CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-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-disabled skin-theme-clientpref-day vector-toc-available" lang="sl" dir="ltr"> <head> <meta charset="UTF-8"> <title>Babilonska matematika - Wikipedija, prosta enciklopedija</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-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-disabled skin-theme-clientpref-day vector-toc-available";var cookie=document.cookie.match(/(?:^|; )slwikimwclientpreferences=([^;]+)/);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 full","wgMonthNames":["","januar","februar","marec","april","maj","junij","julij","avgust","september","oktober","november","december"],"wgRequestId":"01d57a97-648a-479c-91d1-f28684413582","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Babilonska_matematika","wgTitle":"Babilonska matematika","wgCurRevisionId":5239386,"wgRevisionId":5239386,"wgArticleId":405030,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["Strani s čarobnimi povezavami ISBN","Zgodovina matematike","Mezopotamija","Babilonska matematika"],"wgPageViewLanguage":"sl","wgPageContentLanguage":"sl","wgPageContentModel":"wikitext","wgRelevantPageName":"Babilonska_matematika","wgRelevantArticleId":405030,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":true, "wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"sl","pageLanguageDir":"ltr","pageVariantFallbacks":"sl"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":true,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":20000,"wgRelatedArticlesCompat":[],"wgCentralAuthMobileDomain":false,"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q787931","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","ext.cite.styles":"ready","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","ext.wikimediamessages.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","wikibase.client.init":"ready","ext.wikimediaBadges":"ready"};RLPAGEMODULES=["ext.cite.ux-enhancements","mediawiki.page.media","site","mediawiki.page.ready","mediawiki.toc","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.gadget.CommonsDirekt","ext.gadget.switcher","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","wikibase.sidebar.tracking"];</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=sl&modules=ext.cite.styles%7Cext.math.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.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=sl&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=sl&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.4"> <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/0/0b/Ybc7289-bw.jpg"> <meta property="og:image:width" content="1200"> <meta property="og:image:height" content="1118"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/0/0b/Ybc7289-bw.jpg"> <meta property="og:image:width" content="800"> <meta property="og:image:height" content="746"> <meta property="og:image:width" content="640"> <meta property="og:image:height" content="596"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Babilonska matematika - Wikipedija, prosta enciklopedija"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//sl.m.wikipedia.org/wiki/Babilonska_matematika"> <link rel="alternate" type="application/x-wiki" title="Uredi" href="/w/index.php?title=Babilonska_matematika&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="Wikipedija (sl)"> <link rel="EditURI" type="application/rsd+xml" href="//sl.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://sl.wikipedia.org/wiki/Babilonska_matematika"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.sl"> <link rel="alternate" type="application/atom+xml" title="Atom-vir strani »Wikipedija«" href="/w/index.php?title=Posebno:ZadnjeSpremembe&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-Babilonska_matematika rootpage-Babilonska_matematika skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Pojdi na vsebino</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="Projekt"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="Glavni meni" > <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">Glavni meni</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">Glavni meni</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">prestavi v stransko letvico</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">skrij</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navigacija </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage" class="mw-list-item"><a href="/wiki/Glavna_stran" title="Obiščite glavno stran [z]" accesskey="z"><span>Glavna stran</span></a></li><li id="n-introduction" class="mw-list-item"><a href="/wiki/Pomo%C4%8D:Uvod"><span>Naučite se urejati</span></a></li><li id="n-Izbrani-članki" class="mw-list-item"><a href="/wiki/Wikipedija:Izbrani_%C4%8Dlanki"><span>Izbrani članki</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Posebno:Naklju%C4%8Dno" title="Naložite naključno stran [x]" accesskey="x"><span>Naključna stran</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Posebno:ZadnjeSpremembe" title="Seznam zadnjih sprememb Wikipedije [r]" accesskey="r"><span>Zadnje spremembe</span></a></li> </ul> </div> </div> <div id="p-obcestvo" class="vector-menu mw-portlet mw-portlet-obcestvo" > <div class="vector-menu-heading"> Skupnost </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-help" class="mw-list-item"><a href="/wiki/Pomo%C4%8D:Vsebina" title="Kraj, kjer lahko prejmete pomoč"><span>Pomoč</span></a></li><li id="n-Pod-lipo" class="mw-list-item"><a href="/wiki/Wikipedija:Pod_lipo"><span>Pod lipo</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedija:Portal_skupnosti" title="O projektu, kaj lahko storite, kje lahko kaj najdete"><span>Portal skupnosti</span></a></li><li id="n-contact" class="mw-list-item"><a href="/wiki/Wikipedija:Stik_z_nami"><span>Stik z nami</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Glavna_stran" 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="Wikipedija" src="/static/images/mobile/copyright/wikipedia-wordmark-sl.svg" style="width: 7.4375em; height: 1.375em;"> <img class="mw-logo-tagline" alt="prosta enciklopedija" src="/static/images/mobile/copyright/wikipedia-tagline-sl.svg" width="118" height="13" style="width: 7.375em; height: 0.8125em;"> </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/Posebno:Iskanje" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Preiščite viki [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Iskanje</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="Iskanje v Wikipediji" aria-label="Iskanje v Wikipediji" autocapitalize="sentences" title="Preiščite viki [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Posebno:Iskanje"> </div> <button class="cdx-button cdx-search-input__end-button">Išči</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Osebna orodja"> <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="Videz"> <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="Videz" > <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">Videz</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_sl.wikipedia.org&uselang=sl" class=""><span>Denarni prispevki</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=Posebno:Registracija&returnto=Babilonska+matematika" title="Predlagamo vam, da si ustvarite račun in se prijavite, vendar to ni obvezno." class=""><span>Ustvari račun</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=Posebno:Prijava&returnto=Babilonska+matematika" title="Prijava je zaželena, vendar ni obvezna [o]" accesskey="o" class=""><span>Prijava</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="Več možnosti" > <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="Osebna orodja" > <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">Osebna orodja</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Uporabniški meni" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_sl.wikipedia.org&uselang=sl"><span>Denarni prispevki</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Posebno:Registracija&returnto=Babilonska+matematika" title="Predlagamo vam, da si ustvarite račun in se prijavite, vendar to ni obvezno."><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Ustvari račun</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Posebno:Prijava&returnto=Babilonska+matematika" title="Prijava je zaželena, vendar ni obvezna [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Prijava</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"> Strani za neprijavljene urejevalce <a href="/wiki/Pomo%C4%8D:Uvod" aria-label="Več o urejanju"><span>več o tem</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/Posebno:MojiPrispevki" title="Seznam urejanj s tega IP-naslova [y]" accesskey="y"><span>Prispevki</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Posebno:MojPogovor" title="Pogovor o urejanjih s tega IP-naslova [n]" accesskey="n"><span>Pogovorna stran</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="Projekt"> <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="Vsebina" 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">Vsebina</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">prestavi v stransko letvico</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">skrij</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">Uvod</div> </a> </li> <li id="toc-Začetki" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Začetki"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Začetki</span> </div> </a> <ul id="toc-Začetki-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Babilonske_številke" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Babilonske_številke"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Babilonske številke</span> </div> </a> <ul id="toc-Babilonske_številke-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sumerska_matematika" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Sumerska_matematika"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Sumerska matematika</span> </div> </a> <ul id="toc-Sumerska_matematika-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Starobabilonska_matematika_(2000–1600_pr._n._št.)" