CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-sticky-header-enabled vector-toc-available" lang="be" dir="ltr"> <head> <meta charset="UTF-8"> <title>Плоскасць — Вікіпедыя</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-sticky-header-enabled vector-toc-available";var cookie=document.cookie.match(/(?:^|; )bewikimwclientpreferences=([^;]+)/);if(cookie){cookie[1].split('%2C').forEach(function(pref){className=className.replace(new RegExp('(^| )'+pref.replace(/-clientpref-\w+$|[^\w-]+/g,'')+'-clientpref-\\w+( |$)'),'$1'+pref+'$2');});}document.documentElement.className=className;}());RLCONF={"wgBreakFrames":false,"wgSeparatorTransformTable":[",\t."," \t,"],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"dmy", "wgMonthNames":["","студзень","люты","сакавік","красавік","Май","чэрвень","ліпень","жнівень","верасень","кастрычнік","лістапад","снежань"],"wgRequestId":"7d6a5ada-dadb-4998-b27d-9dde7148054c","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Плоскасць","wgTitle":"Плоскасць","wgCurRevisionId":4651345,"wgRevisionId":4651345,"wgArticleId":23338,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["Эўклідава геаметрыя","Аксіяматычныя тэрміны"],"wgPageViewLanguage":"be","wgPageContentLanguage":"be","wgPageContentModel":"wikitext","wgRelevantPageName":"Плоскасць","wgRelevantArticleId":23338,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"wikipedia", "wgCiteReferencePreviewsActive":true,"wgFlaggedRevsParams":{"tags":{"accuracy":{"levels":1}}},"wgStableRevisionId":4651345,"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"be","pageLanguageDir":"ltr","pageVariantFallbacks":"be"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":true,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":5000,"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q17285","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false,"wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false};RLSTATE={ "ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready","user.options":"loading","ext.math.styles":"ready","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","ext.flaggedRevs.basic":"ready","mediawiki.codex.messagebox.styles":"ready","ext.wikimediamessages.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","wikibase.client.init":"ready","ext.wikimediaBadges":"ready"};RLPAGEMODULES=["mediawiki.page.media","site","mediawiki.page.ready","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.flaggedRevs.advanced","ext.gadget.edittop","ext.gadget.collapserefs","ext.gadget.wikibugs","ext.gadget.navboxNavigation","ext.gadget.directLinkToCommons","ext.gadget.Statistics","ext.urlShortener.toolbar","ext.centralauth.centralautologin","mmv.bootstrap","ext.popups", "ext.visualEditor.desktopArticleTarget.init","ext.visualEditor.targetLoader","ext.echo.centralauth","ext.eventLogging","ext.wikimediaEvents","ext.navigationTiming","ext.uls.interface","ext.cx.eventlogging.campaigns","ext.cx.uls.quick.actions","wikibase.client.vector-2022","ext.checkUser.clientHints","ext.growthExperiments.SuggestedEditSession"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=be&modules=ext.flaggedRevs.basic%7Cext.math.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.styles%7Cmediawiki.codex.messagebox.styles%7Cskins.vector.icons%2Cstyles%7Cskins.vector.search.codex.styles%7Cwikibase.client.init&only=styles&skin=vector-2022"> <script async="" src="/w/load.php?lang=be&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=be&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.16"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Intersecting_planes.svg/1200px-Intersecting_planes.svg.png"> <meta property="og:image:width" content="1200"> <meta property="og:image:height" content="1080"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Intersecting_planes.svg/800px-Intersecting_planes.svg.png"> <meta property="og:image:width" content="800"> <meta property="og:image:height" content="720"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Intersecting_planes.svg/640px-Intersecting_planes.svg.png"> <meta property="og:image:width" content="640"> <meta property="og:image:height" content="576"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Плоскасць — Вікіпедыя"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//be.m.wikipedia.org/wiki/%D0%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%B0%D1%81%D1%86%D1%8C"> <link rel="alternate" type="application/x-wiki" title="Правіць" href="/w/index.php?title=%D0%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%B0%D1%81%D1%86%D1%8C&action=edit"> <link rel="apple-touch-icon" href="/static/apple-touch/wikipedia.png"> <link rel="icon" href="/static/favicon/wikipedia.ico"> <link rel="search" type="application/opensearchdescription+xml" href="/w/rest.php/v1/search" title="Вікіпедыя (be)"> <link rel="EditURI" type="application/rsd+xml" href="//be.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://be.wikipedia.org/wiki/%D0%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%B0%D1%81%D1%86%D1%8C"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.be"> <link rel="alternate" type="application/atom+xml" title="Вікіпедыя струмень Atom" href="/w/index.php?title=%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:RecentChanges&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-Плоскасць rootpage-Плоскасць skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Перайсці да зместу</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="Праект"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" title="Галоўнае меню" > <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="Галоўнае меню" > <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">Галоўнае меню</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">Галоўнае меню</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">перанесці да бакавой панэлі</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">схаваць</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Навігацыя </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage" class="mw-list-item"><a href="/wiki/%D0%93%D0%B0%D0%BB%D0%BE%D1%9E%D0%BD%D0%B0%D1%8F_%D1%81%D1%82%D0%B0%D1%80%D0%BE%D0%BD%D0%BA%D0%B0" title="Адкрыць Галоўную старонку [z]" accesskey="z"><span>Галоўная старонка</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/%D0%92%D1%96%D0%BA%D1%96%D0%BF%D0%B5%D0%B4%D1%8B%D1%8F:%D0%A1%D1%83%D0%BF%D0%BE%D0%BB%D1%8C%D0%BD%D0%B0%D1%81%D1%86%D1%8C" title="Пра праект, чым можна заняцца, дзе што шукаць"><span>Супольнасць</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:RecentChanges" title="Пералік нядаўніх змяненняў у віксе. [r]" accesskey="r"><span>Апошнія змены</span></a></li><li id="n-newpages" class="mw-list-item"><a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:NewPages"><span>Новыя старонкі</span></a></li><li id="n-Village-pump" class="mw-list-item"><a href="/wiki/%D0%92%D1%96%D0%BA%D1%96%D0%BF%D0%B5%D0%B4%D1%8B%D1%8F:%D0%A4%D0%BE%D1%80%D1%83%D0%BC"><span>Форум</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:Random" title="Паказаць выпадковую старонку [x]" accesskey="x"><span>Выпадковая старонка</span></a></li><li id="n-help" class="mw-list-item"><a href="/wiki/%D0%92%D1%96%D0%BA%D1%96%D0%BF%D0%B5%D0%B4%D1%8B%D1%8F:%D0%94%D0%B0%D0%B2%D0%B5%D0%B4%D0%BA%D0%B0" title="Дзе можна атрымаць тлумачэнні."><span>Даведка</span></a></li><li id="n-bug_in_article" class="mw-list-item"><a href="/wiki/%D0%92%D1%96%D0%BA%D1%96%D0%BF%D0%B5%D0%B4%D1%8B%D1%8F:%D0%9F%D0%B0%D0%B2%D0%B5%D0%B4%D0%B0%D0%BC%D0%BB%D0%B5%D0%BD%D0%BD%D1%96_%D0%BF%D1%80%D0%B0_%D0%BF%D0%B0%D0%BC%D1%8B%D0%BB%D0%BA%D1%96"><span>Паведаміць пра памылку</span></a></li><li id="n-specialpages" class="mw-list-item"><a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:SpecialPages"><span>Адмысловыя старонкі</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/%D0%93%D0%B0%D0%BB%D0%BE%D1%9E%D0%BD%D0%B0%D1%8F_%D1%81%D1%82%D0%B0%D1%80%D0%BE%D0%BD%D0%BA%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="Вікіпедыя" src="/static/images/mobile/copyright/wikipedia-wordmark-be.svg" style="width: 7.625em; height: 1.3125em;"> <img class="mw-logo-tagline" alt="" src="/static/images/mobile/copyright/wikipedia-tagline-be.svg" width="117" height="12" style="width: 7.3125em; height: 0.75em;"> </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%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:Search" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Знайсці ў Вікіпедыі [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Пошук</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="Шукаць у Вікіпедыі" aria-label="Шукаць у Вікіпедыі" autocapitalize="sentences" title="Знайсці ў Вікіпедыі [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Адмысловае:Search"> </div> <button class="cdx-button cdx-search-input__end-button">Пошук</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Асабістыя інструменты"> <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="Выгляд"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <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="Выгляд" > <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">Выгляд</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="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=be.wikipedia.org&uselang=be" class=""><span>Ахвяраваць</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%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:CreateAccount&returnto=%D0%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%B0%D1%81%D1%86%D1%8C" title="Вам прапануецца стварыць уліковы запіс і ўвайсці ў сістэму, але гэта не абавязкова" class=""><span>Стварыць уліковы запіс</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%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:UserLogin&returnto=%D0%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%B0%D1%81%D1%86%D1%8C" title="Вам прапануецца ўвайсці ў сістэму, але гэта неабавязкова. [o]" accesskey="o" class=""><span>Увайсці</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="Больш магчымасцей" > <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="Асабістыя інструменты" > <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">Асабістыя інструменты</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Меню ўдзельніка" > <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="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=be.wikipedia.org&uselang=be"><span>Ахвяраваць</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:CreateAccount&returnto=%D0%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%B0%D1%81%D1%86%D1%8C" title="Вам прапануецца стварыць уліковы запіс і ўвайсці ў сістэму, але гэта не абавязкова"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Стварыць уліковы запіс</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:UserLogin&returnto=%D0%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%B0%D1%81%D1%86%D1%8C" title="Вам прапануецца ўвайсці ў сістэму, але гэта неабавязкова. