" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ilo mw-list-item"><a href="https://ilo.wikipedia.org/wiki/Nalatak_a_sirkulo" title="Nalatak a sirkulo — илокански" lang="ilo" hreflang="ilo" data-title="Nalatak a sirkulo" data-language-autonym="Ilokano" data-language-local-name="илокански" class="interlanguage-link-target"><span>Ilokano</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Lingkaran_besar" title="Lingkaran besar — индонезиски" lang="id" hreflang="id" data-title="Lingkaran besar" 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-is mw-list-item"><a href="https://is.wikipedia.org/wiki/St%C3%B3rbaugur" title="Stórbaugur — исландски" lang="is" hreflang="is" data-title="Stórbaugur" 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/Cerchio_massimo" title="Cerchio massimo — италијански" lang="it" hreflang="it" data-title="Cerchio massimo" 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%9E%D7%A2%D7%92%D7%9C_%D7%92%D7%93%D7%95%D7%9C" title="מעגל גדול — хебрејски" lang="he" hreflang="he" data-title="מעגל גדול" data-language-autonym="עברית" data-language-local-name="хебрејски" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Circulus_magnus" title="Circulus magnus — латински" lang="la" hreflang="la" data-title="Circulus magnus" data-language-autonym="Latina" data-language-local-name="латински" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Grousskrees" title="Grousskrees — луксембуршки" lang="lb" hreflang="lb" data-title="Grousskrees" data-language-autonym="Lëtzebuergesch" data-language-local-name="луксембуршки" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Didysis_apskritimas" title="Didysis apskritimas — литвански" lang="lt" hreflang="lt" data-title="Didysis apskritimas" 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/F%C5%91k%C3%B6r" title="Főkör — унгарски" lang="hu" hreflang="hu" data-title="Főkör" data-language-autonym="Magyar" data-language-local-name="унгарски" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Bulatan_agung" title="Bulatan agung — малајски" lang="ms" hreflang="ms" data-title="Bulatan agung" 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-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Grootcirkel" title="Grootcirkel — холандски" lang="nl" hreflang="nl" data-title="Grootcirkel" 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/%E5%A4%A7%E5%86%86" title="大円 — јапонски" lang="ja" hreflang="ja" data-title="大円" 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-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Storsirkel" title="Storsirkel — норвешки букмол" lang="nb" hreflang="nb" data-title="Storsirkel" 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/Storsirkel" title="Storsirkel — норвешки нинорск" lang="nn" hreflang="nn" data-title="Storsirkel" 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/Grand_cercle" title="Grand cercle — окситански" lang="oc" hreflang="oc" data-title="Grand cercle" data-language-autonym="Occitan" data-language-local-name="окситански" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Ko%C5%82o_wielkie" title="Koło wielkie — полски" lang="pl" hreflang="pl" data-title="Koło wielkie" 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/C%C3%ADrculo_m%C3%A1ximo" title="Círculo máximo — португалски" lang="pt" hreflang="pt" data-title="Círculo máximo" 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/Cerc_mare" title="Cerc mare — романски" lang="ro" hreflang="ro" data-title="Cerc mare" data-language-autonym="Română" data-language-local-name="романски" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%92%D0%B5%D0%BB%D0%B8%D0%BA%D1%8B%D0%B9_%D0%BA%D1%80%D1%83%D0%B3" title="Великый круг — русински" lang="rue" hreflang="rue" data-title="Великый круг" data-language-autonym="Русиньскый" data-language-local-name="русински" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%91%D0%BE%D0%BB%D1%8C%D1%88%D0%BE%D0%B9_%D0%BA%D1%80%D1%83%D0%B3" title="Большой круг — руски" lang="ru" hreflang="ru" data-title="Большой