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Starobabilonska_matematika_(2000–1600_pr._n._št.)"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Starobabilonska matematika (2000–1600 pr. n. št.)</span> </div> </a> <button aria-controls="toc-Starobabilonska_matematika_(2000–1600_pr._n._št.)-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Vklopi podrazdelek Starobabilonska matematika (2000–1600 pr. n. št.)</span> </button> <ul id="toc-Starobabilonska_matematika_(2000–1600_pr._n._št.)-sublist" class="vector-toc-list"> <li id="toc-Aritmetika" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Aritmetika"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Aritmetika</span> </div> </a> <ul id="toc-Aritmetika-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Algebra" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Algebra"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Algebra</span> </div> </a> <ul id="toc-Algebra-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Računanje_rasti" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Računanje_rasti"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Računanje rasti</span> </div> </a> <ul id="toc-Računanje_rasti-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Plimpton_322" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Plimpton_322"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Plimpton 322</span> </div> </a> <ul id="toc-Plimpton_322-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Geometrija" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Geometrija"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.5</span> <span>Geometrija</span> </div> </a> <ul id="toc-Geometrija-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Vpliv_na_druge_civilizacije" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Vpliv_na_druge_civilizacije"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Vpliv na druge civilizacije</span> </div> </a> <ul id="toc-Vpliv_na_druge_civilizacije-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sklici" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Sklici"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Sklici</span> </div> </a> <ul id="toc-Sklici-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Viri" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Viri"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Viri</span> </div> </a> <ul id="toc-Viri-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="Vsebina" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Vklopi kazalo vsebine" > <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">Vklopi kazalo vsebine</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">Babilonska matematika</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="P9jdi na članek v drugem jeziku. Na voljo v 28 jezikih." > <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-28" 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">28 jezikov</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A7%D9%84%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A%D8%A7%D8%AA_%D9%81%D9%8A_%D8%A8%D9%84%D8%A7%D8%AF_%D8%A7%D9%84%D8%B1%D8%A7%D9%81%D8%AF%D9%8A%D9%86" title="الرياضيات في بلاد الرافدين – arabščina" lang="ar" hreflang="ar" data-title="الرياضيات في بلاد الرافدين" data-language-autonym="العربية" data-language-local-name="arabščina" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Matem%C3%A0tiques_de_Babil%C3%B2nia" title="Matemàtiques de Babilònia – katalonščina" lang="ca" hreflang="ca" data-title="Matemàtiques de Babilònia" data-language-autonym="Català" data-language-local-name="katalonščina" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Babylonische_Mathematik" title="Babylonische Mathematik – nemščina" lang="de" hreflang="de" data-title="Babylonische Mathematik" data-language-autonym="Deutsch" data-language-local-name="nemščina" 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%92%CE%B1%CE%B2%CF%85%CE%BB%CF%89%CE%BD%CE%B9%CE%B1%CE%BA%CE%AC_%CE%BC%CE%B1%CE%B8%CE%B7%CE%BC%CE%B1%CF%84%CE%B9%CE%BA%CE%AC" title="Βαβυλωνιακά μαθηματικά – grščina" lang="el" hreflang="el" data-title="Βαβυλωνιακά μαθηματικά" data-language-autonym="Ελληνικά" data-language-local-name="grščina" 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/Babylonian_mathematics" title="Babylonian mathematics – angleščina" lang="en" hreflang="en" data-title="Babylonian mathematics" data-language-autonym="English" data-language-local-name="angleščina" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Matem%C3%A1tica_babil%C3%B3nica" title="Matemática babilónica – španščina" lang="es" hreflang="es" data-title="Matemática babilónica" data-language-autonym="Español" data-language-local-name="španščina" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C%D8%A7%D8%AA_%D8%A8%D8%A7%D8%A8%D9%84%DB%8C%D8%A7%D9%86" title="ریاضیات بابلیان – perzijščina" lang="fa" hreflang="fa" data-title="ریاضیات بابلیان" data-language-autonym="فارسی" data-language-local-name="perzijščina" 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/Babylonialainen_matematiikka" title="Babylonialainen matematiikka – finščina" lang="fi" hreflang="fi" data-title="Babylonialainen matematiikka" data-language-autonym="Suomi" data-language-local-name="finščina" 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/Math%C3%A9matiques_m%C3%A9sopotamiennes" title="Mathématiques mésopotamiennes – francoščina" lang="fr" hreflang="fr" data-title="Mathématiques mésopotamiennes" data-language-autonym="Français" data-language-local-name="francoščina" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Babiloni_matematika" title="Babiloni matematika – madžarščina" lang="hu" hreflang="hu" data-title="Babiloni matematika" data-language-autonym="Magyar" data-language-local-name="madžarščina" 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/%D4%B2%D5%A1%D5%A2%D5%A5%D5%AC%D5%B8%D5%B6%D5%B5%D5%A1%D5%B6_%D5%B4%D5%A1%D5%A9%D5%A5%D5%B4%D5%A1%D5%BF%D5%AB%D5%AF%D5%A1" title="Բաբելոնյան մաթեմատիկա – armenščina" lang="hy" hreflang="hy" data-title="Բաբելոնյան մաթեմատիկա" data-language-autonym="Հայերեն" data-language-local-name="armenščina" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Matematika_Babilonia" title="Matematika Babilonia – indonezijščina" lang="id" hreflang="id" data-title="Matematika Babilonia" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonezijščina" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Matematica_babilonese" title="Matematica babilonese – italijanščina" lang="it" hreflang="it" data-title="Matematica babilonese" data-language-autonym="Italiano" data-language-local-name="italijanščina" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%90%E3%83%93%E3%83%AD%E3%83%8B%E3%82%A2%E6%95%B0%E5%AD%A6" title="バビロニア数学 – japonščina" lang="ja" hreflang="ja" data-title="バビロニア数学" data-language-autonym="日本語" data-language-local-name="japonščina" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%91%D0%B0%D0%B1%D1%8B%D0%BB_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%D1%81%D1%8B" title="Бабыл математикасы – kazaščina" lang="kk" hreflang="kk" data-title="Бабыл математикасы" data-language-autonym="Қазақша" data-language-local-name="kazaščina" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B0%94%EB%B9%8C%EB%A1%9C%EB%8B%88%EC%95%84_%EC%88%98%ED%95%99" title="바빌로니아 수학 – korejščina" lang="ko" hreflang="ko" data-title="바빌로니아 수학" data-language-autonym="한국어" data-language-local-name="korejščina" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Matematika_Babilone" title="Matematika Babilone – litovščina" lang="lt" hreflang="lt" data-title="Matematika Babilone" data-language-autonym="Lietuvių" data-language-local-name="litovščina" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AC%E0%B4%BE%E0%B4%AC%E0%B4%BF%E0%B4%B2%E0%B5%8B%E0%B4%A3%E0%B4%BF%E0%B4%AF%E0%B5%BB_%E0%B4%97%E0%B4%A3%E0%B4%BF%E0%B4%A4%E0%B4%B6%E0%B4%BE%E0%B4%B8%E0%B5%8D%E0%B4%A4%E0%B5%8D%E0%B4%B0%E0%B4%82" title="ബാബിലോണിയൻ ഗണിതശാസ്ത്രം – malajalamščina" lang="ml" hreflang="ml" data-title="ബാബിലോണിയൻ ഗണിതശാസ്ത്രം" data-language-autonym="മലയാളം" data-language-local-name="malajalamščina" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Babylonsk_matematikk" title="Babylonsk matematikk – novonorveščina" lang="nn" hreflang="nn" data-title="Babylonsk matematikk" data-language-autonym="Norsk nynorsk" data-language-local-name="novonorveščina" 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/Babylonsk_matematikk" title="Babylonsk matematikk – knjižna norveščina" lang="nb" hreflang="nb" data-title="Babylonsk matematikk" data-language-autonym="Norsk bokmål" data-language-local-name="knjižna norveščina" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Matem%C3%A1tica_babil%C3%B4nica" title="Matemática babilônica – portugalščina" lang="pt" hreflang="pt" data-title="Matemática