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Увайсці</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"> Старонкі для ананімных рэдактараў <a href="/wiki/%D0%94%D0%B0%D0%B2%D0%B5%D0%B4%D0%BA%D0%B0:%D0%94%D0%B0%D0%B2%D0%B5%D0%B4%D0%BA%D0%B0" aria-label="Даведацца больш пра праўку"><span>даведацца больш</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%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:MyContributions" title="Спіс правак, зробленых з гэтага IP-адраса [y]" accesskey="y"><span>Уклад</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:MyTalk" title="Размовы пра праўкі, зробленыя з гэтага IP-адраса [n]" accesskey="n"><span>Размовы</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Праект"> <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="Змест" 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">Змест</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">перанесці да бакавой панэлі</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">схаваць</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">Пачатак</div> </a> </li> <li id="toc-Ураўненні_плоскасці" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ураўненні_плоскасці"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Ураўненні плоскасці</span> </div> </a> <ul id="toc-Ураўненні_плоскасці-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Спасылкі" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Спасылкі"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Спасылкі</span> </div> </a> <ul id="toc-Спасылкі-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="Змест" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Змест" > <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="Пераключыць змест" > <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">Пераключыць змест</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">Плоскасць</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="Перайсці да артыкула на іншай мове. Даступны на 88 мовах." > <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-88" 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">88 моў</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/Vlak" title="Vlak – афрыкаанс" lang="af" hreflang="af" data-title="Vlak" data-language-autonym="Afrikaans" data-language-local-name="афрыкаанс" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Ebene_(Mathematik)" title="Ebene (Mathematik) – швейцарская нямецкая" lang="gsw" hreflang="gsw" data-title="Ebene (Mathematik)" data-language-autonym="Alemannisch" data-language-local-name="швейцарская нямецкая" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%B3%D8%AA%D9%88_(%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A%D8%A7%D8%AA)" title="مستو (رياضيات) – арабская" lang="ar" hreflang="ar" data-title="مستو (رياضيات)" data-language-autonym="العربية" data-language-local-name="арабская" 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/Planu_(xeometr%C3%ADa)" title="Planu (xeometría) – астурыйская" lang="ast" hreflang="ast" data-title="Planu (xeometría)" data-language-autonym="Asturianu" data-language-local-name="астурыйская" 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/M%C3%BCst%C9%99vi" title="Müstəvi – азербайджанская" lang="az" hreflang="az" data-title="Müstəvi" data-language-autonym="Azərbaycanca" data-language-local-name="азербайджанская" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%AF%D2%AB%D1%8B%D0%BB%D1%8B%D2%A1" title="Яҫылыҡ – башкірская" lang="ba" hreflang="ba" data-title="Яҫылыҡ" data-language-autonym="Башҡортса" data-language-local-name="башкірская" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%A0%D0%BE%D1%9E%D0%BD%D1%96%D1%86%D0%B0" title="Роўніца – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Роўніца" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B2%D0%BD%D0%B8%D0%BD%D0%B0_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Равнина (математика) – балгарская" lang="bg" hreflang="bg" data-title="Равнина (математика)" data-language-autonym="Български" data-language-local-name="балгарская" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B8%E0%A6%AE%E0%A6%A4%E0%A6%B2" title="সমতল – бенгальская" lang="bn" hreflang="bn" data-title="সমতল" data-language-autonym="বাংলা" data-language-local-name="бенгальская" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Ravan" title="Ravan – баснійская" lang="bs" hreflang="bs" data-title="Ravan" data-language-autonym="Bosanski" data-language-local-name="баснійская" 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/Pla" title="Pla – каталанская" lang="ca" hreflang="ca" data-title="Pla" data-language-autonym="Català" data-language-local-name="каталанская" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-chr mw-list-item"><a href="https://chr.wikipedia.org/wiki/%E1%8E%AD%E1%8F%AB%E1%8E%BE%E1%8F%97%E1%8F%A2_%E1%8F%97%E1%8F%8E%E1%8F%8D%E1%8F%97_%E1%8E%A4%E1%8E%AC%E1%8F%A9%E1%8E%B5" title="ᎭᏫᎾᏗᏢ ᏗᏎᏍᏗ ᎤᎬᏩᎵ – чэрокі" lang="chr" hreflang="chr" data-title="ᎭᏫᎾᏗᏢ ᏗᏎᏍᏗ ᎤᎬᏩᎵ" data-language-autonym="ᏣᎳᎩ" data-language-local-name="чэрокі" class="interlanguage-link-target"><span>ᏣᎳᎩ</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DA%95%D9%88%D9%88%D8%AA%DB%95%D8%AE%D8%AA" title="ڕووتەخت – цэнтральнакурдская" lang="ckb" hreflang="ckb" data-title="ڕووتەخت" data-language-autonym="کوردی" data-language-local-name="цэнтральнакурдская" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Rovina" title="Rovina – чэшская" lang="cs" hreflang="cs" data-title="Rovina" data-language-autonym="Čeština" data-language-local-name="чэшская" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9B%D0%B0%D0%BF%D1%82%D0%B0%D0%BA" title="Лаптак – чувашская" lang="cv" hreflang="cv" data-title="Лаптак" data-language-autonym="Чӑвашла" data-language-local-name="чувашская" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Pl%C3%A2n_geometraidd" title="Plân geometraidd – валійская" lang="cy" hreflang="cy" data-title="Plân geometraidd" data-language-autonym="Cymraeg" data-language-local-name="валійская" 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/Plan_(matematik)" title="Plan (matematik) – дацкая" lang="da" hreflang="da" data-title="Plan (matematik)" data-language-autonym="Dansk" data-language-local-name="дацкая" 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/Ebene_(Mathematik)" title="Ebene (Mathematik) – нямецкая" lang="de" hreflang="de" data-title="Ebene (Mathematik)" data-language-autonym="Deutsch" data-language-local-name="нямецкая" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%95%CF%80%CE%AF%CF%80%CE%B5%CE%B4%CE%BF" title="Επίπεδο – грэчаская" lang="el" hreflang="el" data-title="Επίπεδο" data-language-autonym="Ελληνικά" data-language-local-name="грэчаская" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Euclidean_plane" title="Euclidean plane – англійская" lang="en" hreflang="en" data-title="Euclidean plane" data-language-autonym="English" data-language-local-name="англійская" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Ebeno_(matematiko)" title="Ebeno (matematiko) – эсперанта" lang="eo" hreflang="eo" data-title="Ebeno (matematiko)" data-language-autonym="Esperanto" data-language-local-name="эсперанта" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Plano_(geometr%C3%ADa)" title="Plano (geometría) – іспанская" lang="es" hreflang="es" data-title="Plano (geometría)" data-language-autonym="Español" data-language-local-name="іспанская" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Tasand" title="Tasand – эстонская" lang="et" hreflang="et" data-title="Tasand" data-language-autonym="Eesti" data-language-local-name="эстонская" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Plano" title="Plano – баскская" lang="eu" hreflang="eu" data-title="Plano" data-language-autonym="Euskara" data-language-local-name="баскская" 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%B5%D9%81%D8%AD%D9%87_(%D9%87%D9%86%D8%AF%D8%B3%D9%87)" title="صفحه (هندسه) – фарсі" lang="fa" hreflang="fa" data-title="صفحه (هندسه)" data-language-autonym="فارسی" data-language-local-name="фарсі" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Taso" title="Taso – фінская" lang="fi" hreflang="fi" data-title="Taso" data-language-autonym="Suomi" data-language-local-name="фінская" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Plan_(math%C3%A9matiques)" title="Plan (mathématiques) – французская" lang="fr" hreflang="fr" data-title="Plan (mathématiques)" data-language-autonym="Français" data-language-local-name="французская" 