круг" data-language-autonym="Русский" data-language-local-name="руски" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Great_circle" title="Great circle — Simple English" lang="en-simple" hreflang="en-simple" data-title="Great circle" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Veliki_krog" title="Veliki krog — словенечки" lang="sl" hreflang="sl" data-title="Veliki krog" data-language-autonym="Slovenščina" data-language-local-name="словенечки" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%92%D0%B5%D0%BB%D0%B8%D0%BA%D0%B0_%D0%BA%D1%80%D1%83%D0%B6%D0%BD%D0%B8%D1%86%D0%B0" title="Велика кружница — српски" lang="sr" hreflang="sr" data-title="Велика кружница" 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/Velika_kru%C5%BEnica" title="Velika kružnica — српскохрватски" lang="sh" hreflang="sh" data-title="Velika kružnica" 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-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Isoympyr%C3%A4" title="Isoympyrä — фински" lang="fi" hreflang="fi" data-title="Isoympyrä" 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/Storcirkel" title="Storcirkel — шведски" lang="sv" hreflang="sv" data-title="Storcirkel" data-language-autonym="Svenska" data-language-local-name="шведски" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AA%E0%AF%86%E0%AE%B0%E0%AF%81_%E0%AE%B5%E0%AE%9F%E0%AF%8D%E0%AE%9F%E0%AE%AE%E0%AF%8D" title="பெரு வட்டம் — тамилски" lang="ta" hreflang="ta" data-title="பெரு வட்டம்" data-language-autonym="தமிழ்" data-language-local-name="тамилски" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%A7%E0%B8%87%E0%B8%81%E0%B8%A5%E0%B8%A1%E0%B9%83%E0%B8%AB%E0%B8%8D%E0%B9%88" title="วงกลมใหญ่ — тајландски" lang="th" hreflang="th" data-title="วงกลมใหญ่" data-language-autonym="ไทย" data-language-local-name="тајландски" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/B%C3%BCy%C3%BCk_daire" title="Büyük daire — турски" lang="tr" hreflang="tr" data-title="Büyük daire" 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%92%D0%B5%D0%BB%D0%B8%D0%BA%D0%B5_%D0%BA%D0%BE%D0%BB%D0%BE" title="Велике коло — украински" lang="uk" hreflang="uk" data-title="Велике коло" data-language-autonym="Українська" data-language-local-name="украински" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%AF%D8%A7%D8%A6%D8%B1%DB%81_%D8%B9%D8%B8%DB%8C%D9%85" title="دائرہ عظیم — урду" lang="ur" hreflang="ur" data-title="دائرہ عظیم" data-language-autonym="اردو" data-language-local-name="урду" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/%C4%90%C6%B0%E1%BB%9Dng_tr%C3%B2n_l%E1%BB%9Bn" title="Đường tròn lớn — виетнамски" lang="vi" hreflang="vi" data-title="Đường tròn lớn" 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-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%A4%A7%E5%9C%86" title="大圆 — ву" lang="wuu" hreflang="wuu" data-title="大圆" 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/%E5%A4%A7%E5%9C%93" title="大圓 — кантонски" lang="yue" hreflang="yue" data-title="大圓" 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/%E5%A4%A7%E5%9C%86" title="大圆 — кинески" lang="zh" hreflang="zh" data-title="大圆" data-language-autonym="中文" data-language-local-name="кинески" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q146657#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%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="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%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" 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" > 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[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 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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:Grosskreis.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/25/Grosskreis.svg/220px-Grosskreis.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/25/Grosskreis.svg/330px-Grosskreis.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/25/Grosskreis.svg/440px-Grosskreis.svg.png 2x" data-file-width="283" data-file-height="283" /></a><figcaption>Неколку големи кружници (задебелени линии). <a href="/wiki/%D0%9D%D0%B0%D0%BA%D0%BB%D0%BE%D0%BD" class="mw-disambig" title="Наклон">Наклонот</a> на двете црни кружници во однос на екваторот (сино) изнесува 55° односно 60°.