babilônica" data-language-autonym="Português" data-language-local-name="portugalščina" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Matematica_babilonian%C4%83" title="Matematica babiloniană – romunščina" lang="ro" hreflang="ro" data-title="Matematica babiloniană" data-language-autonym="Română" data-language-local-name="romunščina" 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%92%D0%B0%D0%B2%D0%B8%D0%BB%D0%BE%D0%BD%D1%81%D0%BA%D0%B0%D1%8F_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Вавилонская математика – ruščina" lang="ru" hreflang="ru" data-title="Вавилонская математика" data-language-autonym="Русский" data-language-local-name="ruščina" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Babil_matemati%C4%9Fi" title="Babil matematiği – turščina" lang="tr" hreflang="tr" data-title="Babil matematiği" data-language-autonym="Türkçe" data-language-local-name="turščina" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%92%D0%B0%D0%B2%D0%B8%D0%BB%D0%BE%D0%BD%D1%81%D1%8C%D0%BA%D0%B0_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Вавилонська математика – ukrajinščina" lang="uk" hreflang="uk" data-title="Вавилонська математика" data-language-autonym="Українська" data-language-local-name="ukrajinščina" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/To%C3%A1n_h%E1%BB%8Dc_Babylon" title="Toán học Babylon – vietnamščina" lang="vi" hreflang="vi" data-title="Toán học Babylon" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamščina" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%B7%B4%E6%AF%94%E4%BC%A6%E6%95%B0%E5%AD%A6" title="巴比伦数学 – kitajščina" lang="zh" hreflang="zh" data-title="巴比伦数学" data-language-autonym="中文" data-language-local-name="kitajščina" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E5%85%A9%E6%B2%B3%E6%95%B8%E5%AD%B8%E5%8F%B2" title="兩河數學史 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="兩河數學史" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</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/Q787931#sitelinks-wikipedia" title="Uredi medjezikovne povezave" class="wbc-editpage">Uredi povezave</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Imenski prostori"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <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/Babilonska_matematika" title="Ogled vsebinske strani [c]" accesskey="c"><span>Stran</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Pogovor:Babilonska_matematika&action=edit&redlink=1" rel="discussion" class="new" title="Pogovor o vsebinski strani (stran ne obstaja) [t]" accesskey="t"><span>Pogovor</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="Spremeni različico jezika" > <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">slovenščina</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="Pogledi"> <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/Babilonska_matematika"><span>Preberi</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Babilonska_matematika&veaction=edit" title="Uredite to stran [v]" accesskey="v"><span>Uredi stran</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Babilonska_matematika&action=edit" title="Uredi izvorno kodo te strani [e]" accesskey="e"><span>Uredi kodo</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Babilonska_matematika&action=history" title="Prejšnje redakcije te strani [h]" accesskey="h"><span>Zgodovina</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Orodja strani"> <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="Orodja" > <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">Orodja</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">Orodja</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">prestavi v stransko letvico</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">skrij</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Več možnosti" > <div class="vector-menu-heading"> Dejanja </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/Babilonska_matematika"><span>Preberi</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Babilonska_matematika&veaction=edit" title="Uredite to stran [v]" accesskey="v"><span>Uredi stran</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Babilonska_matematika&action=edit" title="Uredi izvorno kodo te strani [e]" accesskey="e"><span>Uredi kodo</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Babilonska_matematika&action=history"><span>Zgodovina</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Splošno </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Posebno:KajSePovezujeSem/Babilonska_matematika" title="Seznam vseh strani, ki se povezujejo sem [j]" accesskey="j"><span>Kaj se povezuje sem</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Posebno:RecentChangesLinked/Babilonska_matematika" rel="nofollow" title="Zadnje spremembe na straneh, s katerimi se povezuje ta stran [k]" accesskey="k"><span>Povezane spremembe</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Posebno:PosebneStrani" title="Seznam vseh posebnih strani [q]" accesskey="q"><span>Posebne strani</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Babilonska_matematika&oldid=5239386" title="Trajna povezava na to redakcijo strani"><span>Trajna povezava</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Babilonska_matematika&action=info" title="Več informacij o tej strani"><span>Podatki o strani</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Posebno:Navedi&page=Babilonska_matematika&id=5239386&wpFormIdentifier=titleform" title="Informacije o tem, kako navajati to stran"><span>Navedba članka</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Posebno:UrlShortener&url=https%3A%2F%2Fsl.wikipedia.org%2Fwiki%2FBabilonska_matematika"><span>Pridobi skrajšani URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Posebno:QrCode&url=https%3A%2F%2Fsl.wikipedia.org%2Fwiki%2FBabilonska_matematika"><span>Prenesi kodo QR</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"> Tiskanje/izvoz </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=Posebno:Book&bookcmd=book_creator&referer=Babilonska+matematika"><span>Ustvari e-knjigo</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Posebno:DownloadAsPdf&page=Babilonska_matematika&action=show-download-screen"><span>Prenesi kot PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Babilonska_matematika&printable=yes" title="Različica te strani za tisk [p]" accesskey="p"><span>Različica za tisk</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"> V drugih projektih </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:Babylonian_mathematics" hreflang="en"><span>Wikimedijina zbirka</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/Q787931" title="Povezava na ustrezni predmet v podatkovni shrambi [g]" accesskey="g"><span>Predmet v Wikipodatkih</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="Orodja strani"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Videz"> <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">Videz</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">prestavi v stransko letvico</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">skrij</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">Iz Wikipedije, proste enciklopedije</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="sl" dir="ltr"><figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Slika:Ybc7289-bw.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Ybc7289-bw.jpg/250px-Ybc7289-bw.jpg" decoding="async" width="250" height="233" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/0/0b/Ybc7289-bw.jpg 1.5x" data-file-width="338" data-file-height="315" /></a><figcaption>Babilonska glinasta tablica YBC 7289: na diagonali je zapisana približna vrednost <a href="/wiki/Kvadratni_koren_%C5%A1tevila_2" title="Kvadratni koren števila 2">kvadratnega korena števila 2</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4afc1e27d418021bf10898eb44a7f5f315735ff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.098ex; height:3.009ex;" alt="{\displaystyle {\sqrt {2}}}"></span>), točna na štiri šestdesetiške digite 1 24 51 10 (1 + 24/60 + 51/60<sup>2</sup> + 10/60<sup>3</sup> = 1,41421296... ) oziroma sedem desetiških digitov. Na tablici je izračun <a href="/wiki/Dol%C5%BEina" title="Dolžina">dolžine</a> <a href="/wiki/Diagonala" title="Diagonala">diagonale</a> <a href="/wiki/Kvadrat_(geometrija)" title="Kvadrat (geometrija)">kvadrata</a> s stranico 30. Rezultat je 42 25 35 oziroma 42,4263888...</figcaption></figure> <p><b>Babilonska matematika</b>, znana tudi kot <b>asirsko-babilonska matematika</b>,<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> je bila <a href="/wiki/Matematika" title="Matematika">matematika</a>, ki so jo od zgodnje <a href="/wiki/Sumerija" title="Sumerija">Sumerije</a> do padca <a href="/wiki/Babilon" title="Babilon">Babilona</a> leta 539 pr. n. št. razvila ali prakticirala ljudstva v <a href="/wiki/Mezopotamija" title="Mezopotamija">Mezopotamiji</a>. Babilonska matematična besedila so obsežna in lepo urejena.<sup id="cite_ref-Aboe_7-0" class="reference"><a href="#cite_note-Aboe-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Po času se lahko razdeli na dve različni obdobji: starobabilonsko obdobje (1830-1531 pr. n. št.) in (predvsem) <a href="/wiki/Selevkidsko_cesarstvo" title="Selevkidsko cesarstvo">selevkidsko</a> obdobje v zadnjih treh ali štirih stoletjih pr. n. št.. Po vsebini med njima ni bilo skoraj nobenih razlik. Babilonska matematika je tako po značaju kot po vsebini ostala nespremenjena skoraj dve tisočletji.