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/Pl%C3%A1na_(matamaitic)" title="Plána (matamaitic) – ірландская" lang="ga" hreflang="ga" data-title="Plána (matamaitic)" data-language-autonym="Gaeilge" data-language-local-name="ірландская" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E5%B9%B3%E9%9D%A2" title="平面 – Gan" lang="gan" hreflang="gan" data-title="平面" data-language-autonym="贛語" data-language-local-name="Gan" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Plan_(mat%C3%A9matik)" title="Plan (matématik) – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Plan (matématik)" 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-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Plano_(xeometr%C3%ADa)" title="Plano (xeometría) – галісійская" lang="gl" hreflang="gl" data-title="Plano (xeometría)" data-language-autonym="Galego" data-language-local-name="галісійская" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%99%D7%A9%D7%95%D7%A8_(%D7%92%D7%90%D7%95%D7%9E%D7%98%D7%A8%D7%99%D7%94)" title="מישור (גאומטריה) – іўрыт" lang="he" hreflang="he" data-title="מישור (גאומטריה)" data-language-autonym="עברית" data-language-local-name="іўрыт" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B8%E0%A4%AE%E0%A4%A4%E0%A4%B2_(%E0%A4%9C%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%AE%E0%A4%BF%E0%A4%A4%E0%A4%BF)" title="समतल (ज्यामिति) – хіндзі" lang="hi" hreflang="hi" data-title="समतल (ज्यामिति)" data-language-autonym="हिन्दी" data-language-local-name="хіндзі" 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/Ravnina" title="Ravnina – харвацкая" lang="hr" hreflang="hr" data-title="Ravnina" data-language-autonym="Hrvatski" data-language-local-name="харвацкая" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/S%C3%ADk_(geometria)" title="Sík (geometria) – венгерская" lang="hu" hreflang="hu" data-title="Sík (geometria)" data-language-autonym="Magyar" data-language-local-name="венгерская" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%80%D5%A1%D6%80%D5%A9%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Հարթություն – армянская" lang="hy" hreflang="hy" data-title="Հարթություն" data-language-autonym="Հայերեն" data-language-local-name="армянская" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Plano" title="Plano – інтэрлінгва" lang="ia" hreflang="ia" data-title="Plano" data-language-autonym="Interlingua" data-language-local-name="інтэрлінгва" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Bidang_(geometri)" title="Bidang (geometri) – інданезійская" lang="id" hreflang="id" data-title="Bidang (geometri)" data-language-autonym="Bahasa Indonesia" data-language-local-name="інданезійская" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Plano_(matematiko)" title="Plano (matematiko) – іда" lang="io" hreflang="io" data-title="Plano (matematiko)" data-language-autonym="Ido" data-language-local-name="іда" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Sl%C3%A9tta_(r%C3%BAmfr%C3%A6%C3%B0i)" title="Slétta (rúmfræði) – ісландская" lang="is" hreflang="is" data-title="Slétta (rúmfræði)" data-language-autonym="Íslenska" data-language-local-name="ісландская" 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/Piano_(geometria)" title="Piano (geometria) – італьянская" lang="it" hreflang="it" data-title="Piano (geometria)" data-language-autonym="Italiano" data-language-local-name="італьянская" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%B9%B3%E9%9D%A2" title="平面 – японская" lang="ja" hreflang="ja" data-title="平面" data-language-autonym="日本語" data-language-local-name="японская" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Plien_(matimatix)" title="Plien (matimatix) – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Plien (matimatix)" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A1%E1%83%98%E1%83%91%E1%83%A0%E1%83%A2%E1%83%A7%E1%83%94" title="სიბრტყე – грузінская" lang="ka" hreflang="ka" data-title="სიბრტყე" data-language-autonym="ქართული" data-language-local-name="грузінская" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Agni_(tanzeggit)" title="Agni (tanzeggit) – кабільская" lang="kab" hreflang="kab" data-title="Agni (tanzeggit)" data-language-autonym="Taqbaylit" data-language-local-name="кабільская" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%96%D0%B0%D0%B7%D1%8B%D2%9B%D1%82%D1%8B%D2%9B_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F)" title="Жазықтық (геометрия) – казахская" lang="kk" hreflang="kk" data-title="Жазықтық (геометрия)" data-language-autonym="Қазақша" data-language-local-name="казахская" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%94%E1%9F%92%E1%9E%9B%E1%9E%84%E1%9F%8B" title="ប្លង់ – кхмерская" lang="km" hreflang="km" data-title="ប្លង់" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="кхмерская" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%8F%89%EB%A9%B4" title="평면 – карэйская" lang="ko" hreflang="ko" data-title="평면" data-language-autonym="한국어" data-language-local-name="карэйская" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%A2%D0%B5%D0%B3%D0%B8%D0%B7%D0%B4%D0%B8%D0%BA" title="Тегиздик – кіргізская" lang="ky" hreflang="ky" data-title="Тегиздик" data-language-autonym="Кыргызча" data-language-local-name="кіргізская" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Planum_(geometria)" title="Planum (geometria) – лацінская" lang="la" hreflang="la" data-title="Planum (geometria)" data-language-autonym="Latina" data-language-local-name="лацінская" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Plok%C5%A1tuma" title="Plokštuma – літоўская" lang="lt" hreflang="lt" data-title="Plokštuma" data-language-autonym="Lietuvių" data-language-local-name="літоўская" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Plakne" title="Plakne – латышская" lang="lv" hreflang="lv" data-title="Plakne" data-language-autonym="Latviešu" data-language-local-name="латышская" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Lemaka_(je%C3%B4metria)" title="Lemaka (jeômetria) – малагасійская" lang="mg" hreflang="mg" data-title="Lemaka (jeômetria)" data-language-autonym="Malagasy" data-language-local-name="малагасійская" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A0%D0%B0%D0%BC%D0%BD%D0%B8%D0%BD%D0%B0_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Рамнина (математика) – македонская" lang="mk" hreflang="mk" data-title="Рамнина (математика)" data-language-autonym="Македонски" data-language-local-name="македонская" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Satah" title="Satah – малайская" lang="ms" hreflang="ms" data-title="Satah" data-language-autonym="Bahasa Melayu" data-language-local-name="малайская" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Flach_(Mathematik)" title="Flach (Mathematik) – ніжненямецкая" lang="nds" hreflang="nds" data-title="Flach (Mathematik)" data-language-autonym="Plattdüütsch" data-language-local-name="ніжненямецкая" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Vlak_(meetkunde)" title="Vlak (meetkunde) – нідэрландская" lang="nl" hreflang="nl" data-title="Vlak (meetkunde)" data-language-autonym="Nederlands" data-language-local-name="нідэрландская" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Plan_i_matematikk" title="Plan i matematikk – нарвежская (нюношк)" lang="nn" hreflang="nn" data-title="Plan i matematikk" data-language-autonym="Norsk nynorsk" data-language-local-name="нарвежская (нюношк)" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Plan_(matematikk)" title="Plan (matematikk) – нарвежская (букмол)" lang="nb" hreflang="nb" data-title="Plan (matematikk)" data-language-autonym="Norsk bokmål" data-language-local-name="нарвежская (букмол)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/P%C5%82aszczyzna" title="Płaszczyzna – польская" lang="pl" hreflang="pl" data-title="Płaszczyzna" data-language-autonym="Polski" data-language-local-name="польская" 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/Plano_(geometria)" title="Plano (geometria) – партугальская" lang="pt" hreflang="pt" data-title="Plano (geometria)" data-language-autonym="Português" data-language-local-name="партугальская" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/P%27allta" title="P'allta – кечуа" lang="qu" hreflang="qu" data-title="P'allta" data-language-autonym="Runa Simi" data-language-local-name="кечуа" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Plan_(geometrie)" title="Plan (geometrie) – румынская" lang="ro" hreflang="ro" data-title="Plan (geometrie)" data-language-autonym="Română" data-language-local-name="румынская" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%BE%D1%81%D1%82%D1%8C" title="Плоскость – руская" lang="ru" hreflang="ru" data-title="Плоскость" data-language-autonym="Русский" data-language-local-name="руская" 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%A5%D0%B0%D0%BF%D1%82%D0%B0%D0%BB" title="Хаптал – якуцкая" lang="sah" hreflang="sah" data-title="Хаптал" data-language-autonym="Саха тыла" data-language-local-name="якуцкая" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Ravan" title="Ravan – сербскахарвацкая" lang="sh" hreflang="sh" data-title="Ravan" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="сербскахарвацкая" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Plane_(mathematics)" title="Plane (mathematics) – Simple English" lang="en-simple" hreflang="en-simple" data-title="Plane (mathematics)" 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/Rovina_(geometria)" title="Rovina (geometria) – славацкая" lang="sk" hreflang="sk" data-title="Rovina (geometria)" data-language-autonym="Slovenčina" data-language-local-name="славацкая" 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/Ravnina" title="Ravnina – славенская" lang="sl" hreflang="sl" data-title="Ravnina" data-language-autonym="Slovenščina" data-language-local-name="славенская" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Mutsendo" title="Mutsendo – шона" lang="sn" hreflang="sn" data-title="Mutsendo" data-language-autonym="ChiShona" data-language-local-name="шона" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Rrafshi_Euklidian" title="Rrafshi Euklidian – албанская" lang="sq" hreflang="sq" data-title="Rrafshi Euklidian" data-language-autonym="Shqip" data-language-local-name="албанская" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B2%D0%B0%D0%BD" title="Раван – сербская" lang="sr" hreflang="sr" data-title="Раван" data-language-autonym="Српски / srpski" data-language-local-name="сербская" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Plan_(geometri)" title="Plan (geometri) – шведская" lang="sv" hreflang="sv" data-title="Plan (geometri)" data-language-autonym="Svenska" data-language-local-name="шведская" 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%A4%E0%AE%B3%E0%AE%AE%E0%AF%8D_(%E0%AE%B5%E0%AE%9F%E0%AE%BF%E0%AE%B5%E0%AE%B5%E0%AE%BF%E0%AE%AF%E0%AE%B2%E0%AF%8D)" title="தளம் (வடிவவியல்) – тамільская" lang="ta" hreflang="ta" data-title="தளம் (வடிவவியல்)" data-language-autonym="தமிழ்" data-language-local-name="тамільская" 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%A3%E0%B8%B0%E0%B8%99%E0%B8%B2%E0%B8%9A" title="ระนาบ – тайская" lang="th" hreflang="th" data-title="ระนาบ" data-language-autonym="ไทย" data-language-local-name="тайская" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Plano_(heometriya)" title="Plano (heometriya) – Tagalog" lang="tl" hreflang="tl" data-title="Plano (heometriya)" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/D%C3%BCzlem" title="Düzlem – турэцкая" lang="tr" hreflang="tr" data-title="Düzlem" data-language-autonym="Türkçe" data-language-local-name="турэцкая" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%AF%D1%81%D1%81%D1%8B%D0%BB%D1%8B%D0%BA_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Яссылык (математика) – татарская" lang="tt" hreflang="tt" data-title="Яссылык (математика)" data-language-autonym="Татарча / tatarça" data-language-local-name="татарская" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9F%D0%BB%D0%BE%D1%89%D0%B8%D0%BD%D0%B0" title="Площина – украінская" lang="uk" hreflang="uk" data-title="Площина" data-language-autonym="Українська" data-language-local-name="украінская" 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/%D9%85%D8%B3%D8%AA%D9%88%DB%8C_(%DB%81%D9%86%D8%AF%D8%B3%DB%81)" title="مستوی (ہندسہ) – урду" lang="ur" hreflang="ur" data-title="مستوی (ہندسہ)" data-language-autonym="اردو" data-language-local-name="урду" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Tekislik" title="Tekislik – узбекская" lang="uz" hreflang="uz" data-title="Tekislik" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="узбекская" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/M%E1%BA%B7t_ph%E1%BA%B3ng_(to%C3%A1n_h%E1%BB%8Dc)" title="Mặt phẳng (toán học) – в’етнамская" lang="vi" hreflang="vi" data-title="Mặt phẳng (toán học)" data-language-autonym="Tiếng Việt" data-language-local-name="в’етнамская" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Plano_(heyometriya)" title="Plano (heyometriya) – варай" lang="war" hreflang="war" data-title="Plano (heyometriya)" data-language-autonym="Winaray" data-language-local-name="варай" 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/%E5%B9%B3%E9%9D%A2" title="平面 – ву" lang="wuu" hreflang="wuu" data-title="平面" 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-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A4%D7%9C%D7%90%D7%9A" title="פלאך – ідыш" lang="yi" hreflang="yi" data-title="פלאך" data-language-autonym="ייִדיש" data-language-local-name="ідыш" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%B9%B3%E9%9D%A2_(%E6%95%B0%E5%AD%A6)" title="平面 (数学) – кітайская" lang="zh" hreflang="zh" data-title="平面 (数学)" data-language-autonym="中文" data-language-local-name="кітайская" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/P%C3%AE%E2%81%BF-b%C4%ABn" title="Pîⁿ-bīn – Minnan" lang="nan" hreflang="nan" data-title="Pîⁿ-bīn" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%9D%A2_(%E5%B9%BE%E4%BD%95)" title="面 (幾何) – кантонскі дыялект кітайскай" lang="yue" hreflang="yue" data-title="面 (幾何)" data-language-autonym="粵語" data-language-local-name="кантонскі дыялект кітайскай" class="interlanguage-link-target"><span>粵語</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/Q17285#sitelinks-wikipedia" title="Правіць міжмоўныя спасылкі" class="wbc-editpage">Правіць спасылкі</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="Прасторы назваў"> <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%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%B0%D1%81%D1%86%D1%8C" title="Паказаць уласна змест старонкі [c]" accesskey="c"><span>Старонка</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%D0%A0%D0%B0%D0%B7%D0%BC%D0%BE%D0%B2%D1%8B:%D0%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%B0%D1%81%D1%86%D1%8C&action=edit&redlink=1" rel="discussion" class="new" title="Размовы пра змест гэтай старонкі (няма такой старонкі) [t]" accesskey="t"><span>Размовы</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="Змяніць моўны варыянт" > <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">беларуская</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="Віды"> <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%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%B0%D1%81%D1%86%D1%8C"><span>Чытаць</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%D0%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%B0%D1%81%D1%86%D1%8C&veaction=edit" title="Правіць старонку [v]" accesskey="v"><span>Правіць</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%D0%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%B0%D1%81%D1%86%D1%8C&action=edit" title="Правіць зыходны код гэтай старонкі [e]" accesskey="e"><span>Правіць зыходнік</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%D0%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%B0%D1%81%D1%86%D1%8C&action=history" title="Ранейшыя версіі гэтай старонкі. [h]" accesskey="h"><span>Паказаць гісторыю</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <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="Інструменты" > <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">Інструменты</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">Інструменты</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">перанесці да бакавой панэлі</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">схаваць</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Больш магчымасцей" > <div class="vector-menu-heading"> Дзеянні </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%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%B0%D1%81%D1%86%D1%8C"><span>Чытаць</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%B0%D1%81%D1%86%D1%8C&veaction=edit" title="Правіць старонку [v]" accesskey="v"><span>Правіць</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%B0%D1%81%D1%86%D1%8C&action=edit" title="Правіць зыходны код гэтай старонкі [e]" accesskey="e"><span>Правіць зыходнік</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%B0%D1%81%D1%86%D1%8C&action=history"><span>Паказаць гісторыю</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Агульныя </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:WhatLinksHere/%D0%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%B0%D1%81%D1%86%D1%8C" title="Спіс вікістаронак, якія спасылаюцца сюды [j]" accesskey="j"><span>Сюды спасылаюцца</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:RecentChangesLinked/%D0%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%B0%D1%81%D1%86%D1%8C" rel="nofollow" title="Нядаўнія змены ў старонках, на якія спасылаецца гэтая старонка [k]" accesskey="k"><span>Звязаныя праўкі</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=%D0%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%B0%D1%81%D1%86%D1%8C&oldid=4651345" title="Нязменная спасылка на гэтую версію гэтай старонкі"><span>Нязменная спасылка</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=%D0%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%B0%D1%81%D1%86%D1%8C&action=info" title="Больш звестак пра гэту старонку"><span>Звесткі пра старонку</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:CiteThisPage&page=%D0%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%B0%D1%81%D1%86%D1%8C&id=4651345&wpFormIdentifier=titleform" title="Інфармацыя пра тое, як цытаваць гэтую старонку"><span>Цытаваць гэту старонку</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:UrlShortener&url=https%3A%2F%2Fbe.wikipedia.org%2Fwiki%2F%25D0%259F%25D0%25BB%25D0%25BE%25D1%2581%25D0%25BA%25D0%25B0%25D1%2581%25D1%2586%25D1%258C"><span>Атрымаць скарочаны URL-адрас</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:QrCode&url=https%3A%2F%2Fbe.wikipedia.org%2Fwiki%2F%25D0%259F%25D0%25BB%25D0%25BE%25D1%2581%25D0%25BA%25D0%25B0%25D1%2581%25D1%2586%25D1%258C"><span>Спампаваць 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"> Друк/экспарт </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%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:Book&bookcmd=book_creator&referer=%D0%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%B0%D1%81%D1%86%D1%8C"><span>Стварыць кнігу</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:DownloadAsPdf&page=%D0%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%B0%D1%81%D1%86%D1%8C&action=show-download-screen"><span>Спампаваць як PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=%D0%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%B0%D1%81%D1%86%D1%8C&printable=yes" title="Друкавальная версія гэтай старонкі [p]" accesskey="p"><span>Для друку</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"> У іншых праектах </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/Category:Euclidean_planes" hreflang="en"><span>Вікісховішча</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/Q17285" title="Спасылка на звязаны элемент рэпазітара даных [g]" accesskey="g"><span>Элемент Вікіданых</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Выгляд"> <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">Выгляд</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">перанесці да бакавой панэлі</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">схаваць</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">З Вікіпедыі, свабоднай энцыклапедыі</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="be" dir="ltr"><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Intersecting_planes.