</figcaption></figure> <p><b>Голема кружница</b> или <b>ортодрома</b><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> — пресекот на една <a href="/wiki/%D0%A1%D1%84%D0%B5%D1%80%D0%B0" title="Сфера">сфера</a> со <a href="/wiki/%D0%A0%D0%B0%D0%BC%D0%BD%D0%B8%D0%BD%D0%B0_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0)" class="mw-redirect" title="Рамнина (геометрија)">рамнина</a> која минува низ центарот на сферата и претставува најголемата кружница што може да се смести во сферата. Кружницата се карекува „голема“ наспроти општа („мала“) кружница, каде рамнината не минува низ центарот. Секој <a href="/wiki/%D0%9F%D1%80%D0%B5%D1%87%D0%BD%D0%B8%D0%BA" title="Пречник">пречник</a> на големата кружница се совпаѓа со пречникот на сферата, па затоа сите големи кружници имаат меѓусебно иста <a href="/wiki/%D0%9E%D0%B1%D0%B8%D0%BA%D0%BE%D0%BB%D0%BA%D0%B0" class="mw-redirect" title="Обиколка">обиколка</a> и ист центар како сферата. Секоја <a href="/wiki/%D0%9A%D1%80%D1%83%D0%B6%D0%BD%D0%B8%D1%86%D0%B0" title="Кружница">кружница</a> во <a href="/wiki/%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4%D0%BE%D0%B2_%D0%BF%D1%80%D0%BE%D1%81%D1%82%D0%BE%D1%80" title="Евклидов простор">Евклидовиот простор</a> е голема кружница на точно една сфера. </p><p>Низ секои две точки на површината на сферата минува по една голема кружница. Малиот лак на големата кружница помеѓу две точки е најмалото (површинско) растојание помеѓу нив. Во оваа смисла, малиот лак е исто што и „правата линија“ во <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)">сферната геометрија</a>. Големите кружници се <a href="/w/index.php?title=%D0%93%D0%B5%D0%BE%D0%B4%D0%B5%D0%B7%D0%B8%D1%81%D0%BA%D0%B0_%D0%BB%D0%B8%D0%BD%D0%B8%D1%98%D0%B0&action=edit&redlink=1" class="new" title="Геодезиска линија (страницата не постои)">геодезиски линии</a> на сферата. </p><p>Во повеќе димензии, големите кружници на една <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"><i>n</i>-сфера</a> се пресеците на <i>n</i>-сферата со две рамнини што минуваат низ почетокот во Евклидовиот простор <b>R</b><sup><i>n</i>+1</sup>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Геодезија"><span id=".D0.93.D0.B5.D0.BE.D0.B4.D0.B5.D0.B7.D0.B8.D1.98.D0.B0"></span>Геодезија</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%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&veaction=edit&section=1" title="Уреди го одделот „Геодезија“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%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&action=edit&section=1" title="Уреди изворен код на одделот: Геодезија"><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">Поврзано: <a href="/wiki/%D0%93%D0%B5%D0%BE%D0%B4%D0%B5%D0%B7%D0%B8%D1%98%D0%B0" title="Геодезија">Геодезија</a></div> <figure class="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:LoxodromeOrthodrome_mk.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/LoxodromeOrthodrome_mk.svg/280px-LoxodromeOrthodrome_mk.svg.png" decoding="async" width="280" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/LoxodromeOrthodrome_mk.svg/420px-LoxodromeOrthodrome_mk.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/52/LoxodromeOrthodrome_mk.svg/560px-LoxodromeOrthodrome_mk.svg.png 2x" data-file-width="700" data-file-height="550" /></a><figcaption>Споредба помеѓу голема кружница (ортодрома) и <a href="/w/index.php?title=%D0%9B%D0%BE%D0%BA%D1%81%D0%BE%D0%B4%D1%80%D0%BE%D0%BC%D0%B0&action=edit&redlink=1" class="new" title="Локсодрома (страницата не постои)">локсодрома</a>.