<sup id="cite_ref-Aboe_7-1" class="reference"><a href="#cite_note-Aboe-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> V nasprotju z <a href="/w/index.php?title=Egip%C4%8Danska_matematika&action=edit&redlink=1" class="new" title="Egipčanska matematika (stran ne obstaja)">egipčansko matematiko</a>, za katero je zelo malo pisnih virov, je babilonska matematika bogato dokumentirana na približno 400 glinastih tablicah, ki so jih izkopali od 1860. let. Besedila so pisana v <a href="/wiki/Klinopis" title="Klinopis">klinopisu</a> na tablice iz vlažne gline in nato zapečene ali posušene na soncu. Večina odkritih tablic je iz obdobja 1800 do 1600 pr. n. št. in obravnava <a href="/wiki/Ulomek" title="Ulomek">ulomke</a>, <a href="/wiki/Algebra" title="Algebra">algebro</a>, <a href="/wiki/Kvadratna_ena%C4%8Dba" title="Kvadratna enačba">kvadratne</a> in <a href="/w/index.php?title=Kubi%C4%8Dna_ena%C4%8Dba&action=edit&redlink=1" class="new" title="Kubična enačba (stran ne obstaja)">kubične</a> enačbe in <a href="/wiki/Pitagorov_izrek" title="Pitagorov izrek">Pitagorov izrek</a>. Na tablici YBC 7289 je aproksimacija <a href="/wiki/Kvadratni_koren_%C5%A1tevila_2" title="Kvadratni koren števila 2">kvadratnega korena števila 2</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4afc1e27d418021bf10898eb44a7f5f315735ff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.098ex; height:3.009ex;" alt="{\displaystyle {\sqrt {2}}}"></span>), točna na tri <a href="/wiki/%C5%A0estdeseti%C5%A1ki_%C5%A1tevilski_sistem" title="Šestdesetiški številski sistem">šestdesetiška</a> oziroma sedem <a href="/wiki/Deseti%C5%A1ki_%C5%A1tevilski_sistem" title="Desetiški številski sistem">desetiških</a> decimalnih mest. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Začetki"><span id="Za.C4.8Detki"></span>Začetki</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Babilonska_matematika&veaction=edit&section=1" title="Uredi razdelek: Začetki" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Babilonska_matematika&action=edit&section=1" title="Urejanje izvorne kode razdelka: Začetki"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Babilonska matematika je niz numeričnih in bolj zahtevnih matematičnih operacij, ki so se razvile na antičnem <a href="/wiki/Bli%C5%BEnji_vzhod" title="Bližnji vzhod">Bližnjem vzhodu</a>, zapisanih v klinopisu na glinastih tablicah, predvsem v <a href="/wiki/Sumer%C5%A1%C4%8Dina" title="Sumerščina">sumerskem</a> in <a href="/wiki/Akad%C5%A1%C4%8Dina" title="Akadščina">akadskem</a> jeziku. Zaradi obilja podatkov iz starobabilonskega obdobja v zgodnjem 2. tisočletju pr. n. št. je njihovo preučevanje osredotočeno ravno na to obdobje. O tem, kdaj je najzgodnejša babilonska matematika nastala, je bilo v preteklosti veliko razprav. Zgodovinarji so predlagali datume od 5. do 3. tisočletja pr. n. št.. </p><p>Naziv babilonska verjetno ni najbolj primeren, ker so se že v 5. tisočletju pr. n. št. uporabljali pripomočki za računanje, na primer popisani koščki gline (<i>bullae</i>) in žetoni. </p> <div class="mw-heading mw-heading2"><h2 id="Babilonske_številke"><span id="Babilonske_.C5.A1tevilke"></span>Babilonske številke</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Babilonska_matematika&veaction=edit&section=2" title="Uredi razdelek: Babilonske številke" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Babilonska_matematika&action=edit&section=2" title="Urejanje izvorne kode razdelka: Babilonske številke"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><div class="noprint relarticle mainarticle"><i>Glavni članek: <a href="/wiki/Babilonske_%C5%A1tevilke" title="Babilonske številke">babilonske številke</a>.</i></div></dd></dl> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Slika:Babylonian_numerals.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Babylonian_numerals.svg/250px-Babylonian_numerals.svg.png" decoding="async" width="250" height="148" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Babylonian_numerals.svg/375px-Babylonian_numerals.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Babylonian_numerals.svg/500px-Babylonian_numerals.svg.png 2x" data-file-width="806" data-file-height="478" /></a><figcaption><a href="/wiki/Babilonske_%C5%A1tevilke" title="Babilonske številke">Babilonske številke</a></figcaption></figure> <p>Babilonci so uporabljali <a href="/wiki/%C5%A0estdeseti%C5%A1ki_%C5%A1tevilski_sistem" title="Šestdesetiški številski sistem">šestdesetiški številski sistem</a> z osnovo <a href="/wiki/60_(%C5%A1tevilo)" title="60 (število)">60</a>. Sistem se še danes uporablja na primer za <a href="/wiki/Merjenje" class="mw-redirect" title="Merjenje">merjenje</a> <a href="/wiki/%C4%8Cas" title="Čas">časa</a> (<a href="/wiki/Ura" title="Ura">ura</a> ima 60 minut in <a href="/wiki/Minuta" title="Minuta">minuta</a> 60 <a href="/wiki/Sekunda" title="Sekunda">sekund</a>) in <a href="/wiki/Kot" title="Kot">kota</a> (<a href="/w/index.php?title=Polni_kot&action=edit&redlink=1" class="new" title="Polni kot (stran ne obstaja)">polni kot</a> ima 360°). Babilonci so v matematiko vnesli velik napredek, predvsem zaradi dveh dejstev. Število 60 je <a href="/w/index.php?title=Izredno_zelo_sestavljeno_%C5%A1tevilo&action=edit&redlink=1" class="new" title="Izredno zelo sestavljeno število (stran ne obstaja)">izredno</a> <a href="/wiki/Zelo_sestavljeno_%C5%A1tevilo" title="Zelo sestavljeno število">zelo sestavljeno število</a>, ki je deljivo z 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 in s samim seboj, kar omogoča enostavno računanje z ulomki. Poleg tega so, za razliko od <a href="/wiki/Egip%C4%8Dani" title="Egipčani">Egipčanov</a> in <a href="/wiki/Rimske_%C5%A1tevilke" title="Rimske številke">Rimljanov</a>, uvedli sistem mestnih vrednosti, v katerem vrednost številke ni odvisna samo od nje same, ampak tudi od njene lege v zapisu števila. Sistem je bil precej podoben sodobnemu <a href="/wiki/Deseti%C5%A1ki_%C5%A1tevilski_sistem" title="Desetiški številski sistem">desetiškemu sistemu</a>. Vrednosti mest so padale od leve proti desni, tako da se je na primer število 734 zapisalo s 7·100 + 3·10 + 4. </p> <div class="mw-heading mw-heading2"><h2 id="Sumerska_matematika">Sumerska matematika</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Babilonska_matematika&veaction=edit&section=3" title="Uredi razdelek: Sumerska matematika" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Babilonska_matematika&action=edit&section=3" title="Urejanje izvorne kode razdelka: Sumerska matematika"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Sumerci so po letu 3000 pr. n. št. razvili zapleten sistem merskih enot. Po letu 2600 pr. n. št. so na glinaste tablice že zapisovali tabele za množenje in se ukvarjali z <a href="/wiki/Geometrija" title="Geometrija">geometrijskimi</a> nalogami in problemi z <a href="/wiki/Deljenje" title="Deljenje">deljenjem</a>. Iz tega obdobja so tudi najstarejši sledovi babilonskih številk.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Starobabilonska_matematika_(2000–1600_pr._n._št.)"><span id="Starobabilonska_matematika_.282000.E2.80.931600_pr._n._.C5.A1t..29"></span>Starobabilonska matematika (2000–1600 pr. n. št.)</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Babilonska_matematika&veaction=edit&section=4" title="Uredi razdelek: Starobabilonska matematika (2000–1600 pr. n. št.)" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Babilonska_matematika&action=edit&section=4" title="Urejanje izvorne kode razdelka: Starobabilonska matematika (2000–1600 pr. n. št.)"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Večina glinastih tablic z matematično vsebino je iz starobabilonskega obdobja, zato se matematika običajno imenuje babilonska. Prva skupina tablic vsebuje matematične sezname in tabele, druga pa matematične probleme in izdelane rešitve. </p> <div class="mw-heading mw-heading3"><h3 id="Aritmetika">Aritmetika</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Babilonska_matematika&veaction=edit&section=5" title="Uredi razdelek: Aritmetika" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Babilonska_matematika&action=edit&section=5" title="Urejanje izvorne kode razdelka: Aritmetika"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Babilonci so si pri <a href="/wiki/Aritmetika" title="Aritmetika">aritmetiki</a> pomagali z že izračunanimi tabelami. Na dveh tablicah iz leta 2000 pr. n. št., ki so jih leta 1854 odkrili v <a href="/wiki/Larsa" title="Larsa">Sankari</a> ob <a href="/wiki/Evfrat" title="Evfrat">Evfratu</a>, so zapisani <a href="/wiki/Kvadratno_%C5%A1tevilo" title="Kvadratno število">kvadrati</a> števil do 59 in <a href="/w/index.php?title=Kub&action=edit&redlink=1" class="new" title="Kub (stran ne obstaja)">kubi</a> števil do 32. Za poenostavitev množenja so uporabljali tabele kvadratov in naslednji enačbi: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ab={\frac {(a+b)^{2}-a^{2}-b^{2}}{2}}\!\,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mi>b</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <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> </mrow> <mn>2</mn> </mfrac> </mrow> <mspace width="negativethinmathspace" /> <mspace width="thinmathspace" /> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ab={\frac {(a+b)^{2}-a^{2}-b^{2}}{2}}\!\,,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b644c94bd3feb3e2811948209e5c26759ee528f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:24.757ex; height:5.843ex;" alt="{\displaystyle ab={\frac {(a+b)^{2}-a^{2}-b^{2}}{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 ab={\frac {(a+b)^{2}-(a-b)^{2}}{4}}\!\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mi>b</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mi>b</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mn>4</mn> </mfrac> </mrow> <mspace width="negativethinmathspace" /> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ab={\frac {(a+b)^{2}-(a-b)^{2}}{4}}\!\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3f92f7d07634cc19c19778d8d21a0c0ffab2fa46" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:25.512ex; height:5.843ex;" alt="{\displaystyle ab={\frac {(a+b)^{2}-(a-b)^{2}}{4}}\!\,.}"></span></dd></dl> <p>Babilonci niso imeli algoritma za dolgo deljenje. Namesto tega so uporabljali enačbo: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {a}{b}}=a\cdot {\frac {1}{b}}\!\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mi>b</mi> </mfrac> </mrow> <mo>=</mo> <mi>a</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>b</mi> </mfrac> </mrow> <mspace width="negativethinmathspace" /> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {a}{b}}=a\cdot {\frac {1}{b}}\!\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c2be20a36c2c92763b9a799db622217f7f0b6aba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:10.072ex; height:5.343ex;" alt="{\displaystyle {\frac {a}{b}}=a\cdot {\frac {1}{b}}\!\,}"></span></dd></dl> <p>in tabelo obratnih vrednosti. Števila, katerih prafaktorji so bili samo 2, 3 in 5, so imela v šestdesetiškem zapisu končne <a href="/wiki/Obratna_vrednost" class="mw-redirect" title="Obratna vrednost">obratne vrednosti</a>. Arheologi so odkrili veliko tablic z obsežnimi seznami obratnih vrednosti. </p><p>Obratne vrednosti, na primer 1/7, 1/11, 1/13, v šestdesetiškem zapisu nimajo končnih vrednosti. Za izračun 1/13 ali deljenje s 13 so Babilonci uporabljali približke, na primer: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{13}}={\frac {7}{91}}=7\cdot {\frac {1}{91}}\approx 7\cdot {\frac {1}{90}}=7\cdot {\frac {40}{3600}}={\frac {280}{3600}}={\frac {4}{60}}+{\frac {40}{3600}}\!\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>13</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>7</mn> <mn>91</mn> </mfrac> </mrow> <mo>=</mo> <mn>7</mn> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>91</mn> </mfrac> </mrow> <mo>≈</mo> <mn>7</mn> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>90</mn> </mfrac> </mrow> <mo>=</mo> <mn>7</mn> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>40</mn> <mn>3600</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>280</mn> <mn>3600</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>4</mn> <mn>60</mn> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>40</mn> <mn>3600</mn> </mfrac> </mrow> <mspace width="negativethinmathspace" /> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{13}}={\frac {7}{91}}=7\cdot {\frac {1}{91}}\approx 7\cdot {\frac {1}{90}}=7\cdot {\frac {40}{3600}}={\frac {280}{3600}}={\frac {4}{60}}+{\frac {40}{3600}}\!\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ada0bf0f51ac389b49141ef48bf449e789834694" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:62.866ex; height:5.176ex;" alt="{\displaystyle {\frac {1}{13}}={\frac {7}{91}}=7\cdot {\frac {1}{91}}\approx 7\cdot {\frac {1}{90}}=7\cdot {\frac {40}{3600}}={\frac {280}{3600}}={\frac {4}{60}}+{\frac {40}{3600}}\!\,.}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Algebra">Algebra</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Babilonska_matematika&veaction=edit&section=6" title="Uredi razdelek: Algebra" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Babilonska_matematika&action=edit&section=6" title="Urejanje izvorne kode razdelka: Algebra"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Babilonci so poleg aritmetičnih izračunov razvili tudi <a href="/wiki/Algebra" title="Algebra">algebrske</a> metode za reševanje <a href="/wiki/Ena%C4%8Dba" title="Enačba">enačb</a>. Tudi pri njih so si pomagali s tabelami že izračunanih vrednosti. </p><p>Za reševanje kvadratnih enačb so uporabljali standardno kvadratno enačbo v obliki: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ x^{2}+bx=c\!\,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>b</mi> <mi>x</mi> <mo>=</mo> <mi>c</mi> <mspace width="negativethinmathspace" /> <mspace width="thinmathspace" /> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ x^{2}+bx=c\!\,,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c2811237441a57da3fb8246eb622302299658aa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.884ex; height:3.009ex;" alt="{\displaystyle \ x^{2}+bx=c\!\,,}"></span></dd></dl> <p>v kateri <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\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d73aa5354c24942dab5316be466465a9d171510" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.617ex; height:1.676ex;" alt="{\displaystyle a\,}"></span> in <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\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b1bcf19f4ec75b1d2cc0be001e58a314fb0a940" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.385ex; height:2.176ex;" alt="{\displaystyle b\,}"></span> nista nujno bila <a href="/wiki/Celo_%C5%A1tevilo" title="Celo število">celi števili</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8573e7d95140b0d4068258d8162e189563baee6b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.394ex; height:1.676ex;" alt="{\displaystyle c\,}"></span> pa je bil vedno pozitiven. Vedeli so, da je rešitev takšne enačbe: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x=-{\frac {b}{2}}+{\sqrt {\left({\frac {b}{2}}\right)^{2}+c}}\!\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>b</mi> <mn>2</mn> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>b</mi> <mn>2</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>c</mi> </msqrt> </mrow> <mspace width="negativethinmathspace" /> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x=-{\frac {b}{2}}+{\sqrt {\left({\frac {b}{2}}\right)^{2}+c}}\!\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86f9c1dd917025647757c03bf18ff024af37f826" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:24.367ex; height:7.676ex;" alt="{\displaystyle x=-{\frac {b}{2}}+{\sqrt {\left({\frac {b}{2}}\right)^{2}+c}}\!\,.}"></span></dd></dl> <p>Iz tabel kvadratov so nato poiskali njihove kvadratne korene. Vedno so uporabljali samo pozitivne korene, ker so bili edini smiselni za reševanje realnih problemov. Na ta način so znali izračunati na primer stranice <a href="/wiki/Pravokotnik" title="Pravokotnik">pravokotnika</a>, za katerega so vedeli ploščino in razliko med <a href="/wiki/Dol%C5%BEina" title="Dolžina">dolžino</a> in <a href="/wiki/%C5%A0irina" class="mw-redirect" title="Širina">širino</a>. </p><p>Za reševanje nekaterih kubičnih enačb so porabljali preglednice vrednosti n<sup>3</sup> + n<sup>2</sup>. Za zgled se predpostavi enačbo: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ ax^{3}+bx^{2}=c\!\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>a</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>+</mo> <mi>b</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mi>c</mi> <mspace width="negativethinmathspace" /> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ ax^{3}+bx^{2}=c\!\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a3bd173bee28169c67a76ab13cfcd5e4b6de649f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:15.168ex; height:2.843ex;" alt="{\displaystyle \ ax^{3}+bx^{2}=c\!\,.}"></span></dd></dl> <p>Z množenjem enačbe z <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^{2}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a^{2}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb67869400ac0ebe17e3669755f701b1c2b4179d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.671ex; height:2.676ex;" alt="{\displaystyle a^{2}\,}"></span> in deljenjem z <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^{3}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b^{3}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/73cfd25c058157b3b382c6861b8c683e0e1debd4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.439ex; height:2.676ex;" alt="{\displaystyle b^{3}\,}"></span> se dobi: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {ax}{b}}\right)^{3}+\left({\frac {ax}{b}}\right)^{2}={\frac {ca^{2}}{b^{3}}}\!\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>a</mi> <mi>x</mi> </mrow> <mi>b</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>a</mi> <mi>x</mi> </mrow> <mi>b</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>c</mi> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mfrac> </mrow> <mspace width="negativethinmathspace" /> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {ax}{b}}\right)^{3}+\left({\frac {ax}{b}}\right)^{2}={\frac {ca^{2}}{b^{3}}}\!\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d27ba358561827b7fde31e713f67c1dc055c7fb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:25.163ex; height:6.009ex;" alt="{\displaystyle \left({\frac {ax}{b}}\right)^{3}+\left({\frac {ax}{b}}\right)^{2}={\frac {ca^{2}}{b^{3}}}\!\,.}"></span></dd></dl> <p>S substitucijo <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y=ax/b\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>=</mo> <mi>a</mi> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>b</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y=ax/b\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ed86f988f9862072b7694889c7507234ac311904" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.361ex; height:2.843ex;" alt="{\displaystyle y=ax/b\,}"></span> se dobi enačbo: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y^{3}+y^{2}={\frac {ca^{2}}{b^{3}}}\!