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Intersecting_planes.svg/220px-Intersecting_planes.svg.png" decoding="async" width="220" height="198" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Intersecting_planes.svg/330px-Intersecting_planes.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Intersecting_planes.svg/440px-Intersecting_planes.svg.png 2x" data-file-width="360" data-file-height="324" /></a><figcaption>Дзве плоскасці, якія перасякаюцца</figcaption></figure> <p><b>Пло́скасць</b> — адно з асноўных паняццяў <a href="/wiki/%D0%93%D0%B5%D0%B0%D0%BC%D0%B5%D1%82%D1%80%D1%8B%D1%8F" title="Геаметрыя">геаметрыі</a>. Плоскасць — гэта бясконцая <a href="/wiki/%D0%9F%D0%B0%D0%B2%D0%B5%D1%80%D1%85%D0%BD%D1%8F" title="Паверхня">паверхня</a>, да якой належаць усе <a href="/wiki/%D0%9F%D1%80%D0%B0%D0%BC%D0%B0%D1%8F" title="Прамая">прамыя</a>, што праходзяць праз якія-небудзь два <a href="/wiki/%D0%9F%D1%83%D0%BD%D0%BA%D1%82" title="Пункт">пункты</a> плоскасці. У <a href="/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра">алгебры</a> плоскасць вызначаецца як двухмерная <a href="/w/index.php?title=%D0%90%D1%84%D1%96%D0%BD%D0%BD%D0%B0%D1%8F_%D0%BF%D1%80%D0%B0%D1%81%D1%82%D0%BE%D1%80%D0%B0&action=edit&redlink=1" class="new" title="Афінная прастора (няма такой старонкі)">афінная прастора</a>. </p><p>У <a href="/wiki/%D0%9F%D0%BB%D0%B0%D0%BD%D1%96%D0%BC%D0%B5%D1%82%D1%80%D1%8B%D1%8F" title="Планіметрыя">планіметрыі</a> плоскасць разглядаецца як <a href="/wiki/%D0%A3%D0%BD%D1%96%D0%B2%D0%B5%D1%80%D1%81%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0%D0%B5_%D0%BC%D0%BD%D0%BE%D1%81%D1%82%D0%B2%D0%B0" title="Універсальнае мноства">універсум</a>, да якога належаць усе <a href="/wiki/%D0%93%D0%B5%D0%B0%D0%BC%D0%B5%D1%82%D1%80%D1%8B%D1%87%D0%BD%D0%B0%D1%8F_%D1%84%D1%96%D0%B3%D1%83%D1%80%D0%B0" title="Геаметрычная фігура">геаметрычныя фігуры</a>. <a href="/wiki/%D0%A1%D1%82%D1%8D%D1%80%D1%8D%D0%B0%D0%BC%D0%B5%D1%82%D1%80%D1%8B%D1%8F" title="Стэрэаметрыя">Стэрэаметрыя</a> разглядае <a href="/wiki/%D0%91%D0%B5%D1%81%D0%BA%D0%B0%D0%BD%D0%B5%D1%87%D0%BD%D0%B0%D0%B5_%D0%BC%D0%BD%D0%BE%D1%81%D1%82%D0%B2%D0%B0" title="Бесканечнае мноства">бесканечнае мноства</a> плоскасцей, размешчаных у <a href="/wiki/%D0%9F%D1%80%D0%B0%D1%81%D1%82%D0%BE%D1%80%D0%B0" title="Прастора">прасторы</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Ураўненні_плоскасці"><span id=".D0.A3.D1.80.D0.B0.D1.9E.D0.BD.D0.B5.D0.BD.D0.BD.D1.96_.D0.BF.D0.BB.D0.BE.D1.81.D0.BA.D0.B0.D1.81.D1.86.D1.96"></span>Ураўненні плоскасці</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%B0%D1%81%D1%86%D1%8C&veaction=edit&section=1" title="Правіць раздзел: Ураўненні плоскасці" class="mw-editsection-visualeditor"><span>правіць</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%B0%D1%81%D1%86%D1%8C&action=edit&section=1" title="Правіць зыходнік раздзела: Ураўненні плоскасці"><span>правіць зыходнік</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Плоскасць</b> — алгебраічная паверхня першага парадку: у дэкартавай сістэме каардынат плоскасць можна задаць <a href="/wiki/%D0%A3%D1%80%D0%B0%D1%9E%D0%BD%D0%B5%D0%BD%D0%BD%D0%B5" title="Ураўненне">ураўненнем</a> першай ступені. </p> <ul><li><i>Агульнае ураўненне (поўнае) плоскасці</i></li></ul> <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 Ax+By+Cz+D=0,\qquad (1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mi>x</mi> <mo>+</mo> <mi>B</mi> <mi>y</mi> <mo>+</mo> <mi>C</mi> <mi>z</mi> <mo>+</mo> <mi>D</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mspace width="2em" /> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Ax+By+Cz+D=0,\qquad (1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e18fe1d8178c4384f8bc9e4f9ec7ee5ea7ca7bb9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:32.204ex; height:2.843ex;" alt="{\displaystyle Ax+By+Cz+D=0,\qquad (1)}"></span></dd></dl> <dl><dd>дзе <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A,B,C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>,</mo> <mi>B</mi> <mo>,</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A,B,C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ce2acf22b93dfbd22373336bd9c22dbd98a49d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.341ex; height:2.509ex;" alt="{\displaystyle A,B,C}"></span> і <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 D}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f34a0c600395e5d4345287e21fb26efd386990e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}"></span> — канстанты, прычым хоць адзін з лікаў <span style="white-space: nowrap; font-family: times, serif, palatino linotype, new athena unicode, athena, gentium, code2000; font-size: 120%;"><i>A</i></span>, <span style="white-space: nowrap; font-family: times, serif, palatino linotype, new athena unicode, athena, gentium, code2000; font-size: 120%;"><i>B</i></span> і <span style="white-space: nowrap; font-family: times, serif, palatino linotype, new athena unicode, athena, gentium, code2000; font-size: 120%;"><i>C</i></span> не роўны нулю (што раўназначна няроўнасці <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |A|+|B|+|C|\neq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>≠</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |A|+|B|+|C|\neq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/49f2b3bc924200b5d5f63aa62abba918444c3b8f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.096ex; height:2.843ex;" alt="{\displaystyle |A|+|B|+|C|\neq 0}"></span>); у <a href="/wiki/%D0%92%D0%B5%D0%BA%D1%82%D0%B0%D1%80_(%D0%BC%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D0%BA%D0%B0)" title="Вектар (матэматыка)">вектарнай</a> форме:</dd></dl> <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 (\mathbf {r} ,\mathbf {N} )+D=0,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">N</mi> </mrow> <mo stretchy="false">)</mo> <mo>+</mo> <mi>D</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (\mathbf {r} ,\mathbf {N} )+D=0,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1214ab92bc5b9ec584bd7bc5d3c707805cacd90f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.709ex; height:2.843ex;" alt="{\displaystyle (\mathbf {r} ,\mathbf {N} )+D=0,}"></span></dd></dl> <dl><dd>дзе <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 \mathbf {r} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {r} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eca0f46511c4c986c48b254073732c0bd98ae0c1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.102ex; height:1.676ex;" alt="{\displaystyle \mathbf {r} }"></span> — радыус-вектар пункта <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 M(x,y,z)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M(x,y,z)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/490cecb2172d0679a32adb9e538bcbc1959a2d0f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.893ex; height:2.843ex;" alt="{\displaystyle M(x,y,z)}"></span>, вектар <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 \mathbf {N} =(A,B,C)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">N</mi> </mrow> <mo>=</mo> <mo stretchy="false">(</mo> <mi>A</mi> <mo>,</mo> <mi>B</mi> <mo>,</mo> <mi>C</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {N} =(A,B,C)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45d6ea6579821c950219958bce4368a75c6139c9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.341ex; height:2.843ex;" alt="{\displaystyle \mathbf {N} =(A,B,C)}"></span> перпендыкулярны да плоскасці (нармальны вектар). <i>Накіравальныя <a href="/wiki/%D0%9A%D0%BE%D1%81%D1%96%D0%BD%D1%83%D1%81" class="mw-redirect" title="Косінус">косінусы</a></i> вектары <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 \mathbf {N} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">N</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {N} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c2f63b6cd6d63ee9b7be0b7e4d14099d7153bd43" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.091ex; height:2.176ex;" alt="{\displaystyle \mathbf {N} }"></span>:</dd> <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 \cos \alpha ={\frac {A}{\sqrt {A^{2}+B^{2}+C^{2}}}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>A</mi> <msqrt> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos \alpha ={\frac {A}{\sqrt {A^{2}+B^{2}+C^{2}}}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8d00867efb0d804ff822751fe796818880b77c58" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:26.039ex; height:6.676ex;" alt="{\displaystyle \cos \alpha ={\frac {A}{\sqrt {A^{2}+B^{2}+C^{2}}}},}"></span></dd> <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 \cos \beta ={\frac {B}{\sqrt {A^{2}+B^{2}+C^{2}}}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡</mo> <mi>β</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>B</mi> <msqrt> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos \beta ={\frac {B}{\sqrt {A^{2}+B^{2}+C^{2}}}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fdf81bca109801c8aac8b19b2da4c63583c9663f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:25.884ex; height:6.509ex;" alt="{\displaystyle \cos \beta ={\frac {B}{\sqrt {A^{2}+B^{2}+C^{2}}}},}"></span></dd> <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 \cos \gamma ={\frac {C}{\sqrt {A^{2}+B^{2}+C^{2}}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡</mo> <mi>γ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>C</mi> <msqrt> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos \gamma ={\frac {C}{\sqrt {A^{2}+B^{2}+C^{2}}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5939a17c840da3a4e04028b81fa905b0c24625a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:25.814ex; height:6.676ex;" alt="{\displaystyle \cos \gamma ={\frac {C}{\sqrt {A^{2}+B^{2}+C^{2}}}}.