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Sjå kjelda til Kuleramme – Wikipedia

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title="Om prosjektet, kva du kan gjera, kvar du finn saker og ting"><span>Arbeidskontoret</span></a></li><li id="n-samfunnshuset" class="mw-list-item"><a href="/wiki/Wikipedia:Samfunnshuset"><span>Samfunnshuset</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Spesial:Siste_endringar" title="Liste over dei siste endringane som er gjorde på wikien. [r]" accesskey="r"><span>Siste endringar</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Spesial:Tilfeldig_side" title="Vis ei tilfeldig side [x]" accesskey="x"><span>Tilfeldig side</span></a></li><li id="n-help" class="mw-list-item"><a href="/wiki/Hjelp:Innhald" title="Hjelp til å bruke alle funksjonane."><span>Hjelp</span></a></li><li id="n-kontakt" class="mw-list-item"><a href="/wiki/Wikipedia:Kontakt"><span>Kontakt</span></a></li> </ul> </div> </div> <div id="p-query" class="vector-menu mw-portlet mw-portlet-query emptyPortlet" > <div class="vector-menu-heading"> Eksterne søk </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> På andre prosjekt </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q12806" title="Lenkje til tilknytt element [g]" accesskey="g"><span>Wikidata-element</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Hovudside" 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="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="det frie oppslagsverket" src="/static/images/mobile/copyright/wikipedia-tagline-nn.svg" width="120" height="13" style="width: 7.5em; 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/Spesial:S%C3%B8k" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Søk gjennom Wikipedia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Søk</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="Søk i Wikipedia" aria-label="Søk i Wikipedia" autocapitalize="sentences" title="Søk gjennom Wikipedia [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Spesial:Søk"> </div> <button class="cdx-button cdx-search-input__end-button">Søk</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Personlege verktøy"> <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="Utsjånad"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Endre skriftstørrelse, bredde og farge på siden." > <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="Utsjånad" > <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">Utsjånad</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&amp;utm_medium=sidebar&amp;utm_campaign=C13_nn.wikipedia.org&amp;uselang=nn" class=""><span>Gåver</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=Spesial:Opprett_konto&amp;returnto=Kuleramme&amp;returntoquery=action%3Dedit" title="Me oppfordrar til at du oppretter ein konto og loggar inn, men det er ikkje påkravd." class=""><span>Opprett konto</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=Spesial:Logg_inn&amp;returnto=Kuleramme&amp;returntoquery=action%3Dedit" title="Det er ikkje obligatorisk å logga inn, men medfører mange fordelar. [o]" accesskey="o" class=""><span>Logg inn</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="Fleire val" > <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="Personlege verktøy" > <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">Personlege verktøy</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Brukarmeny" > <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&amp;utm_medium=sidebar&amp;utm_campaign=C13_nn.wikipedia.org&amp;uselang=nn"><span>Gåver</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Spesial:Opprett_konto&amp;returnto=Kuleramme&amp;returntoquery=action%3Dedit" title="Me oppfordrar til at du oppretter ein konto og loggar inn, men det er ikkje påkravd."><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Opprett konto</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Spesial:Logg_inn&amp;returnto=Kuleramme&amp;returntoquery=action%3Dedit" title="Det er ikkje obligatorisk å logga inn, men medfører mange fordelar. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Logg inn</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"> Sider for utlogga bidragsytarar <a href="/wiki/Hjelp:Introduksjon" aria-label="Lær meir om redigering"><span>lær meir</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/Spesial:Bidraga_mine" title="Liste over endringar gjorde frå denne IP-adressa [y]" accesskey="y"><span>Bidrag</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Spesial:Diskusjonssida_mi" title="Diskusjon om endringar gjorde av denne ip-adressa [n]" accesskey="n"><span>Diskusjon</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"><!-- CentralNotice --></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="Nettstad"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <h1 id="firstHeading" class="firstHeading mw-first-heading">Sjå kjelda til Kuleramme</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="Denne artikkelen finst berre på dette språket. Legg til artikkelen på andre språk" > <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-0" 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">Legg til språk</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> <div class="after-portlet after-portlet-lang"><span class="uls-after-portlet-link"></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namnerom"> <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/Kuleramme" title="Vis innhaldssida [c]" accesskey="c"><span>Artikkel</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Diskusjon:Kuleramme" rel="discussion" title="Diskusjon om innhaldssida [t]" accesskey="t"><span>Diskusjon</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="Endre språkvariant" > <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">norsk nynorsk</span> 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Husk å ta med alle detaljene ovenfor.</div></div><hr /> <p>Du kan sjå og kopiere kjeldekoden til denne sida. </p><textarea readonly="" accesskey="," id="wpTextbox1" cols="80" rows="25" style="" class="mw-editfont-monospace" lang="nn" dir="ltr" name="wpTextbox1">[[Fil:Boulier1.JPG|mini|høyre|Ei kinesisk kuleramme]] Ei '''kuleramme''' eller eit '''reknebrett''' (også kalla '''abakus''') er ein [[reiskap]] brukt som hjelperåd til å telja eller rekna med. Ei kuleramme er laga av ei ramme med fleire [[stav]]ar eller [[tråd]]ar. Kvar tråd har [[kule]]r på som kan takast fram og tilbake. Ein tel ved å flytta kulene på trådane i samsvar med eit system, og finn løysinga frå stoda åt kulene etter at rekninga vert ferdig. Kulerammer er i dag mest brukte i aust- og søraust-Asia, særleg i [[Kina]] og [[Japan]]. == Bruk == [[Fil:abacus addition.png|mini|venstre|Addisjon av 32 og 9 med ei kuleramme]] Den kinesiske kuleramma har vanlegvis sju eller fleire stavar som står for, frå høgre til venstre, eintal, tital, hundretal, osb. Kvar stav er delt opp i to avdelingar. Den øvre avdelinga har to kuler medan den nedre har fem. Kvar kule under skiljelista har verdien 1 når ho er flytta opp mot skiljelista, og verdien 0 når ho er flytta ned mot ramma. I den øvre gruppa har kvar kule verdien 5 når ho er flytta ned mot skiljelista og 0 når ho er flytta opp mot ramma. Ein kan dimed visa fram ikkje berre tala frå 0 til 9, men også tala A-F frå [[sekstentalsystemet]]. Biletet til venstre viser korleis ein bruker ei kuleramme for å leggja saman to tal, 32 og 9 i dette dømet. Ein tek ei tom kuleramme (steg 1), og set kuler slik at dei viser fram det fyrste talet, her 32. For å gjera det må ein flytta opp to kuler frå den lågare avdelinga (verdi 1+1) mot skiljelista på eintalsstaven, og tre kuler mot skiljelista på titalsstaven (verdi 10+10+10) (steg 2). Det neste steget er å leggja til 9. I det meste vanlege systemet tek ein 9 som 10-1 i addisjon, det vil sei, ein legg til 10 og so trekk frå 1. Ein byrjar difor med å flytta to kuler frå den høgare avdelinga ned mot skiljelista for å addera 10 (steg 3). Når begge kuler ligg mot skiljelista på eintalsstaven er det ein regel at ein må flytta opp ei kule på den neste staven (steg 4), og flytta tilbake dei to kulene på den fyrste staven (steg 5). No trekk ein frå 1, ved å flytta ned ei kule på eintalsstaven (steg 6) for å få løysinga, 41. For å trekka frå gjer ein det same, bortsett frå at ein flyttar kuler vekk frå skiljelista istaden for motatt skiljelista. Det finst òg reglar for [[ganging]], [[deling]], [[kvadratrot|kvadratrøtter]] og [[kubikkrot|kubikkrøtter]]. Ein som er vant med kuleramme kan finna løysingar fortare enn