\,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>c</mi> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mfrac> </mrow> <mspace width="negativethinmathspace" /> <mspace width="thinmathspace" /> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y^{3}+y^{2}={\frac {ca^{2}}{b^{3}}}\!\,,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dec1d992f430d3980642292627a63553b6ddbe6a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:15.142ex; height:6.009ex;" alt="{\displaystyle y^{3}+y^{2}={\frac {ca^{2}}{b^{3}}}\!\,,}"></span></dd></dl> <p>ki je rešljiva tako, da se v tabeli <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 n^{3}+n^{2}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n^{3}+n^{2}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a43f8f615e2a8188fd83198d8efae0cad08546d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:8.125ex; height:2.843ex;" alt="{\displaystyle n^{3}+n^{2}\,}"></span> poišče vrednost, ki je najbližja vrednosti desne strani enačbe. Babilonci so to dosegli brez algebrskih zapisov, kar kaže na njihovo globoko razumevanje problema. Splošne metode za reševanje kubičnih enačb niso poznali. </p> <div class="mw-heading mw-heading3"><h3 id="Računanje_rasti"><span id="Ra.C4.8Dunanje_rasti"></span>Računanje rasti</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Babilonska_matematika&veaction=edit&section=7" title="Uredi razdelek: Računanje rasti" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Babilonska_matematika&action=edit&section=7" title="Urejanje izvorne kode razdelka: Računanje rasti"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Babilonci so modelirali <a href="/wiki/Eksponentna_funkcija" title="Eksponentna funkcija">eksponentno</a> rast, nenaravno rast (z eno od <a href="/w/index.php?title=Sigmoida&action=edit&redlink=1" class="new" title="Sigmoida (stran ne obstaja)">sigmoidnih</a> funkcij) in čas podvojitve. Slednjega so uporabljali za računanje <a href="/wiki/Obresti" title="Obresti">obresti</a>. </p><p>Na glinasti tablici iz obdobja okoli leta 2000 pr. n. št. je naslednja naloga: »Izračunaj čas podvojitve (kapitala) za (navadno) mesečno obrestno mero 1/60«. Izračun pokaže, da znaša letna obrestna mera 12/60, se pravi 20 %, torej se kapital podvoji v 5-ih letih.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Plimpton_322">Plimpton 322</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Babilonska_matematika&veaction=edit&section=8" title="Uredi razdelek: Plimpton 322" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Babilonska_matematika&action=edit&section=8" title="Urejanje izvorne kode razdelka: Plimpton 322"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Tablica <a href="/w/index.php?title=Plimpton_322&action=edit&redlink=1" class="new" title="Plimpton 322 (stran ne obstaja)">Plimpton 322</a> vsebuje seznam <a href="/wiki/Pitagorejska_trojica" title="Pitagorejska trojica">pitagorejskih trojic</a>, se pravi takšnih celih števil <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\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d73aa5354c24942dab5316be466465a9d171510" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.617ex; height:1.676ex;" alt="{\displaystyle a\,}"></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 b\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b1bcf19f4ec75b1d2cc0be001e58a314fb0a940" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.385ex; height:2.176ex;" alt="{\displaystyle b\,}"></span> in <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\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8573e7d95140b0d4068258d8162e189563baee6b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.394ex; height:1.676ex;" alt="{\displaystyle c\,}"></span>, za katere je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a^{2}+b^{2}=c^{2}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <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> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a^{2}+b^{2}=c^{2}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4e89a8fb02916280c36043b2937ade5d8315304" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:12.723ex; height:2.843ex;" alt="{\displaystyle a^{2}+b^{2}=c^{2}\,}"></span>. Število trojic na tablici je preveliko in števila so prevelika, da so jih dobili na silo. </p><p>O tem je bilo napisano veliko razprav, vključno z nekaterimi špekulacijami, glede tega, ali je tabela služila kot zgodnja <a href="/wiki/Trigonometrija" title="Trigonometrija">trigonometrična</a> tablica. Vprašanje, kako je bila izračunana, nima istega odgovora kot vprašanje, čemu je služila. Na prvo vprašanje se najbolj zadovoljivo odgovori, da z recipročnimi pari, kar so prvič predlagali pred približno sto leti. Odgovor na drugo vprašanje je, da so z njimi reševali probleme z nekaterimi vrstami <a href="/wiki/Pravokotni_trikotnik" title="Pravokotni trikotnik">pravokotnih trikotnikov</a>.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Geometrija">Geometrija</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Babilonska_matematika&veaction=edit&section=9" title="Uredi razdelek: Geometrija" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Babilonska_matematika&action=edit&section=9" title="Urejanje izvorne kode razdelka: Geometrija"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Babilonci so poznali pravila za računanje <a href="/wiki/Prostornina" title="Prostornina">prostornin</a> in <a href="/wiki/Plo%C5%A1%C4%8Dina" title="Ploščina">ploščin</a>. <a href="/wiki/Obseg" title="Obseg">Obseg</a> <a href="/wiki/Krog" title="Krog">kroga</a> so računali kot tri njegove <a href="/wiki/Premer" title="Premer">premere</a>, njegovo ploščino pa kot 1/12 kvadrata premera, kar bi bilo res, če bi bilo število <a href="/wiki/Pi" title="Pi"><i>π</i></a> enako 3. Prostornino <a href="/wiki/Valj" title="Valj">valja</a> so računali kot zmnožek osnovne ploskve in višine, prostornino <a href="/w/index.php?title=Prisekani_sto%C5%BEec&action=edit&redlink=1" class="new" title="Prisekani stožec (stran ne obstaja)">prisekanega stožca</a> in <a href="/w/index.php?title=Prisekana_kvadratna_piramida&action=edit&redlink=1" class="new" title="Prisekana kvadratna piramida (stran ne obstaja)">prisekane kvadratne piramide</a> pa so napačno računali kot zmnožek višine in polovice vsot obeh osnovnih ploskev. Poznali so tudi <a href="/wiki/Pitagorov_izrek" title="Pitagorov izrek">Pitagorov izrek</a>. </p><p>V babilonskih besedilih je <i>π</i> ≈ 3, kar je dovolj točno za arhitekturne projekte tistega časa. To vrednost se omenja tudi pri opisu Salomonovega templja v Hebrejski bibliji.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> Babilonci so se zavedali, da je vrednost samo približna. Na eni od babilonskih matematičnih tablic iz 19.-17. stoletja pr. n. št., ki so jih leta 1936 izkopali v bližini Suse, so odkrili izračun <i>π</i> = 25/8 (= 3,125). Vrednost je samo približno 0,5 % manjša od njegove točne vrednosti.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p><p>Enota za merjenje razdalje je bila babilonska milja, ki je merila približno 11,3 km. Enoto za razdaljo so kasneje pretvorili v časovno miljo, ki so jo uporabljali za računanje potovanja Sonca, se pravi časa.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p><p>Babilonci so poznali izreke o razmerjih stranic podobnih trikotnikov. Zaradi pomanjkljive predstave o merjenju kota, so namesto tega preučevali stranice trikotnikov.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p><p>Babilonski astronomi so točno zapisovali vzhode in zahode zvezd, gibanje planetov ter <a href="/wiki/Son%C4%8Dev_mrk" title="Sončev mrk">Sončeve</a> in <a href="/wiki/Lunin_mrk" title="Lunin mrk">Lunine mrke</a>, ki so zahtevali poznavanje kotnih razdalj, merjenih na nebesnem svodu.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Otto_Eduard_Neugebauer" title="Otto Eduard Neugebauer">Otto Eduard Neugebauer</a> je v 1950. letih odkril, da so za računanje <a href="/wiki/Efemeride" title="Efemeride">efemeride</a> (tabel astronomskih leg) uporabljali tudi nekakšno <a href="/w/index.php?title=Fourierova_analiza&action=edit&redlink=1" class="new" title="Fourierova analiza (stran ne obstaja)">Fourierovo analizo</a>.