</figcaption></figure> <p><a href="/wiki/%D0%97%D0%B5%D0%BC%D1%98%D0%B0" class="mw-disambig" title="Земја">Земјата</a> не е совршена сфера, туку <a href="/wiki/%D0%A1%D1%84%D0%B5%D1%80%D0%BE%D0%B8%D0%B4" title="Сфероид">сплеснат сфероид</a> или <a href="/w/index.php?title=%D0%95%D0%BB%D0%B8%D0%BF%D1%81%D0%BE%D0%B8%D0%B4&action=edit&redlink=1" class="new" title="Елипсоид (страницата не постои)">елипсоид</a>, што значи дека најмалото растојание помеѓу две точки (геодезиска линија) не претставува вистинска голема кружница. Екваторскиот полупречник на Земјата изнесува околу 6378,137 <a href="/wiki/%D0%9A%D0%B8%D0%BB%D0%BE%D0%BC%D0%B5%D1%82%D0%B0%D1%80" title="Километар">км</a>, а поларниот е околу 6356,752 км (за ~ 21,4 км помалку). Но и покрај тоа, сферниот модел се зема за прва приближност. </p><p>При исцртувањето на долгосежни воздухопловни и морепловни патишта на рамна карта (на пр. <a href="/w/index.php?title=%D0%9C%D0%B5%D1%80%D0%BA%D0%B0%D1%82%D0%BE%D1%80%D0%BE%D0%B2%D0%B0_%D0%BF%D1%80%D0%BE%D0%B5%D0%BA%D1%86%D0%B8%D1%98%D0%B0&action=edit&redlink=1" class="new" title="Меркаторова проекција (страницата не постои)">Меркаторова проекција</a>), патиштата изгледаат закривени. Ова се јавува поради тоа што лежат на големи кружници, па затоа претставениот (исправен) пат на картата ќе биде подолг. Исклучок од ова е <a href="/w/index.php?title=%D0%93%D0%BD%D0%BE%D0%BC%D0%BE%D0%BD&action=edit&redlink=1" class="new" title="Гномон (страницата не постои)">гномонската</a> проекција, каде сите прави линии претставуваат големи кружници. </p><p>Ако Земјата ја земеме за сферична, <a href="/wiki/%D0%9C%D0%B5%D1%80%D0%B8%D0%B4%D0%B8%D1%98%D0%B0%D0%BD" title="Меридијан">меридијаните</a> би биле големи кружници, исто како <a href="/wiki/%D0%95%D0%BA%D0%B2%D0%B0%D1%82%D0%BE%D1%80" title="Екватор">екваторот</a>. <a href="/wiki/%D0%9D%D0%B0%D0%BF%D0%BE%D1%80%D0%B5%D0%B4%D0%BD%D0%B8%D0%BA" title="Напоредник">Напоредниците</a> (освен екваторот) не се големи кружници бидејќи се помали од екваторот; нивните центри не лежат во центарот на Земјата, туку претставуваат мали кружници. Бидејќи Земјата не е совршено сферична, екваторот (кој е голема кружница) изнесува 40.075 км, додека пак меридијанската линија север-југ (која е елипса) изнесува речиси 40.008 км. <a href="/w/index.php?title=%D0%9A%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D0%BD%D0%B0_%D1%81%D1%80%D0%B5%D0%B4%D0%B8%D0%BD%D0%B0&action=edit&redlink=1" class="new" title="Квадратна средина (страницата не постои)">Квадратната средина</a> на овие крајности дава пристојна приближност на просечната обиколка на големата кружница, што изнесува околу 40041,5 км. </p><p>Примери за големи кружници на <a href="/wiki/%D0%9D%D0%B5%D0%B1%D0%B5%D1%81%D0%BD%D0%B0_%D1%81%D1%84%D0%B5%D1%80%D0%B0" title="Небесна сфера">небесната сфера</a> се <a href="/wiki/%D0%A5%D0%BE%D1%80%D0%B8%D0%B7%D0%BE%D0%BD%D1%82%D1%81%D0%BA%D0%B8_%D0%BA%D0%BE%D0%BE%D1%80%D0%B4%D0%B8%D0%BD%D0%B0%D1%82%D0%B5%D0%BD_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC" title="Хоризонтски координатен систем">небесниот хоризонт</a>, <a href="/wiki/%D0%9D%D0%B5%D0%B1%D0%B5%D1%81%D0%B5%D0%BD_%D0%B5%D0%BA%D0%B2%D0%B0%D1%82%D0%BE%D1%80" title="Небесен екватор">небесниот екватор</a> и <a href="/wiki/%D0%95%D0%BA%D0%BB%D0%B8%D0%BF%D1%82%D0%B8%D0%BA%D0%B0" title="Еклиптика">еклиптиката</a>. </p><p>Бродовите и воздухопловите користат големи кружници кога струите и ветриштата не се значајни фактори. Така, времетраењето на летот може (приближно) да се добие според растојанието на големата кружница помеѓу два аеродрома. Освен по голема кружница, воздухопловите летаат и по други патишта, кајшто можат да ја искористат <a href="/w/index.php?title=%D0%9C%D0%BB%D0%B0%D0%B7%D0%BD%D0%B0_%D1%81%D1%82%D1%80%D1%83%D1%98%D0%B0&action=edit&redlink=1" class="new" title="Млазна струја (страницата не постои)">млазната струја</a>. </p><p>За полесна пловидба, големите кружници честопати се делат на помали <a href="/w/index.php?title=%D0%9B%D0%BE%D0%BA%D1%81%D0%BE%D0%B4%D1%80%D0%BE%D0%BC%D0%B0&action=edit&redlink=1" class="new" title="Локсодрома (страницата не постои)">локсодроми</a>, што овозможува држење на постојан курс помеѓу патните точки долж големата кружница. </p> <div style="clear:both;"></div> <div class="mw-heading mw-heading2"><h2 id="Добивање_на_најкратки_патеки"><span id=".D0.94.D0.BE.D0.B1.D0.B8.D0.B2.D0.B0.D1.9A.D0.B5_.D0.BD.D0.B0_.D0.BD.D0.B0.D1.98.D0.BA.D1.80.D0.B0.D1.82.D0.BA.D0.B8_.D0.BF.D0.B0.D1.82.D0.B5.D0.BA.D0.B8"></span>Добивање на најкратки патеки</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%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&veaction=edit&section=2" title="Уреди го одделот „Добивање на најкратки патеки“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%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&action=edit&section=2" title="Уреди изворен код на одделот: Добивање на најкратки патеки"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="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:Greatcircle_Jetstream_routes_mk.