}"></span></dd></dl> <dl><dd>Калі адзін з каэфіцыентаў ва ўраўненні плоскасці — нуль, ураўненне называецца <i>няпоўным</i>. Пры <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 D=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d375dfda80ee8df1d1d7aa8b962114044e464305" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.185ex; height:2.176ex;" alt="{\displaystyle D=0}"></span> плоскасць праходзіць праз пачатак каардынат, пры <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75c34024483e6fb7c89e45aff3882ebf11d95a00" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.004ex; height:2.176ex;" alt="{\displaystyle A=0}"></span> (або <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 B=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af1d79a64f775646f76d79a452ca8e1082fb1f17" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.025ex; height:2.176ex;" alt="{\displaystyle B=0}"></span>, <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 C=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f750a7094a396d89a81974cdf35783db2bb287b0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.027ex; height:2.176ex;" alt="{\displaystyle C=0}"></span>) плоскасць паралельная восі <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 Ox}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Ox}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d69bd718df9e6a0005953a22f0af2b9794ee70f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.103ex; height:2.176ex;" alt="{\displaystyle Ox}"></span> (адпаведна <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 Oy}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Oy}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b0971aed4330d41f75a2f97f4b11dd883958a3c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.929ex; height:2.509ex;" alt="{\displaystyle Oy}"></span> або <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 Oz}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Oz}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ade7218877bd912fd376e9b0a1664470d0c7c24e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.861ex; height:2.176ex;" alt="{\displaystyle Oz}"></span>). Пры <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A=B=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mi>B</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=B=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86f86f736b242670afc5462dc46af0d72b58e99f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.866ex; height:2.176ex;" alt="{\displaystyle A=B=0}"></span> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A=C=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mi>C</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=C=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00b2a06976382ad46a09a8e8da3485ff0d089fd7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.869ex; height:2.176ex;" alt="{\displaystyle A=C=0}"></span>, або <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 B=C=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mo>=</mo> <mi>C</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B=C=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d966abd402b0d20318abe297b7c201a657e99034" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.89ex; height:2.176ex;" alt="{\displaystyle B=C=0}"></span>) плоскасць паралельная плоскасці <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 Oxy}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mi>x</mi> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Oxy}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/beb767e241f4141a4a4b39e0c81fc02f06537329" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.258ex; height:2.509ex;" alt="{\displaystyle Oxy}"></span> (адпаведна <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 Oxz}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mi>x</mi> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Oxz}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/891818c2696562c9a59507f3ed2bcbebd737123c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.191ex; height:2.176ex;" alt="{\displaystyle Oxz}"></span> або <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 Oyz}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mi>y</mi> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Oyz}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/99b1dcb6901fe4e733f928a2fb5241f3a935a0d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.017ex; height:2.509ex;" alt="{\displaystyle Oyz}"></span>).</dd></dl> <ul><li><i>Ураўненне плоскасці ў <a href="/wiki/%D0%90%D0%B4%D1%80%D1%8D%D0%B7%D0%B0%D0%BA" title="Адрэзак">адрэзках</a>:</i></li></ul> <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 {\frac {x}{a}}+{\frac {y}{b}}+{\frac {z}{c}}=1,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>x</mi> <mi>a</mi> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>y</mi> <mi>b</mi> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>z</mi> <mi>c</mi> </mfrac> </mrow> <mo>=</mo> <mn>1</mn> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {x}{a}}+{\frac {y}{b}}+{\frac {z}{c}}=1,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/966c73950eb3a0c89260caeaa6b8ec567049881c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:16.67ex; height:5.009ex;" alt="{\displaystyle {\frac {x}{a}}+{\frac {y}{b}}+{\frac {z}{c}}=1,}"></span></dd></dl> <dl><dd>дзе <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a=-D/A,b=-D/B,c=-D/C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>=</mo> <mo>−</mo> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>A</mi> <mo>,</mo> <mi>b</mi> <mo>=</mo> <mo>−</mo> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>B</mi> <mo>,</mo> <mi>c</mi> <mo>=</mo> <mo>−</mo> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a=-D/A,b=-D/B,c=-D/C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3230d199e8ef12e79e94d73940c9cd22d4d156d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:34.555ex; height:2.843ex;" alt="{\displaystyle a=-D/A,b=-D/B,c=-D/C}"></span> — адрэзкі, якія плоскасць адсякае на восях <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 Ox,Oy}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mi>x</mi> <mo>,</mo> <mi>O</mi> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Ox,Oy}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/29fa3ac2d20cedf1b9a529fba40f43f8e586057c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.066ex; height:2.509ex;" alt="{\displaystyle Ox,Oy}"></span> і <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 Oz}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Oz}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ade7218877bd912fd376e9b0a1664470d0c7c24e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.861ex; height:2.176ex;" alt="{\displaystyle Oz}"></span>.</dd></dl> <ul><li><i>Ураўненне плоскасці, якая праходзіць праз пункт</i> <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 M(x_{0},y_{0},z_{0})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <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 M(x_{0},y_{0},z_{0})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c592a83d9a7f916b48e0e0701bea025142eb2219" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.032ex; height:2.843ex;" alt="{\displaystyle M(x_{0},y_{0},z_{0})}"></span> <i>перпендыкулярна вектару нармалі</i> <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 \mathbf {N} (A,B,C)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">N</mi> </mrow> <mo stretchy="false">(</mo> <mi>A</mi> <mo>,</mo> <mi>B</mi> <mo>,</mo> <mi>C</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {N} (A,B,C)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/adc4bbe54c92576352e2381b777f05c42a069e5c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.242ex; height:2.843ex;" alt="{\displaystyle \mathbf {N} (A,B,C)}"></span>:</li></ul> <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 A(x-x_{0})+B(y-y_{0})+C(z-z_{0})=0;}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>−</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>+</mo> <mi>B</mi> <mo stretchy="false">(</mo> <mi>y</mi> <mo>−</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>+</mo> <mi>C</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo>−</mo> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> <mo>;</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A(x-x_{0})+B(y-y_{0})+C(z-z_{0})=0;}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b7850eb07855ee9bf7f5c8e4e4df6c3e3e95473" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:40.097ex; height:2.843ex;" alt="{\displaystyle A(x-x_{0})+B(y-y_{0})+C(z-z_{0})=0;}"></span></dd></dl> <dl><dd>у вектарнай форме:</dd></dl> <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 ((\mathbf {r} -\mathbf {r_{0}} ),\mathbf {N} )=0.