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Vpliv_na_druge_civilizacije">Vpliv na druge civilizacije</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Babilonska_matematika&veaction=edit&section=10" title="Uredi razdelek: Vpliv na druge civilizacije" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Babilonska_matematika&action=edit&section=10" title="Urejanje izvorne kode razdelka: Vpliv na druge civilizacije"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ob ponovnem odkritju babilonske civilizacije je postalo jasno, da so si grški in helenistični matematiki in astronomi, še posebej <a href="/wiki/Hiparh" title="Hiparh">Hiparh</a>, večino znanja sposodili pri Babiloncih. </p><p>Nemški asiriolog Franz Xaver Kugler je v svoji knjigi <i>Babilonsko lunarno računanje</i> (<i>Die Babylonische Mondrechnung</i>)<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> objavil, da <a href="/wiki/Ptolemaj" title="Ptolemaj">Ptolemaj</a> v svojem <i>Almagestu IV.2</i> trdi, da je Hiparh izračunal bolj točne čase Luninih men od tistih, ki so mu bile znane <i>»od še starejših astronomov«</i>, tako da je primerjal kaldejska in svoja opazovanja Luninih mrkov. Kugler je odkril, da so periode, ki jih je Ptolemaj pripisoval Hiparhu, uporabljali že stari Babilonci. Hiparh je torej s svojimi opazovanji samo potrdil vrednosti period, odkritih v kaldejskem obdobju. </p><p>Jasno je, da sta imela Hiparh in za njim Ptolemaj skoraj popoln seznam več stoletij trajajočih opazovanj mrkov. Podatki so bili najverjetneje povzeti iz tabel kaldejskih rutinskih dnevnih opazovanj, v katerih so bili zapisani vsi pomembni dogodki. Ohranjeni zapisi so iz obdobja 652 pr. n. št do 130 n. št., dogodki pa so se verjetno dokumentirali že od vladavine babilonskega kralja <a href="/wiki/Nabonasar" title="Nabonasar">Nabonasarja</a>. Ptolemaj je začel svojo kronologijo s prvim dnem egipčanskega koledarja prvega leta vladanja Nabonasarja, se pravi 26. februarja 747 pr. n. št.. </p><p>Neobdelani podatki v dnevnih zapisih so bili zelo nepregledni in težko uporabni, zato so nedvomno že Kaldejci pripravili izvlečke, na primer pregled vseh opaženih mrkov, ki so jim omogočili izračun periodičnosti pojavov. Babilonci so podatke uporabili tudi v sistemu B: </p> <ul><li>223 <a href="/wiki/Sinodski_mesec" title="Sinodski mesec">sinodskih mesecev</a> = 239 vrnitev v anomalijo (<a href="/wiki/Anomalisti%C4%8Dni_mesec" title="Anomalistični mesec">anomalistični mesec</a>) = 242 vrnitev v zemljepisno širino (<a href="/wiki/Drakonski_mesec" title="Drakonski mesec">drakonski mesec</a>). Obdobje je zdaj znano kot <a href="/wiki/Saro%C5%A1ki_cikel" title="Saroški cikel">saroški cikel</a>, ki je uporaben za napovedovanje Sončevih in Luninih mrkov.</li> <li>251 (sinodskih) mesecev = 269 vrnitev v anomalijo</li> <li>5458 (sinodskih) mesecev = 5923 vrnitev v zemljepisno širino</li></ul> <p>1 sinodski mesec = 29;31:50:08:20 dni v šestdesetiškem, oziroma 29,53059413... dni v decimalnem zapisu, oziroma 29 dni 12 ur 44 minut 3⅓ sekund. Babilonci so vse periode računali v sinodskih mesecih, morda zato, ker so uporabljali <a href="/wiki/Babilonski_koledar" title="Babilonski koledar">lunisolarni koledar</a>. Zaradi povezav z različnimi letnimi dogodki so bila leta različno dolga. </p><p>Poznali so tudi različne povezave med periodami <a href="/wiki/Planet" title="Planet">planetov</a>. Izračune, ki jih Ptolemaj v <i>Almagestu IX.3</i> pripisuje Hiparhu, so uporabljali že Babilonci, kar dokazujejo zapisi na glinastih tablicah. </p><p>Vse znanje se je preneslo na <a href="/wiki/Stari_Grki" class="mw-redirect" title="Stari Grki">stare Grke</a> verjetno kmalu po <a href="/wiki/Aleksander_Veliki" title="Aleksander Veliki">Aleksandrovi</a> osvojitvi Mezopotamije leta 331 pr. n. št.. Kasnejši klasični filozof <a href="/wiki/Simplikij" title="Simplikij">Simplikij</a> (začetek 6. stoletja n. št.) je trdil, da je Aleksander Veliki ukazal, naj se vsi zgodovinski astronomski zapisi pod nadzorom letopisca <a href="/w/index.php?title=Kalisten&action=edit&redlink=1" class="new" title="Kalisten (stran ne obstaja)">Kalistena</a> iz Olinta prevedejo v grščino in pošljejo njegovemu stricu <a href="/wiki/Aristotel" title="Aristotel">Aristotelu</a>. Simplikij je kljub temu, da je zelo pozen vir, dokaj zanesljiv. Nekaj časa je preživel v izgnanstvu na <a href="/wiki/Sasanidsko_cesarstvo" title="Sasanidsko cesarstvo">sasanidskem</a> (perzijskem) dvoru, kjer bi lahko imel dostop do virov, ki so se na Zahodu izgubili. </p><p>Aristotelov učenec <a href="/wiki/Kalip" title="Kalip">Kalip</a> iz Kizika je uvedel 76 letni cikel, s katerim je izboljšal 19 letni <a href="/w/index.php?title=Metonov_cikel&action=edit&redlink=1" class="new" title="Metonov cikel (stran ne obstaja)">Metonov cikel</a>. Prvo leto njegovega prvega cikla se je začelo 28. junija 330 pr. n. št., kasneje pa je lunarne mesece verjetno štel od prvega meseca po Aleksandrovi odločilni zmagi v bitki pri Gavgameli leta 331 pr. n. št.. Tudi Kalip je dobil podatke morda iz babilonskih virov. Znano je tudi, da je babilonski svečenik Beros okoli leta 281 pr. n. št. za novega vladarja <a href="/wiki/Antioh_I._Soter" title="Antioh I. Soter">Antioha I.</a> napisal knjigo o (precej mitološki) zgodovini Babilonije z naslovom <i>Babyloniaca</i>. Antioh je na grškem otoku Kosu kasneje ustanovil šolo <a href="/wiki/Astrologija" title="Astrologija">astrologije</a>. Drugi kandidat, ki bi Grke lahko učil babilonske astronomije/astrologije, je bil <a href="/w/index.php?title=Sudin&action=edit&redlink=1" class="new" title="Sudin (stran ne obstaja)">Sudin</a>, ki je v poznem 3. stoletju pr. n. št. živel na dvoru <a href="/wiki/Atal_I._Soter" title="Atal I. Soter">Atala I. Soterja</a>. </p><p>Prevod astronomskih zapisov je vsekakor zahteva poglobljeno znanje klinopisa, jezika in postopkov, zato se zdi verjetno, da je to opravilo nekaj neznanih Kaldejcev. </p><p>Babilonski zapisi so bili datirani v mesecih, ki so imeli 29 ali 30 dni in letih, ki so imela 12 ali 13 mesecev. V tistem času niso uporabljali koledarja, ki bi temeljil na primer na metonskem ciklu, ampak so vsak mesec začeli s pojavom mlade Lune. Računanje časovnih intervalov med astronomskimi dogodki je zato zelo zapleteno in utrudljivo. </p><p>Hiparh je to morda opravil s prenosom zapisov v <a href="/w/index.php?title=Egip%C4%8Danski_koledar&action=edit&redlink=1" class="new" title="Egipčanski koledar (stran ne obstaja)">egipčanski koledar</a>, ki je imel vedno 365 dni, razdeljenih na 12 mesecev po 30 dni in 5 dodatnih dni. Računanje intervalov je s tem postalo mnogo lažje. Ptolemaj je vse dogodke datiral po tem koledarju in celo pripomnil, da je <i>»vse, kar ja naredil Hiparh, samo pretvorba opazovanj planetov v bolj uporabno obliko«</i> (<i>Almagest IX.2</i>). <a href="/wiki/Plinij_starej%C5%A1i" title="Plinij starejši">Plinij starejši</a> je v svoji <i>Naturalis Historia</i> II.IX(53) o napovedovanju mrkov napisal: <i>»Po njihovem času (je <a href="/wiki/Tales" title="Tales">Tales</a>) poti obeh zvezd (Sonca in Lune) 600 let napovedal po Hiparhu...</i>«. To bi lahko pomenilo, da je Hiparh napovedal mrke za obdobje 600 let, kar je zaradi izjemno obsežnega računanja zelo malo verjetno. Hiparh je namesto tega verjetno naredil seznam vseh mrkov od Nabonaserjevega do svojega časa. </p><p>Drugi sledovi babilonskega znanja v Hiparhovih delih so: </p> <ul><li>prvo znano grško deljenje kroga na 360 stopinj po 60 ločnih minut,</li> <li>prva skladna raba šestdesetiškega številskega sistema,</li> <li>raba enote <i>pehus</i> (vatel), ki je merila 2° ali 2½° in</li> <li>uporaba kratke periode 248 dni = 9 anomalističnih mesecev.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Sklici">Sklici</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Babilonska_matematika&veaction=edit&section=11" title="Uredi razdelek: Sklici" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Babilonska_matematika&action=edit&section=11" title="Urejanje izvorne kode razdelka: Sklici"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist columns references-column-width" style="column-width: 25em; list-style-type: decimal;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">H. Lewy (1949). <i>Studies in Assyro-Babylonian mathematics and metrology</i>. Orientalia (NS) <b>18</b>: 40–67, 137–170.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text">H. Lewy, H. (1951). <i>Studies in Assyro-Babylonian mathematics and metrology</i>. Orientalia (NS) <b>20</b>: 1–12.</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text"> E.M. Bruins (1953). <i>La classification des nombres dans les mathématiques babyloniennes</i>. Revue d'Assyriologie <b>47</b>: 185–188.</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text">Cazalas (1932). <i>Le calcul de la table mathématique AO 6456</i>. Revue d'Assyriologie <b>29</b>: 183–188.</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text">S. Langdon (1918). <i>Assyriological notes: Mathematical observations on the Scheil-Esagila tablet</i>. Revue d'Assyriologie <b>15</b>: 110–112.</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><a href="#cite_ref-6">↑</a></span> <span class="reference-text">E. Robson (2002). <i>Guaranteed genuine originals: The Plimpton Collection and the early history of mathematical Assyriology</i>. IISLET, Dresden, str. 245–292.</span> </li> <li id="cite_note-Aboe-7"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-Aboe_7-0">7,0</a></sup> <sup><a href="#cite_ref-Aboe_7-1">7,1</a></sup></span> <span class="reference-text">A. Aaboe. <i>The culture of Babylonia: Babylonian mathematics, astrology, and astronomy</i>. The Assyrian and Babylonian Empires and other States of the Near East, from the Eighth to the Sixth Centuries B.C. Cambridge University Press, 1991.</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><a href="#cite_ref-8">↑</a></span> <span class="reference-text">D.J. Melville (2003). <i>Third Millennium Chronology, Third Millennium Mathematics</i>. St. Lawrence University.</span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><a href="#cite_ref-9">↑</a></span> <span class="reference-text">M. Hudson. <i>Why the Miracle of Compound Interest leads to Financial Crises</i>.</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><a href="#cite_ref-10">↑</a></span> <span class="reference-text">J.H. Webb. Have we caught your interest?