ein som bruker [[reknemaskin]]. == Historie == [[Fil:Kugleramme.jpg|mini|høgre|Ei kuleramme som var brukt i danske grunnskuler tidleg på 1900-talet]] [[Fil:RomanAbacusRecon.jpg|mini|venstre|Ei rekonstruert romersk kuleramme]] Kulerammer er kjent frå gamle tider. Ein trur at dei fyrst vart brukte av [[sumerarar]] i [[Mesopotamia]], som talde ved hjelp av småstein som dei sette på linjer teikna i sanden. Grekarane og romarane brukte fòrer for å gjera det lettare å flytta teljarane, som utvikla seg til trådane som finst på moderne kulerammer. Kulerammer vart mykje nytta i Europa i mellomalderen når det var vanleg å bruka [[romartal]]a, fordi det var vanskeleg å telja med desse tala. Dei gjekk ut av av bruk etter at Europa gjekk over til det arabiske talsystemet, og er i dag nesten berre brukt som [[leikety|barneleiker]] eller for å lære barn til å telja. == Bakgrunnsstoff == * [http://www.tux.org/~bagleyd/java/AbacusApp.html The Abacus Applet] {{Webarchive|url=https://web.archive.org/web/20130110093126/http://www.tux.org/~bagleyd/java/AbacusApp.html |date=2013-01-10 }} == Kjelder == * ''Encyclopaedia Britannica'', «Abacus» (2005 utg.). * [[:sv:Abakus|Svensk wikipedia]] * [[:en:Chinese abacus|Engelsk wikipedia]] {{Autoritetsdata}} [[Kategori:Matematiske reiskapar]] [[Kategori:Romersk matematikk]] [[Kategori:Mekaniske kalkulatorar]] </textarea><div class="templatesUsed"><div class="mw-templatesUsedExplanation"><p>Malar som er brukte på denne sida: </p></div><ul> <li><a href="/wiki/Mal:Autoritetsdata" title="Mal:Autoritetsdata">Mal:Autoritetsdata</a> (<a href="/w/index.php?title=Mal:Autoritetsdata&amp;action=edit" title="Mal:Autoritetsdata">endre</a>) </li><li><a href="/wiki/Mal:Hlist/styles.css" title="Mal:Hlist/styles.css">Mal:Hlist/styles.css</a> (<a href="/w/index.php?title=Mal:Hlist/styles.css&amp;action=edit" title="Mal:Hlist/styles.css">endre</a>) </li><li><a href="/wiki/Mal:Webarchive" title="Mal:Webarchive">Mal:Webarchive</a> (<a href="/w/index.php?title=Mal:Webarchive&amp;action=edit" title="Mal:Webarchive">endre</a>) </li><li><a href="/wiki/Modul:Authority_control" title="Modul:Authority control">Modul:Authority control</a> (<a href="/w/index.php?title=Modul:Authority_control&amp;action=edit" title="Modul:Authority control">endre</a>) </li><li><a href="/wiki/Modul:Navbar" title="Modul:Navbar">Modul:Navbar</a> (<a href="/w/index.php?title=Modul:Navbar&amp;action=edit" title="Modul:Navbar">endre</a>) </li><li><a href="/wiki/Modul:Navbox" title="Modul:Navbox">Modul:Navbox</a> (<a href="/w/index.php?title=Modul:Navbox&amp;action=edit" title="Modul:Navbox">endre</a>) </li><li><a href="/wiki/Modul:Navbox/configuration" title="Modul:Navbox/configuration">Modul:Navbox/configuration</a> (<a href="/w/index.php?title=Modul:Navbox/configuration&amp;action=edit" title="Modul:Navbox/configuration">endre</a>) </li><li><a href="/wiki/Modul:Navbox/styles.css" title="Modul:Navbox/styles.css">Modul:Navbox/styles.css</a> (<a href="/w/index.php?title=Modul:Navbox/styles.css&amp;action=edit" title="Modul:Navbox/styles.css">endre</a>) </li><li><a href="/wiki/Modul:No_globals" title="Modul:No globals">Modul:No globals</a> (<a href="/w/index.php?title=Modul:No_globals&amp;action=edit" title="Modul:No globals">endre</a>) </li><li><a href="/wiki/Modul:String" title="Modul:String">Modul:String</a> (<a href="/w/index.php?title=Modul:String&amp;action=edit" title="Modul:String">endre</a>) </li><li><a href="/wiki/Modul:Wd" title="Modul:Wd">Modul:Wd</a> (<a href="/w/index.php?title=Modul:Wd&amp;action=edit" title="Modul:Wd">endre</a>) </li><li><a href="/wiki/Modul:Wd/i18n" title="Modul:Wd/i18n">Modul:Wd/i18n</a> (<a href="/w/index.php?title=Modul:Wd/i18n&amp;action=edit" title="Modul:Wd/i18n">endre</a>) </li><li><a href="/wiki/Modul:Webarchive" title="Modul:Webarchive">Modul:Webarchive</a> (<a href="/w/index.php?title=Modul:Webarchive&amp;action=edit" title="Modul:Webarchive">endre</a>) </li></ul></div><p id="mw-returnto">Attende til <a href="/wiki/Kuleramme" title="Kuleramme">Kuleramme</a>.</p> <!--esi <esi:include src="/esitest-fa8a495983347898/content" /> --><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&amp;useformat=desktop" alt="" width="1" height="1" style="border: none; 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