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="bold">r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> <mo stretchy="false">)</mo> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">N</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ((\mathbf {r} -\mathbf {r_{0}} ),\mathbf {N} )=0.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b776e5bb6e914488d806647193cd22ff2aca7d32" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.874ex; height:2.843ex;" alt="{\displaystyle ((\mathbf {r} -\mathbf {r_{0}} ),\mathbf {N} )=0.}"></span></dd></dl> <ul><li><i>Ураўненне плоскасці, якая праходзіць праз тры зададзеныя пункты</i> <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 M(x_{i},y_{i},z_{i})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M(x_{i},y_{i},z_{i})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5548d8501d9746ff6c0fec33f40daffa2364e6f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.268ex; height:2.843ex;" alt="{\displaystyle M(x_{i},y_{i},z_{i})}"></span>, <i>якія не ляжаць на адной прамой</i>:</li></ul> <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 ((\mathbf {r} -\mathbf {r_{1}} ),(\mathbf {r_{2}} -\mathbf {r_{1}} ),(\mathbf {r_{3}} -\mathbf {r_{1}} ))=0,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="bold">r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">1</mn> </mrow> </msub> </mrow> <mo stretchy="false">)</mo> <mo>,</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="bold">r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">2</mn> </mrow> </msub> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="bold">r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">1</mn> </mrow> </msub> </mrow> <mo stretchy="false">)</mo> <mo>,</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="bold">r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">3</mn> </mrow> </msub> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="bold">r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">1</mn> </mrow> </msub> </mrow> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ((\mathbf {r} -\mathbf {r_{1}} ),(\mathbf {r_{2}} -\mathbf {r_{1}} ),(\mathbf {r_{3}} -\mathbf {r_{1}} ))=0,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/14f237ce4a408c3e0eefb9be45f38923d37dd676" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:35.233ex; height:2.843ex;" alt="{\displaystyle ((\mathbf {r} -\mathbf {r_{1}} ),(\mathbf {r_{2}} -\mathbf {r_{1}} ),(\mathbf {r_{3}} -\mathbf {r_{1}} ))=0,}"></span></dd> <dd>дзе <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 (\mathbf {x} ,\mathbf {y} ,\mathbf {z} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">y</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">z</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (\mathbf {x} ,\mathbf {y} ,\mathbf {z} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/69dfcca70e10b6c1789bd21e1ff5fa46abb57646" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.887ex; height:2.843ex;" alt="{\displaystyle (\mathbf {x} ,\mathbf {y} ,\mathbf {z} )}"></span> абазначае <span data-interwiki-lang="ru" data-interwiki-article="Смешанное произведение"><a href="/w/index.php?title=%D0%97%D0%BC%D0%B5%D1%88%D0%B0%D0%BD%D1%8B_%D0%B7%D0%B4%D0%B0%D0%B1%D1%8B%D1%82%D0%B0%D0%BA&action=edit&redlink=1" class="new" title="Змешаны здабытак (няма такой старонкі)"><span class="iw-nonexists">змешаны здабытак</span></a></span><span class="noprint" style="font-style:normal; font-weight:normal;"><sup><a href="https://ru.wikipedia.org/wiki/%D0%A1%D0%BC%D0%B5%D1%88%D0%B0%D0%BD%D0%BD%D0%BE%D0%B5_%D0%BF%D1%80%D0%BE%D0%B8%D0%B7%D0%B2%D0%B5%D0%B4%D0%B5%D0%BD%D0%B8%D0%B5" class="extiw" title="ru:Смешанное произведение"><span title="Смешанное произведение — версія артыкула «Змешаны здабытак» на рускай мове">[ru]</span></a></sup></span> вектараў <span style="white-space: nowrap; font-family: times, serif, palatino linotype, new athena unicode, athena, gentium, code2000; font-size: 120%;"><b>x</b></span>, <span style="white-space: nowrap; font-family: times, serif, palatino linotype, new athena unicode, athena, gentium, code2000; font-size: 120%;"><b>y</b></span> і <span style="white-space: nowrap; font-family: times, serif, palatino linotype, new athena unicode, athena, gentium, code2000; font-size: 120%;"><b>z</b></span>, па-іншаму</dd></dl> <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 \left|{\begin{matrix}x-x_{1}&y-y_{1}&z-z_{1}\\x_{2}-x_{1}&y_{2}-y_{1}&z_{2}-z_{1}\\x_{3}-x_{1}&y_{3}-y_{1}&z_{3}-z_{1}\\\end{matrix}}\right|=0.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>|</mo> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>x</mi> <mo>−</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <mi>y</mi> <mo>−</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <mi>z</mi> <mo>−</mo> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mtd> </mtr> </mtable> </mrow> <mo>|</mo> </mrow> <mo>=</mo> <mn>0.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left|{\begin{matrix}x-x_{1}&y-y_{1}&z-z_{1}\\x_{2}-x_{1}&y_{2}-y_{1}&z_{2}-z_{1}\\x_{3}-x_{1}&y_{3}-y_{1}&z_{3}-z_{1}\\\end{matrix}}\right|=0.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35b85a670312b20dbec839dc2e5f1f72cd68e3db" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.171ex; width:33.545ex; height:9.509ex;" alt="{\displaystyle \left|{\begin{matrix}x-x_{1}&y-y_{1}&z-z_{1}\\x_{2}-x_{1}&y_{2}-y_{1}&z_{2}-z_{1}\\x_{3}-x_{1}&y_{3}-y_{1}&z_{3}-z_{1}\\\end{matrix}}\right|=0.}"></span></dd></dl> <ul><li><i>Нармальнае (нармаванае) ураўненне плоскасці</i></li></ul> <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\cos \alpha +y\cos \beta +z\cos \gamma -p=0,\qquad (2)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> <mo>+</mo> <mi>y</mi> <mi>cos</mi> <mo>⁡</mo> <mi>β</mi> <mo>+</mo> <mi>z</mi> <mi>cos</mi> <mo>⁡</mo> <mi>γ</mi> <mo>−</mo> <mi>p</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mspace width="2em" /> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\cos \alpha +y\cos \beta +z\cos \gamma -p=0,\qquad (2)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2638359a55a9f28038624e0d4472d6ba0b09104d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:41.914ex; height:2.843ex;" alt="{\displaystyle x\cos \alpha +y\cos \beta +z\cos \gamma -p=0,\qquad (2)}"></span></dd></dl> <dl><dd>у вектарнай форме:</dd></dl> <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 (\mathbf {r} ,\mathbf {N^{0}} )\mathbf {-p} =0,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi mathvariant="bold">N</mi> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msup> </mrow> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold">−</mo> <mi mathvariant="bold">p</mi> </mrow> <mo>=</mo> <mn>0</mn> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (\mathbf {r} ,\mathbf {N^{0}} )\mathbf {-p} =0,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a4cbc02a226936da0f360a1b837d7feaa891fd85" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.685ex; height:3.176ex;" alt="{\displaystyle (\mathbf {r} ,\mathbf {N^{0}} )\mathbf {-p} =0,}"></span></dd></dl> <dl><dd>дзе <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 \mathbf {N^{0}} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi mathvariant="bold">N</mi> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msup> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {N^{0}} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c8888f52c5c18fe60aef25da606ef57664999654" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.269ex; height:2.676ex;" alt="{\displaystyle \mathbf {N^{0}} }"></span> — адзінкавы вектар, <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 p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></span> — адлегласць плоскасці ад пачатку каардынат. Ураўненне (2) можна атрымаць з ураўнення (1) дамнажэннем на нармавальны множнік</dd></dl> <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 \mu =\pm {\frac {1}{\sqrt {A^{2}+B^{2}+C^{2}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ</mi> <mo>=</mo> <mo>±</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu =\pm {\frac {1}{\sqrt {A^{2}+B^{2}+C^{2}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2cfce7c8bfde8623d9c41c94050aeb69ac9a1a0f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:23.617ex; height:6.509ex;" alt="{\displaystyle \mu =\pm {\frac {1}{\sqrt {A^{2}+B^{2}+C^{2}}}}}"></span></dd></dl> <dl><dd>(знакі <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 \mu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fd47b2a39f7a7856952afec1f1db72c67af6161" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.402ex; height:2.176ex;" alt="{\displaystyle \mu }"></span> і <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 D}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f34a0c600395e5d4345287e21fb26efd386990e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}"></span> супрацьлеглыя).</dd></dl> <div class="mw-heading mw-heading2"><h2 id="Спасылкі"><span id=".D0.A1.D0.BF.D0.B0.D1.81.D1.8B.D0.BB.D0.BA.D1.96"></span>Спасылкі</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%B0%D1%81%D1%86%D1%8C&veaction=edit&section=2" title="Правіць раздзел: Спасылкі" class="mw-editsection-visualeditor"><span>правіць</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%B0%D1%81%D1%86%D1%8C&action=edit&section=2" title="Правіць зыходнік раздзела: Спасылкі"><span>правіць зыходнік</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span typeof="mw:File"><a href="/wiki/%D0%92%D1%96%D0%BA%D1%96%D1%81%D1%85%D0%BE%D0%B2%D1%96%D1%88%D1%87%D0%B0" title="Лагатып Вікісховішча"><img alt="Лагатып Вікісховішча" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> На <a href="/wiki/%D0%92%D1%96%D0%BA%D1%96%D1%81%D1%85%D0%BE%D0%B2%D1%96%D1%88%D1%87%D0%B0" title="Вікісховішча">Вікісховішчы</a> ёсць медыяфайлы па тэме <b><a href="https://commons.wikimedia.org/wiki/Category:Linear_planes" class="extiw" title="commons:Category:Linear planes">Плоскасць</a></b></li> <li><i><a rel="nofollow" class="external text" href="http://slovari.yandex.ru/~книги/БСЭ/Плоскость/">Плоскость <span class="ref-info" style="cursor:help;" title="рускай мовай">(руск.)