</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><a href="#cite_ref-11">↑</a></span> <span class="reference-text">E. Robson. <i>Neither Sherlock Holmes nor Babylon: a reassessment of Plimpton 322</i>. Historia Math. <b>28</b> (3): 202.</span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><a href="#cite_ref-12">↑</a></span> <span class="reference-text">P. Beckmann. <i>A History of Pi</i>. St. Martin's (1971).</span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><a href="#cite_ref-13">↑</a></span> <span class="reference-text">D.G. Romano. <i>Athletics and Mathematics in Archaic Corinth: The Origins of the Greek Stadion</i>. American Philosophical Society, 1993, str. 78.</span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><a href="#cite_ref-14">↑</a></span> <span class="reference-text">E. M. Bruins. <i>Quelques textes mathématiques de la Mission de Suse, 1950</i>.</span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><a href="#cite_ref-15">↑</a></span> <span class="reference-text">E. M. Bruins, M. Rutten. <i>Textes mathématiques de Suse</i>. Mémoires de la Mission archéologique en Iran vol. XXXIV, 1961,</span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><a href="#cite_ref-16">↑</a></span> <span class="reference-text">Eves, 2. poglavje.</span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><a href="#cite_ref-17">↑</a></span> <span class="reference-text">Boyer (1991). <i>Greek Trigonometry and Mensuration</i>. str. 158–159. </span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><a href="#cite_ref-18">↑</a></span> <span class="reference-text">E. Maor (1998). <i>Trigonometric Delights</i>. Princeton University Press. str. 20. <a href="/wiki/Posebno:ViriKnjig/0691095418" class="internal mw-magiclink-isbn">ISBN 0-691-09541-8</a>.</span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><a href="#cite_ref-19">↑</a></span> <span class="reference-text">E. Prestini (2004). <i>The evolution of applied harmonic analysis: models of the real world</i>. Birkhäuser, str. 62. ISBN G-C. Rota, F. Palombi (1997). Indiscrete thoughts, str. 11. Birkhäuser. <a href="/wiki/Posebno:ViriKnjig/9780817638665" class="internal mw-magiclink-isbn">ISBN 978-0-8176-3866-5</a>.</span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><a href="#cite_ref-20">↑</a></span> <span class="reference-text">O. Neugebauer (1969) [1957]. <i>The Exact Sciences in Antiquity</i>. 2. izdaja. Dover Publications. <a href="/wiki/Posebno:ViriKnjig/9780486223322" class="internal mw-magiclink-isbn">ISBN 978-0-486-22332-2</a>.</span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><a href="#cite_ref-21">↑</a></span> <span class="reference-text">L. Brack-Bernsen, M. Brack. <i>Analyzing shell structure from Babylonian and modern times</i>. arXiv:physics/0310126.</span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><a href="#cite_ref-22">↑</a></span> <span class="reference-text">F.X. Kugler. <i>Die Babylonische Mondrechnung</i>. Freiburg im Breisgau, 1900.</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Viri">Viri</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Babilonska_matematika&veaction=edit&section=12" title="Uredi razdelek: Viri" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Babilonska_matematika&action=edit&section=12" title="Urejanje izvorne kode razdelka: Viri"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r5453066">.mw-parser-output .refbegin{font-size:90%;margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-100{font-size:100%}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns dl,.mw-parser-output .refbegin-columns ol,.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li,.mw-parser-output .refbegin-columns dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="refbegin refbegin-columns references-column-count references-column-count-3" style="column-count: 3;"> <ul><li>A. E. Berriman (1956). <i>The Babylonian quadratic equation</i>.</li> <li>C. B. Boyer. <i>A History of Mathematics</i>, 2. dopolnjena izdaja. New York: Wiley (1989) <a href="/wiki/Posebno:ViriKnjig/0471097632" class="internal mw-magiclink-isbn">ISBN 0-471-09763-2</a>, (1991) <a href="/wiki/Posebno:ViriKnjig/0471543977" class="internal mw-magiclink-isbn">ISBN 0-471-54397-7</a>.</li> <li>G. G. Joseph. <i>The Crest of the Peacock</i>. Princeton University Press (15. oktober 2000), <a href="/wiki/Posebno:ViriKnjig/0691006598" class="internal mw-magiclink-isbn">ISBN 0-691-00659-8</a>.</li> <li>D. E. Joyce (1995). <i>Plimpton 322</i>.</li> <li>O. Neugebauer (1969) [1957]. <i>The Exact Sciences in Antiquity</i>, 2. izdaja. Dover Publications. <a href="/wiki/Posebno:ViriKnjig/9780486223322" class="internal mw-magiclink-isbn">ISBN 978-0-486-22332-2</a>.</li> <li>J. J. O'Connor, E.F. Robertson. <i>An overview of Babylonian mathematics</i>. MacTutor History of Mathematics, december 2000.</li> <li>E. Robson (2001). <i>Neither Sherlock Holmes nor Babylon: a reassessment of Plimpton 322</i>. Historia Math. <b>28</b> (3): 167–206. doi: 10.1006/hmat.2001.2317. MR 1849797.</li> <li>E. Robson. <i>Words and pictures: New light on Plimpton 322</i>. The American Mathematical Monthly <b>109</b> (2): 105.</li> <li>E. Robson. <i>Mathematics in Ancient Iraq: A Social History</i>. Princeton University Press (2008).</li> <li>G. J. Toomer (1981). <i>Hipparchus and Babylonian Astronomy</i>.</li></ul> </div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Pridobljeno iz »<a dir="ltr" href="https://sl.wikipedia.org/w/index.php?title=Babilonska_matematika&oldid=5239386">https://sl.wikipedia.org/w/index.php?title=Babilonska_matematika&oldid=5239386</a>«</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Posebno:Kategorije" title="Posebno:Kategorije">Kategorije</a>: <ul><li><a href="/wiki/Kategorija:Zgodovina_matematike" title="Kategorija:Zgodovina matematike">Zgodovina matematike</a></li><li><a href="/wiki/Kategorija:Mezopotamija" title="Kategorija:Mezopotamija">Mezopotamija</a></li><li><a href="/w/index.php?title=Kategorija:Babilonska_matematika&action=edit&redlink=1" class="new" title="Kategorija:Babilonska matematika (stran ne obstaja)">Babilonska matematika</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Skrita kategorija: <ul><li><a href="/wiki/Kategorija:Strani_s_%C4%8Darobnimi_povezavami_ISBN" title="Kategorija:Strani s čarobnimi povezavami ISBN">Strani s čarobnimi povezavami ISBN</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"> Čas zadnje spremembe strani: 12:52, 29. november 2019.</li> <li id="footer-info-copyright">Besedilo se sme prosto uporabljati v skladu z dovoljenjem <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/">Creative Commons Priznanje avtorstva-Deljenje pod enakimi pogoji 4.0</a>; uveljavljajo se lahko dodatni pogoji. Za podrobnosti glej <a class="external text" href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use">Pogoje uporabe</a>.<br /> Wikipedia® je tržna znamka neprofitne organizacije <a rel="nofollow" class="external text" href="https://wikimediafoundation.org">Wikimedia Foundation Inc.</a></li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Pravilnik o zasebnosti</a></li> <li id="footer-places-about"><a href="/wiki/Wikipedija:O_Wikipediji">O Wikipediji</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedija:Splo%C5%A1na_zavrnitev_odgovornosti">Zavrnitve odgovornosti</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Kodeks ravnanja</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Razvijalci</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/sl.wikipedia.org">Statistika</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">O piškotkih</a></li> <li id="footer-places-mobileview"><a href="//sl.m.wikipedia.org/w/index.php?title=Babilonska_matematika&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Mobilni prikaz</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" 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"><img src="/w/resources/assets/poweredby_mediawiki.svg" alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> </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.main-694cf4987f-4gblr","wgBackendResponseTime":147,"wgPageParseReport":{"limitreport":{"cputime":"0.102","walltime":"0.471","ppvisitednodes":{"value":644,"limit":1000000},"postexpandincludesize":{"value":756,"limit":2097152},"templateargumentsize":{"value":51,"limit":2097152},"expansiondepth":{"value":8,"limit":100},"expensivefunctioncount":{"value":0,"limit":500},"unstrip-depth":{"value":0,"limit":20},"unstrip-size":{"value":11077,"limit":5000000},"entityaccesscount":{"value":0,"limit":400},"timingprofile":["100.00% 50.566 1 -total"," 48.00% 24.271 1 Predloga:Sklici"," 27.02% 13.661 1 Predloga:Refbegin"," 6.25% 3.158 1 Predloga:Glavni"," 4.78% 2.417 1 Predloga:Refend"," 4.51% 2.279 1 Predloga:Main_other"]},"scribunto":{"limitreport-timeusage":{"value":"0.002","limit":"10.000"},"limitreport-memusage":{"value":581541,"limit":52428800}},"cachereport":{"origin":"mw-web.eqiad.main-587f7d4878-gz6td","timestamp":"20241120211402","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Babilonska matematika","url":"https:\/\/sl.wikipedia.org\/wiki\/Babilonska_matematika","sameAs":"http:\/\/www.wikidata.org\/entity\/Q787931","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q787931","author":{"@type":"Organization","name":"Sodelavci projektov Wikimedie"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2015-07-05T07:23:30Z","dateModified":"2019-11-29T11:52:26Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/0\/0b\/Ybc7289-bw.jpg"}</script> </body> </html>