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/58/Greatcircle_Jetstream_routes_mk.svg/350px-Greatcircle_Jetstream_routes_mk.svg.png" decoding="async" width="350" height="161" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/58/Greatcircle_Jetstream_routes_mk.svg/525px-Greatcircle_Jetstream_routes_mk.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/58/Greatcircle_Jetstream_routes_mk.svg/700px-Greatcircle_Jetstream_routes_mk.svg.png 2x" data-file-width="815" data-file-height="374" /></a><figcaption>Воздухопловни патишта од <a href="/wiki/%D0%A1%D0%B0%D0%BD_%D0%A4%D1%80%D0%B0%D0%BD%D1%86%D0%B8%D1%81%D0%BA%D0%BE" title="Сан Франциско">Сан Франциско</a> до <a href="/wiki/%D0%A2%D0%BE%D0%BA%D0%B8%D0%BE" title="Токио">Токио</a> по најнепосредната голема кружница (горе), но следејќи ја млазната струја (долу) летајќи на исток.</figcaption></figure> <p>За да докажеме дека малиот лак на една голема кружница е најмалото растојание помеѓу две точки на нејзината површина, применуваме <a href="/w/index.php?title=%D0%92%D0%B0%D1%80%D0%B8%D1%98%D0%B0%D1%86%D0%B8%D0%BE%D0%BD%D0%BE_%D1%81%D0%BC%D0%B5%D1%82%D0%B0%D1%9A%D0%B5&action=edit&redlink=1" class="new" title="Варијационо сметање (страницата не постои)">варијационо сметање</a>. </p><p>Да речеме дека ја имаме класата на сите правилни растојанија од точката <i>p</i> до точката <i>q</i>. Земаме <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>, така што <i>p</i> се совпаѓа со Северниот Пол. Секоја крива на сферата што не се сече со половите (освен можеби во крајните точки) може да се параметрира како </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 \theta =\theta (t),\quad \phi =\phi (t),\quad a\leq t\leq b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> <mo>=</mo> <mi>θ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>,</mo> <mspace width="1em" /> <mi>ϕ</mi> <mo>=</mo> <mi>ϕ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>,</mo> <mspace width="1em" /> <mi>a</mi> <mo>≤</mo> <mi>t</mi> <mo>≤</mo> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta =\theta (t),\quad \phi =\phi (t),\quad a\leq t\leq b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/56f97983083fac5687746ba1317d67fd825ccd24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:32.423ex; height:2.843ex;" alt="{\displaystyle \theta =\theta (t),\quad \phi =\phi (t),\quad a\leq t\leq b}"></span></dd></dl> <p>под услов да допуштиме φ да добива производни реални вредности. Бесконечно малиот (<a href="/wiki/%D0%98%D0%BD%D1%84%D0%B8%D0%BD%D0%B8%D1%82%D0%B5%D0%B7%D0%B8%D0%BC%D0%B0%D0%BB%D0%B0" title="Инфинитезимала">инфинитезимален</a>) лак во овие координати е </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 ds=r{\sqrt {\theta '^{2}+\phi '^{2}\sin ^{2}\theta }}\,dt.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>s</mi> <mo>=</mo> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>θ</mi> <mrow> <mo class="MJX-variant">′</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mo>+</mo> <msup> <mi>ϕ</mi> <mrow> <mo class="MJX-variant">′</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>θ</mi> </msqrt> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <mi>t</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ds=r{\sqrt {\theta '^{2}+\phi '^{2}\sin ^{2}\theta }}\,dt.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d88842e150733aef9c2d0d2c3c23a0a64bc44ffd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:25.971ex; height:4.843ex;" alt="{\displaystyle ds=r{\sqrt {\theta '^{2}+\phi '^{2}\sin ^{2}\theta }}\,dt.