</span></a></i> — артыкул з <a href="/wiki/%D0%92%D1%8F%D0%BB%D1%96%D0%BA%D0%B0%D1%8F_%D1%81%D0%B0%D0%B2%D0%B5%D1%86%D0%BA%D0%B0%D1%8F_%D1%8D%D0%BD%D1%86%D1%8B%D0%BA%D0%BB%D0%B0%D0%BF%D0%B5%D0%B4%D1%8B%D1%8F" title="Вялікая савецкая энцыклапедыя">Вялікай савецкай энцыклапедыі</a></li></ul></div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Узята з "<a dir="ltr" href="https://be.wikipedia.org/w/index.php?title=Плоскасць&oldid=4651345">https://be.wikipedia.org/w/index.php?title=Плоскасць&oldid=4651345</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:Categories" title="Адмысловае:Categories">Катэгорыі</a>: <ul><li><a href="/wiki/%D0%9A%D0%B0%D1%82%D1%8D%D0%B3%D0%BE%D1%80%D1%8B%D1%8F:%D0%AD%D1%9E%D0%BA%D0%BB%D1%96%D0%B4%D0%B0%D0%B2%D0%B0_%D0%B3%D0%B5%D0%B0%D0%BC%D0%B5%D1%82%D1%80%D1%8B%D1%8F" title="Катэгорыя:Эўклідава геаметрыя">Эўклідава геаметрыя</a></li><li><a href="/wiki/%D0%9A%D0%B0%D1%82%D1%8D%D0%B3%D0%BE%D1%80%D1%8B%D1%8F:%D0%90%D0%BA%D1%81%D1%96%D1%8F%D0%BC%D0%B0%D1%82%D1%8B%D1%87%D0%BD%D1%8B%D1%8F_%D1%82%D1%8D%D1%80%D0%BC%D1%96%D0%BD%D1%8B" title="Катэгорыя:Аксіяматычныя тэрміны">Аксіяматычныя тэрміны</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"> Апошняе змяненне старонкі адбылося 11:49, 31 снежня 2023.</li> <li id="footer-info-copyright">Тэкст даступны на ўмовах <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.be">ліцэнзіі Creative Commons Attribution-ShareAlike</a>, у асобных выпадках могуць дзейнічаць дадатковыя ўмовы. Падрабязней гл. <a class="external text" href="https://foundation.wikimedia.org/wiki/Умовы_выкарыстання">Умовы выкарыстання</a>.</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Палітыка прыватнасці</a></li> <li id="footer-places-about"><a href="/wiki/%D0%92%D1%96%D0%BA%D1%96%D0%BF%D0%B5%D0%B4%D1%8B%D1%8F:%D0%A8%D1%82%D0%BE_%D1%82%D0%B0%D0%BA%D0%BE%D0%B5_%D1%81%D0%B2%D0%B0%D0%B1%D0%BE%D0%B4%D0%BD%D0%B0%D1%8F_%D1%8D%D0%BD%D1%86%D1%8B%D0%BA%D0%BB%D0%B0%D0%BF%D0%B5%D0%B4%D1%8B%D1%8F">Пра Вікіпедыю</a></li> <li id="footer-places-disclaimers"><a href="/wiki/%D0%92%D1%96%D0%BA%D1%96%D0%BF%D0%B5%D0%B4%D1%8B%D1%8F:%D0%90%D0%B4%D0%BC%D0%BE%D0%B2%D0%B0_%D0%B0%D0%B4_%D0%B0%D0%B4%D0%BA%D0%B0%D0%B7%D0%BD%D0%B0%D1%81%D1%86%D1%96">Адмова ад адказнасці</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Code of Conduct</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Распрацоўшчыкі</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/be.wikipedia.org">Статыстыка</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Заява пра cookie</a></li> <li id="footer-places-mobileview"><a href="//be.m.wikipedia.org/w/index.php?title=%D0%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%B0%D1%81%D1%86%D1%8C&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Мабільная версія</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/static/images/footer/wikimedia-button.svg" width="84" height="29" alt="Wikimedia Foundation" lang="en" loading="lazy"></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><picture><source media="(min-width: 500px)" srcset="/w/resources/assets/poweredby_mediawiki.svg" width="88" height="31"><img src="/w/resources/assets/mediawiki_compact.svg" alt="Powered by MediaWiki" width="25" height="25" loading="lazy"></picture></a></li> </ul> </footer> </div> </div> </div> <div class="vector-header-container vector-sticky-header-container"> <div id="vector-sticky-header" class="vector-sticky-header"> <div class="vector-sticky-header-start"> <div class="vector-sticky-header-icon-start vector-button-flush-left vector-button-flush-right" aria-hidden="true"> <button class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-sticky-header-search-toggle" tabindex="-1" data-event-name="ui.vector-sticky-search-form.icon"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Пошук</span> </button> </div> <div role="search" class="vector-search-box-vue vector-search-box-show-thumbnail vector-search-box"> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail"> <form action="/w/index.php" id="vector-sticky-search-form" class="cdx-search-input cdx-search-input--has-end-button"> <div 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="Шукаць у Вікіпедыі"> <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Адмысловае:Search"> </div> <button class="cdx-button cdx-search-input__end-button">Пошук</button> </form> </div> </div> </div> <div class="vector-sticky-header-context-bar"> <nav aria-label="Змест" class="vector-toc-landmark"> <div id="vector-sticky-header-toc" class="vector-dropdown mw-portlet mw-portlet-sticky-header-toc vector-sticky-header-toc vector-button-flush-left" > <input type="checkbox" id="vector-sticky-header-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-sticky-header-toc" class="vector-dropdown-checkbox " aria-label="Пераключыць змест" > <label id="vector-sticky-header-toc-label" for="vector-sticky-header-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">Пераключыць змест</span> </label> <div class="vector-dropdown-content"> <div id="vector-sticky-header-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div class="vector-sticky-header-context-bar-primary" aria-hidden="true" ><span class="mw-page-title-main">Плоскасць</span></div> </div> </div> <div class="vector-sticky-header-end" aria-hidden="true"> <div class="vector-sticky-header-icons"> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-talk-sticky-header" tabindex="-1" data-event-name="talk-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbles mw-ui-icon-wikimedia-speechBubbles"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-subject-sticky-header" tabindex="-1" data-event-name="subject-sticky-header"><span class="vector-icon mw-ui-icon-article mw-ui-icon-wikimedia-article"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-history-sticky-header" tabindex="-1" data-event-name="history-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-history mw-ui-icon-wikimedia-wikimedia-history"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only mw-watchlink" id="ca-watchstar-sticky-header" tabindex="-1" data-event-name="watch-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-star mw-ui-icon-wikimedia-wikimedia-star"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-ve-edit-sticky-header" tabindex="-1" data-event-name="ve-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-edit mw-ui-icon-wikimedia-wikimedia-edit"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-edit-sticky-header" tabindex="-1" data-event-name="wikitext-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-wikiText mw-ui-icon-wikimedia-wikimedia-wikiText"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-viewsource-sticky-header" tabindex="-1" data-event-name="ve-edit-protected-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-editLock mw-ui-icon-wikimedia-wikimedia-editLock"></span> <span></span> </a> </div> <div class="vector-sticky-header-buttons"> <button class="cdx-button cdx-button--weight-quiet mw-interlanguage-selector" id="p-lang-btn-sticky-header" tabindex="-1" data-event-name="ui.dropdown-p-lang-btn-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-language mw-ui-icon-wikimedia-wikimedia-language"></span> <span>88 моў</span> </button> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive" id="ca-addsection-sticky-header" tabindex="-1" data-event-name="addsection-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbleAdd-progressive mw-ui-icon-wikimedia-speechBubbleAdd-progressive"></span> <span>Дадаць тэму</span> </a> </div> <div class="vector-sticky-header-icon-end"> <div class="vector-user-links"> </div> </div> </div> </div> </div> <div class="vector-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.canary-55fd9d4764-sztb8","wgBackendResponseTime":182,"wgPageParseReport":{"limitreport":{"cputime":"0.077","walltime":"0.267","ppvisitednodes":{"value":367,"limit":1000000},"postexpandincludesize":{"value":3577,"limit":2097152},"templateargumentsize":{"value":455,"limit":2097152},"expansiondepth":{"value":12,"limit":100},"expensivefunctioncount":{"value":1,"limit":500},"unstrip-depth":{"value":0,"limit":20},"unstrip-size":{"value":1584,"limit":5000000},"entityaccesscount":{"value":0,"limit":400},"timingprofile":["100.00% 51.809 1 -total"," 65.44% 33.903 1 Шаблон:Нп5"," 22.92% 11.874 1 Шаблон:З_ВСЭ"," 17.58% 9.108 1 Шаблон:З"," 11.49% 5.951 1 Шаблон:Ref-ru"," 7.90% 4.094 1 Шаблон:Ref-lang"," 5.23% 2.709 6 Шаблон:Math"," 4.09% 2.121 1 Шаблон:Commonscat-inline"," 4.02% 2.081 1 Шаблон:Ref-info"]},"scribunto":{"limitreport-timeusage":{"value":"0.009","limit":"10.000"},"limitreport-memusage":{"value":864212,"limit":52428800}},"cachereport":{"origin":"mw-web.codfw.main-5d75d7759c-bq4gv","timestamp":"20250210092700","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"\u041f\u043b\u043e\u0441\u043a\u0430\u0441\u0446\u044c","url":"https:\/\/be.wikipedia.org\/wiki\/%D0%9F%D0%BB%D0%BE%D1%81%D0%BA%D0%B0%D1%81%D1%86%D1%8C","sameAs":"http:\/\/www.wikidata.org\/entity\/Q17285","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q17285","author":{"@type":"Organization","name":"\u0423\u0434\u0437\u0435\u043b\u044c\u043d\u0456\u043a\u0456 \u043f\u0440\u0430\u0435\u043a\u0442\u0430\u045e \u0412\u0456\u043a\u0456\u043c\u0435\u0434\u044b\u044f"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2008-03-12T17:19:14Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/7\/7e\/Intersecting_planes.svg"}</script> </body> </html>