}"></span></dd></dl> <p>Така, должината на кривата γ од <i>p</i> до <i>q</i> е <a href="/w/index.php?title=%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D0%BE%D0%BD%D0%B0%D0%BB&action=edit&redlink=1" class="new" title="Функционал (страницата не постои)">функционал</a> на кривата даден со </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[\gamma ]=r\int _{a}^{b}{\sqrt {\theta '^{2}+\phi '^{2}\sin ^{2}\theta }}\,dt.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo stretchy="false">[</mo> <mi>γ</mi> <mo stretchy="false">]</mo> <mo>=</mo> <mi>r</mi> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>θ</mi> <mrow> <mo class="MJX-variant">′</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mo>+</mo> <msup> <mi>ϕ</mi> <mrow> <mo class="MJX-variant">′</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>θ</mi> </msqrt> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <mi>t</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S[\gamma ]=r\int _{a}^{b}{\sqrt {\theta '^{2}+\phi '^{2}\sin ^{2}\theta }}\,dt.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/529ea36236f5ec3d9b1eba8447cc80ca1f04c1a0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:31.896ex; height:6.343ex;" alt="{\displaystyle S[\gamma ]=r\int _{a}^{b}{\sqrt {\theta '^{2}+\phi '^{2}\sin ^{2}\theta }}\,dt.}"></span></dd></dl> <p>Да напоменеме дека <i>S</i>[γ] е барем со должина на меридијанот од <i>p</i> до <i>q</i>: </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[\gamma ]\geq r\int _{a}^{b}|\theta '(t)|\,dt\geq r|\theta (q)-\theta (p)|.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo stretchy="false">[</mo> <mi>γ</mi> <mo stretchy="false">]</mo> <mo>≥</mo> <mi>r</mi> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msup> <mi>θ</mi> <mo>′</mo> </msup> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <mi>t</mi> <mo>≥</mo> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>θ</mi> <mo stretchy="false">(</mo> <mi>q</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>θ</mi> <mo stretchy="false">(</mo> <mi>p</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S[\gamma ]\geq r\int _{a}^{b}|\theta '(t)|\,dt\geq r|\theta (q)-\theta (p)|.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c1bafa3d6f8975b754eeac5ec4354a76e212ee46" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:37.505ex; height:6.343ex;" alt="{\displaystyle S[\gamma ]\geq r\int _{a}^{b}|\theta '(t)|\,dt\geq r|\theta (q)-\theta (p)|.}"></span></dd></dl> <p>Бидејќи почетната и крајната точка се непроменливи, <i>S</i> се сведува на минимум <a href="/wiki/%D0%90%D0%BA%D0%BE_%D0%B8_%D1%81%D0%B0%D0%BC%D0%BE_%D0%B0%D0%BA%D0%BE" title="Ако и само ако">ако и само ако</a> φ' = 0, така што кривата мора да лежи на меридијанот на сферата φ = φ<sub>0</sub> = постојана. Изразено во <a href="/wiki/%D0%94%D0%B5%D0%BA%D0%B0%D1%80%D1%82%D0%BE%D0%B2%D0%B8_%D0%BA%D0%BE%D0%BE%D1%80%D0%B4%D0%B8%D0%BD%D0%B0%D1%82%D0%B8" class="mw-redirect" title="Декартови координати">Декартови координати</a>, тоа би било </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\sin \phi _{0}-y\cos \phi _{0}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mi>sin</mi> <mo>⁡</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>−</mo> <mi>y</mi> <mi>cos</mi> <mo>⁡</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\sin \phi _{0}-y\cos \phi _{0}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a3f841c313c13714f9caa1e350dfd49caf7d676a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:21.981ex; height:2.509ex;" alt="{\displaystyle x\sin \phi _{0}-y\cos \phi _{0}=0}"></span></dd></dl> <p>што е рамнина низ почетокот, т.е. центарот на сферата.. </p> <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%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&veaction=edit&section=3" 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%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&action=edit&section=3" title="Уреди изворен код на одделот: Поврзано"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/w/index.php?title=%D0%93%D0%B5%D0%BE%D0%B4%D0%B5%D0%B7%D0%B8%D1%81%D0%BA%D0%B0_%D0%BB%D0%B8%D0%BD%D0%B8%D1%98%D0%B0&action=edit&redlink=1" class="new" title="Геодезиска линија (страницата не постои)">Геодезиска линија</a></li> <li><a href="/w/index.php?title=%D0%9B%D0%BE%D0%BA%D1%81%D0%BE%D0%B4%D1%80%D0%BE%D0%BC%D0%B0&action=edit&redlink=1" class="new" title="Локсодрома (страницата не постои)">Локсодрома</a></li> <li><a href="/w/index.php?title=%D0%9A%D0%B8%D0%B1%D0%BB%D0%B0&action=edit&redlink=1" class="new" title="Кибла (страницата не постои)">Кибла</a></li> <li><a href="/wiki/%D0%93%D0%BE%D0%BB%D0%B5%D0%BC%D0%B0_%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81%D0%BA%D0%B0" title="Голема полуоска">Голема полуоска</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%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&veaction=edit&section=4" 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%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&action=edit&section=4" 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="аортодрома"><a rel="nofollow" class="external text" href="https://recnik.off.net.mk/recnik/makedonski-leksikon/ортодрома">„ортодрома“</a> — Лексикон на македонскиот јазик</span></span> </li> </ol></div></div> <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%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&veaction=edit&section=5" 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%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&action=edit&section=5" title="Уреди изворен код на одделот: Надворешни врски"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/GreatCircle.html">Голема кружница: опис, прикази и равенки</a> - <a href="/wiki/MathWorld" title="MathWorld">MathWorld</a> <span class="languageicon" style="font-size:0.95em; font-weight:bold; color:#808080ff;">(англиски)</span></li> <li><a rel="nofollow" class="external text" href="http://www.greatcirclemapper.net">Големи кружници на карта</a> - правци на летање по голема кружница на карта и ја пресметува растојанието и траењето <span class="languageicon" style="font-size:0.95em; font-weight:bold; color:#808080ff;">(англиски)</span></li> <li><a rel="nofollow" class="external text" href="http://www.acscdg.com/">Растојанија на големи кружници</a> - графичка алатка за исцртување на големи кружници врз карти <span class="languageicon" style="font-size:0.95em; font-weight:bold; color:#808080ff;">(англиски)</span></li></ul></div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Преземено од „<a dir="ltr" href="https://mk.wikipedia.org/w/index.php?title=Голема_кружница&oldid=5205743">https://mk.wikipedia.org/w/index.php?title=Голема_кружница&oldid=5205743</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%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><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%B4%D0%B5%D0%B7%D0%B8%D1%98%D0%B0" title="Категорија:Геодезија">Геодезија</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%9A%D0%B0%D1%80%D1%82%D0%BE%D0%B3%D1%80%D0%B0%D1%84%D0%B8%D1%98%D0%B0" title="Категорија:Картографија">Картографија</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%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" title="Категорија:Сферна тригонометрија">Сферна тригонометрија</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Скриена категорија: <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%A1%D1%82%D0%B0%D1%82%D0%B8%D0%B8_%D1%81%D0%BE_%D0%BD%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_%D0%BD%D0%B0_%D0%B0%D0%BD%D0%B3%D0%BB%D0%B8%D1%81%D0%BA%D0%B8" title="Категорија:Статии со надворешни врски на англиски">Статии со надворешни врски на англиски</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Последната промена на страницава е извршена на 24 мај 2024 г. во 11:44 ч.</li> <li id="footer-info-copyright">Текстот е достапен под условите на лиценцата <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/">Криејтив комонс Наведи извор-Сподели под исти услови</a>. 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