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class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">premjesti na bočnu traku</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">sakrij</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">Početak</div> </a> </li> <li id="toc-Princip_rada" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Princip_rada"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Princip rada</span> </div> </a> <ul id="toc-Princip_rada-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Istorijat" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Istorijat"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Istorijat</span> </div> </a> <button aria-controls="toc-Istorijat-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>Uključi/isključi podsekciju Istorijat</span> </button> <ul id="toc-Istorijat-sublist" class="vector-toc-list"> <li id="toc-Grčki_abakus" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Grčki_abakus"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Grčki abakus</span> </div> </a> <ul id="toc-Grčki_abakus-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Rimski_abakus" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Rimski_abakus"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Rimski abakus</span> </div> </a> <ul id="toc-Rimski_abakus-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Kineski_abakus" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Kineski_abakus"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Kineski abakus</span> </div> </a> <ul id="toc-Kineski_abakus-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Japanski_abakus" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Japanski_abakus"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Japanski abakus</span> </div> </a> <ul id="toc-Japanski_abakus-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ruski_abakus" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ruski_abakus"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Ruski abakus</span> </div> </a> <ul id="toc-Ruski_abakus-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Drevni_američki_abakus" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Drevni_američki_abakus"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.6</span> <span>Drevni američki abakus</span> </div> </a> <ul id="toc-Drevni_američki_abakus-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Školski_abakus" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Školski_abakus"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.7</span> <span>Školski abakus</span> </div> </a> <ul id="toc-Školski_abakus-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Abakus_kod_slepih" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Abakus_kod_slepih"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.8</span> <span>Abakus kod slepih</span> </div> </a> <ul id="toc-Abakus_kod_slepih-sublist" class="vector-toc-list"> </ul> </li> </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="Sadržaj" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" lang="sh-Latn" dir="ltr"> <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="Prikaži/sakrij sadržaj" > <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">Prikaži/sakrij sadržaj</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" lang="sh-Latn" dir="ltr"><span class="mw-page-title-main">Abakus (računanje)</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" lang="sh-Latn" dir="ltr"> <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="Prijedi na druge jezične varijante članka. Dostupno je na 109 jezika" > <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-109" 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">109 jezika</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Abakus" title="Abakus — Afrikanerski" lang="af" hreflang="af" data-title="Abakus" data-language-autonym="Afrikaans" data-language-local-name="Afrikanerski" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Abaco" title="Abaco — Aragonežanski" lang="an" hreflang="an" data-title="Abaco" data-language-autonym="Aragonés" data-language-local-name="Aragonežanski" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%B9%D8%AF%D8%A7%D8%AF" title="معداد — Arapski" lang="ar" hreflang="ar" data-title="معداد" data-language-autonym="العربية" data-language-local-name="Arapski" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%8F%E0%A6%AC%E0%A6%BE%E0%A6%95%E0%A6%BE%E0%A6%9B" title="এবাকাছ — Asemijski" lang="as" hreflang="as" data-title="এবাকাছ" data-language-autonym="অসমীয়া" data-language-local-name="Asemijski" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/%C3%81bacu" title="Ábacu — Asturijski" lang="ast" hreflang="ast" data-title="Ábacu" data-language-autonym="Asturianu" data-language-local-name="Asturijski" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-ay mw-list-item"><a href="https://ay.wikipedia.org/wiki/Jakhu%C3%B1a" title="Jakhuña — Ajmara" lang="ay" hreflang="ay" data-title="Jakhuña" data-language-autonym="Aymar aru" data-language-local-name="Ajmara" class="interlanguage-link-target"><span>Aymar aru</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Abak" title="Abak — Azerbejdžanski" lang="az" hreflang="az" data-title="Abak" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbejdžanski" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%DA%86%D8%A4%D8%B1%D8%AA%DA%A9%D9%87" title="چؤرتکه — South Azerbaijani" lang="azb" hreflang="azb" data-title="چؤرتکه" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Abakus" title="Abakus — Central Bikol" lang="bcl" hreflang="bcl" data-title="Abakus" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%90%D0%B1%D0%B0%D0%BA" title="Абак — Beloruski" lang="be" hreflang="be" data-title="Абак" data-language-autonym="Беларуская" data-language-local-name="Beloruski" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%90%D0%B1%D0%B0%D0%BA" title="Абак — Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Абак" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%90%D0%B1%D0%B0%D0%BA_(%D1%81%D0%BC%D0%B5%D1%82%D0%B0%D0%BB%D0%BE)" title="Абак (сметало) — Bugarski" lang="bg" hreflang="bg" data-title="Абак (сметало)" data-language-autonym="Български" data-language-local-name="Bugarski" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bi mw-list-item"><a href="https://bi.wikipedia.org/wiki/Abakus" title="Abakus — Bislama" lang="bi" hreflang="bi" data-title="Abakus" data-language-autonym="Bislama" data-language-local-name="Bislama" class="interlanguage-link-target"><span>Bislama</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%85%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%AC%E0%A6%BE%E0%A6%95%E0%A6%BE%E0%A6%B8" title="অ্যাবাকাস — Bengalski" lang="bn" hreflang="bn" data-title="অ্যাবাকাস" data-language-autonym="বাংলা" data-language-local-name="Bengalski" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Abakus_(ra%C4%8Dunaljka)" title="Abakus (računaljka) — Bosanski" lang="bs" hreflang="bs" data-title="Abakus (računaljka)" data-language-autonym="Bosanski" data-language-local-name="Bosanski" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-bxr mw-list-item"><a href="https://bxr.wikipedia.org/wiki/%D0%A1%D0%B0%D0%BC%D0%BF%D0%B8%D0%BD" title="Сампин — Russia Buriat" lang="bxr" hreflang="bxr" data-title="Сампин" data-language-autonym="Буряад" data-language-local-name="Russia Buriat" class="interlanguage-link-target"><span>Буряад</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/%C3%80bac" title="Àbac — Katalonski" lang="ca" hreflang="ca" data-title="Àbac" data-language-autonym="Català" data-language-local-name="Katalonski" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cdo mw-list-item"><a href="https://cdo.wikipedia.org/wiki/S%C3%A1ung-bu%C3%A0ng" title="Sáung-buàng — Mindong" lang="cdo" hreflang="cdo" data-title="Sáung-buàng" data-language-autonym="閩東語 / Mìng-dĕ̤ng-ngṳ̄" data-language-local-name="Mindong" class="interlanguage-link-target"><span>閩東語 / Mìng-dĕ̤ng-ngṳ̄</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Po%C4%8D%C3%ADtadlo" title="Počítadlo — Češki" lang="cs" hreflang="cs" data-title="Počítadlo" data-language-autonym="Čeština" data-language-local-name="Češki" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%90%D0%B1%D0%B0%D0%BA" title="Абак — Čuvaški" lang="cv" hreflang="cv" data-title="Абак" data-language-autonym="Чӑвашла" data-language-local-name="Čuvaški" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Abacws" title="Abacws — Velški" lang="cy" hreflang="cy" data-title="Abacws" data-language-autonym="Cymraeg" data-language-local-name="Velški" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Abacus_(regnemaskine)" title="Abacus (regnemaskine) — Danski" lang="da" hreflang="da" data-title="Abacus (regnemaskine)" data-language-autonym="Dansk" data-language-local-name="Danski" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Abakus_(Rechenhilfsmittel)" title="Abakus (Rechenhilfsmittel) — Nemački" lang="de" hreflang="de" data-title="Abakus (Rechenhilfsmittel)" data-language-autonym="Deutsch" data-language-local-name="Nemački" 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%86%CE%B2%CE%B1%CE%BA%CE%B1%CF%82" title="Άβακας — Grčki" lang="el" hreflang="el" data-title="Άβακας" data-language-autonym="Ελληνικά" data-language-local-name="Grčki" 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/Abacus" title="Abacus — Engleski" lang="en" hreflang="en" data-title="Abacus" data-language-autonym="English" data-language-local-name="Engleski" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Abako_(me%C4%A5anika_kalkulilo)" title="Abako (meĥanika kalkulilo) — Esperanto" lang="eo" hreflang="eo" data-title="Abako (meĥanika kalkulilo)" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/%C3%81baco" title="Ábaco — Španski" lang="es" hreflang="es" data-title="Ábaco" data-language-autonym="Español" data-language-local-name="Španski" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Abakus" title="Abakus — Estonski" lang="et" hreflang="et" data-title="Abakus" data-language-autonym="Eesti" data-language-local-name="Estonski" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Abako" title="Abako — Baskijski" lang="eu" hreflang="eu" data-title="Abako" data-language-autonym="Euskara" data-language-local-name="Baskijski" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%DA%86%D8%B1%D8%AA%DA%A9%D9%87" title="چرتکه — Persijski" lang="fa" hreflang="fa" data-title="چرتکه" data-language-autonym="فارسی" data-language-local-name="Persijski" 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/Helmitaulu" title="Helmitaulu — Finski" lang="fi" hreflang="fi" data-title="Helmitaulu" data-language-autonym="Suomi" data-language-local-name="Finski" 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/Abaque_(calcul)" title="Abaque (calcul) — Francuski" lang="fr" hreflang="fr" data-title="Abaque (calcul)" data-language-autonym="Français" data-language-local-name="Francuski" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Abacas" title="Abacas — Irski" lang="ga" hreflang="ga" data-title="Abacas" data-language-autonym="Gaeilge" data-language-local-name="Irski" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E7%AE%97%E7%9B%A4" title="算盤 — gan kineski" lang="gan" hreflang="gan" data-title="算盤" data-language-autonym="贛語" data-language-local-name="gan kineski" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Bouly%C3%A9" title="Boulyé — Guianan Creole" lang="gcr" hreflang="gcr" data-title="Boulyé" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/%C3%81baco" title="Ábaco — Galski" lang="gl" hreflang="gl" data-title="Ábaco" data-language-autonym="Galego" data-language-local-name="Galski" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-glk mw-list-item"><a href="https://glk.wikipedia.org/wiki/%DA%86%DB%8A%D8%B1%D8%AA%D9%8A%DA%A9%D8%A7" title="چۊرتيکا — Gilaki" lang="glk" hreflang="glk" data-title="چۊرتيکا" data-language-autonym="گیلکی" data-language-local-name="Gilaki" class="interlanguage-link-target"><span>گیلکی</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%AE%E0%AA%A3%E0%AA%95%E0%AA%BE%E0%AA%98%E0%AB%8B%E0%AA%A1%E0%AB%80" title="મણકાઘોડી — Gudžarati" lang="gu" hreflang="gu" data-title="મણકાઘોડી" data-language-autonym="ગુજરાતી" data-language-local-name="Gudžarati" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%97%D7%A9%D7%91%D7%95%D7%A0%D7%99%D7%99%D7%94" title="חשבונייה — Hebrejski" lang="he" hreflang="he" data-title="חשבונייה" data-language-autonym="עברית" data-language-local-name="Hebrejski" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%97%E0%A4%BF%E0%A4%A8%E0%A4%A4%E0%A4%BE%E0%A4%B0%E0%A4%BE" title="गिनतारा — Hindi" lang="hi" hreflang="hi" data-title="गिनतारा" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Abak" title="Abak — Hrvatski" lang="hr" hreflang="hr" data-title="Abak" data-language-autonym="Hrvatski" data-language-local-name="Hrvatski" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Abakusz" title="Abakusz — Mađarski" lang="hu" hreflang="hu" data-title="Abakusz" data-language-autonym="Magyar" data-language-local-name="Mađarski" 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%B1%D5%A2%D5%A1%D5%AF_(%D5%BF%D5%A1%D5%AD%D5%BF%D5%A1%D5%AF)" title="Աբակ (տախտակ) — Jermenski" lang="hy" hreflang="hy" data-title="Աբակ (տախտակ)" data-language-autonym="Հայերեն" data-language-local-name="Jermenski" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Abaco" title="Abaco — Interlingva" lang="ia" hreflang="ia" data-title="Abaco" data-language-autonym="Interlingua" data-language-local-name="Interlingva" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Swipoa" title="Swipoa — Indonezijski" lang="id" hreflang="id" data-title="Swipoa" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonezijski" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Abako" title="Abako — Ido" lang="io" hreflang="io" data-title="Abako" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Talnagrind" title="Talnagrind — Islandski" lang="is" hreflang="is" data-title="Talnagrind" data-language-autonym="Íslenska" data-language-local-name="Islandski" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Abaco" title="Abaco — Italijanski" lang="it" hreflang="it" data-title="Abaco" data-language-autonym="Italiano" data-language-local-name="Italijanski" 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%82%A2%E3%83%90%E3%82%AB%E3%82%B9" title="アバカス — Japanski" lang="ja" hreflang="ja" data-title="アバカス" data-language-autonym="日本語" data-language-local-name="Japanski" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Abakos" title="Abakos — Jamaican Creole English" lang="jam" hreflang="jam" data-title="Abakos" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Simpoa" title="Simpoa — Javanski" lang="jv" hreflang="jv" data-title="Simpoa" data-language-autonym="Jawa" data-language-local-name="Javanski" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%90%E1%83%91%E1%83%90%E1%83%99%E1%83%98" title="აბაკი — Gruzijski" lang="ka" hreflang="ka" data-title="აბაკი" data-language-autonym="ქართული" data-language-local-name="Gruzijski" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kaa mw-list-item"><a href="https://kaa.wikipedia.org/wiki/Abakus" title="Abakus — Kara-kalpaški" lang="kaa" hreflang="kaa" data-title="Abakus" data-language-autonym="Qaraqalpaqsha" data-language-local-name="Kara-kalpaški" class="interlanguage-link-target"><span>Qaraqalpaqsha</span></a></li><li class="interlanguage-link interwiki-ki mw-list-item"><a href="https://ki.wikipedia.org/wiki/Abacus" title="Abacus — Kikuju" lang="ki" hreflang="ki" data-title="Abacus" data-language-autonym="Gĩkũyũ" data-language-local-name="Kikuju" class="interlanguage-link-target"><span>Gĩkũyũ</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%90%D0%B1%D0%B0%D0%BA" title="Абак — Kozački" lang="kk" hreflang="kk" data-title="Абак" data-language-autonym="Қазақша" data-language-local-name="Kozački" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%80%E1%9F%92%E1%9E%94%E1%9E%B6%E1%9E%85%E1%9F%8B%E1%9E%82%E1%9E%B7%E1%9E%8F%E1%9E%9B%E1%9F%81%E1%9E%81" title="ក្បាច់គិតលេខ — Kmerski" lang="km" hreflang="km" data-title="ក្បាច់គិតលេខ" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="Kmerski" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%85%E0%B2%AC%E0%B3%8D%E0%B2%AF%E0%B2%BE%E0%B2%95%E0%B2%B8%E0%B3%8D%E2%80%8C" title="ಅಬ್ಯಾಕಸ್‌ — Kanada" lang="kn" hreflang="kn" data-title="ಅಬ್ಯಾಕಸ್‌" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kanada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%A3%BC%ED%8C%90" title="주판 — Korejski" lang="ko" hreflang="ko" data-title="주판" data-language-autonym="한국어" data-language-local-name="Korejski" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ks mw-list-item"><a href="https://ks.wikipedia.org/wiki/%DA%AF%D9%90%D9%86%D8%AA%D8%A7%D8%B1%D9%95" title="گِنتارٕ — Kašmiri" lang="ks" hreflang="ks" data-title="گِنتارٕ" data-language-autonym="कॉशुर / کٲشُر" data-language-local-name="Kašmiri" class="interlanguage-link-target"><span>कॉशुर / کٲشُر</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%90%D0%B1%D0%B0%D0%BA_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Абак (математика) — Kirgiski" lang="ky" hreflang="ky" data-title="Абак (математика)" data-language-autonym="Кыргызча" data-language-local-name="Kirgiski" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Abacus" title="Abacus — Latinski" lang="la" hreflang="la" data-title="Abacus" data-language-autonym="Latina" data-language-local-name="Latinski" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Abaco" title="Abaco — Lingua Franca Nova" lang="lfn" hreflang="lfn" data-title="Abaco" data-language-autonym="Lingua Franca Nova" data-language-local-name="Lingua Franca Nova" class="interlanguage-link-target"><span>Lingua Franca Nova</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/T%C3%A8lraam" title="Tèlraam — Limburgiš" lang="li" hreflang="li" data-title="Tèlraam" data-language-autonym="Limburgs" data-language-local-name="Limburgiš" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BA%A5%E0%BA%B9%E0%BA%81%E0%BA%84%E0%BA%B4%E0%BA%94" title="ລູກຄິດ — Laoški" lang="lo" hreflang="lo" data-title="ລູກຄິດ" data-language-autonym="ລາວ" data-language-local-name="Laoški" class="interlanguage-link-target"><span>ລາວ</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Abakas" title="Abakas — Litvanski" lang="lt" hreflang="lt" data-title="Abakas" data-language-autonym="Lietuvių" data-language-local-name="Litvanski" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Skait%C4%ABk%C4%BCi" title="Skaitīkļi — Letonski" lang="lv" hreflang="lv" data-title="Skaitīkļi" data-language-autonym="Latviešu" data-language-local-name="Letonski" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A1%D0%BC%D0%B5%D1%82%D0%B0%D0%BB%D0%BA%D0%B0" title="Сметалка — Makedonski" lang="mk" hreflang="mk" data-title="Сметалка" data-language-autonym="Македонски" data-language-local-name="Makedonski" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AE%E0%B4%A3%E0%B4%BF%E0%B4%9A%E0%B5%8D%E0%B4%9A%E0%B4%9F%E0%B5%8D%E0%B4%9F%E0%B4%82" title="മണിച്ചട്ടം — Malajalam" lang="ml" hreflang="ml" data-title="മണിച്ചട്ടം" data-language-autonym="മലയാളം" data-language-local-name="Malajalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A1%D0%B0%D0%BC%D0%BF%D0%B8%D0%BD" title="Сампин — Mongolski" lang="mn" hreflang="mn" data-title="Сампин" data-language-autonym="Монгол" data-language-local-name="Mongolski" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Sempoa" title="Sempoa — Malajski" lang="ms" hreflang="ms" data-title="Sempoa" data-language-autonym="Bahasa Melayu" data-language-local-name="Malajski" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/%C3%81baco" title="Ábaco — Mirandeški" lang="mwl" hreflang="mwl" data-title="Ábaco" data-language-autonym="Mirandés" data-language-local-name="Mirandeški" class="interlanguage-link-target"><span>Mirandés</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%85%E0%A4%AC%E0%A4%BE%E0%A4%95%E0%A4%B8" title="अबाकस — Nepalski" lang="ne" hreflang="ne" data-title="अबाकस" data-language-autonym="नेपाली" data-language-local-name="Nepalski" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Abacus_(rekentuig)" title="Abacus (rekentuig) — Holandski" lang="nl" hreflang="nl" data-title="Abacus (rekentuig)" data-language-autonym="Nederlands" data-language-local-name="Holandski" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Kuleramme" title="Kuleramme — Norveški njorsk" lang="nn" hreflang="nn" data-title="Kuleramme" data-language-autonym="Norsk nynorsk" data-language-local-name="Norveški njorsk" 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/Abakus_(kuleramme)" title="Abakus (kuleramme) — Norveški bokmål" lang="nb" hreflang="nb" data-title="Abakus (kuleramme)" data-language-autonym="Norsk bokmål" data-language-local-name="Norveški bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%85%E0%A8%AC%E0%A9%88%E0%A8%95%E0%A8%B8" title="ਅਬੈਕਸ — Pandžabski" lang="pa" hreflang="pa" data-title="ਅਬੈਕਸ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Pandžabski" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Abakus_(liczyd%C5%82o)" title="Abakus (liczydło) — Poljski" lang="pl" hreflang="pl" data-title="Abakus (liczydło)" data-language-autonym="Polski" data-language-local-name="Poljski" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/%C3%80baco" title="Àbaco — Piedmontese" lang="pms" hreflang="pms" data-title="Àbaco" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%DA%AF%D9%86%D8%AA%D8%A7%D8%B1%D8%A7" title="گنتارا — Western Punjabi" lang="pnb" hreflang="pnb" data-title="گنتارا" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/%C3%81baco" title="Ábaco — Portugalski" lang="pt" hreflang="pt" data-title="Ábaco" data-language-autonym="Português" data-language-local-name="Portugalski" 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/Abac" title="Abac — Rumunski" lang="ro" hreflang="ro" data-title="Abac" data-language-autonym="Română" data-language-local-name="Rumunski" 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%90%D0%B1%D0%B0%D0%BA" title="Абак — Ruski" lang="ru" hreflang="ru" data-title="Абак" data-language-autonym="Русский" data-language-local-name="Ruski" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Badduttuleri" title="Badduttuleri — Sicilijanski" lang="scn" hreflang="scn" data-title="Badduttuleri" data-language-autonym="Sicilianu" data-language-local-name="Sicilijanski" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D8%A2%D8%A8%D8%A7%DA%AA%D8%B3" title="آباڪس — Sindi" lang="sd" hreflang="sd" data-title="آباڪس" data-language-autonym="سنڌي" data-language-local-name="Sindi" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Abacus" title="Abacus — Simple English" lang="en-simple" hreflang="en-simple" data-title="Abacus" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Abakus_(po%C4%8D%C3%ADtacia_tabu%C4%BEka)" title="Abakus (počítacia tabuľka) — Slovački" lang="sk" hreflang="sk" data-title="Abakus (počítacia tabuľka)" data-language-autonym="Slovenčina" data-language-local-name="Slovački" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Abak" title="Abak — Slovenački" lang="sl" hreflang="sl" data-title="Abak" data-language-autonym="Slovenščina" data-language-local-name="Slovenački" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Abakusi" title="Abakusi — Albanski" lang="sq" hreflang="sq" data-title="Abakusi" data-language-autonym="Shqip" data-language-local-name="Albanski" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%90%D0%B1%D0%B0%D0%BA%D1%83%D1%81_(%D1%80%D0%B0%D1%87%D1%83%D0%BD%D0%B0%D1%9A%D0%B5)" title="Абакус (рачунање) — Srpski" lang="sr" hreflang="sr" data-title="Абакус (рачунање)" data-language-autonym="Српски / srpski" data-language-local-name="Srpski" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Sipoah" title="Sipoah — Sudanski" lang="su" hreflang="su" data-title="Sipoah" data-language-autonym="Sunda" data-language-local-name="Sudanski" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Abakus" title="Abakus — Švedski" lang="sv" hreflang="sv" data-title="Abakus" data-language-autonym="Svenska" data-language-local-name="Švedski" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Abakasi" title="Abakasi — Svahili" lang="sw" hreflang="sw" data-title="Abakasi" data-language-autonym="Kiswahili" data-language-local-name="Svahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%8E%E0%AE%A3%E0%AF%8D%E0%AE%9A%E0%AE%9F%E0%AF%8D%E0%AE%9F%E0%AE%AE%E0%AF%8D" title="எண்சட்டம் — Tamilski" lang="ta" hreflang="ta" data-title="எண்சட்டம்" data-language-autonym="தமிழ்" data-language-local-name="Tamilski" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%85%E0%B0%AC%E0%B0%BE%E0%B0%95%E0%B0%B8%E0%B1%8D" title="అబాకస్ — Telugu" lang="te" hreflang="te" data-title="అబాకస్" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%90%D0%B1%D0%B0%D0%BA" title="Абак — Tađik" lang="tg" hreflang="tg" data-title="Абак" data-language-autonym="Тоҷикӣ" data-language-local-name="Tađik" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%A5%E0%B8%B9%E0%B8%81%E0%B8%84%E0%B8%B4%E0%B8%94" title="ลูกคิด — Tajlandski" lang="th" hreflang="th" data-title="ลูกคิด" data-language-autonym="ไทย" data-language-local-name="Tajlandski" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Abakus" title="Abakus — Tagalski" lang="tl" hreflang="tl" data-title="Abakus" data-language-autonym="Tagalog" data-language-local-name="Tagalski" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Abak%C3%BCs" title="Abaküs — Turski" lang="tr" hreflang="tr" data-title="Abaküs" data-language-autonym="Türkçe" data-language-local-name="Turski" 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%90%D0%B1%D0%B0%D0%BA_(%D1%80%D0%B0%D1%85%D1%96%D0%B2%D0%BD%D0%B8%D1%86%D1%8F)" title="Абак (рахівниця) — Ukrajinski" lang="uk" hreflang="uk" data-title="Абак (рахівниця)" data-language-autonym="Українська" data-language-local-name="Ukrajinski" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%DA%AF%D9%86%D8%AA%D8%A7%D8%B1%D8%A7" title="گنتارا — Urdu" lang="ur" hreflang="ur" data-title="گنتارا" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Abak" title="Abak — Uzbečki" lang="uz" hreflang="uz" data-title="Abak" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbečki" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/B%C3%A0n_t%C3%ADnh" title="Bàn tính — Vijetnamski" lang="vi" hreflang="vi" data-title="Bàn tính" data-language-autonym="Tiếng Việt" data-language-local-name="Vijetnamski" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Abacus" title="Abacus — Varej" lang="war" hreflang="war" data-title="Abacus" data-language-autonym="Winaray" data-language-local-name="Varej" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E7%AE%97%E7%9B%98" title="算盘 — Wu kineski" lang="wuu" hreflang="wuu" data-title="算盘" data-language-autonym="吴语" data-language-local-name="Wu kineski" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-xh mw-list-item"><a href="https://xh.wikipedia.org/wiki/I-abacus" title="I-abacus — Khosa" lang="xh" hreflang="xh" data-title="I-abacus" data-language-autonym="IsiXhosa" data-language-local-name="Khosa" class="interlanguage-link-target"><span>IsiXhosa</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%AE%97%E7%9B%98" title="算盘 — Kineski" lang="zh" hreflang="zh" data-title="算盘" data-language-autonym="中文" data-language-local-name="Kineski" 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/%E7%AE%97%E7%9B%A4" title="算盤 — Literary Chinese" lang="lzh" hreflang="lzh" data-title="算盤" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/S%C7%B9g-p%C3%B4a%E2%81%BF" title="Sǹg-pôaⁿ — min nan kineski" lang="nan" hreflang="nan" data-title="Sǹg-pôaⁿ" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="min nan kineski" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%AE%97%E7%9B%A4" title="算盤 — kantonski" lang="yue" hreflang="yue" data-title="算盤" data-language-autonym="粵語" data-language-local-name="kantonski" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q12806#sitelinks-wikipedia" title="Uredi međujezične poveznice" class="wbc-editpage">Uredi veze</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" lang="sh-Latn" dir="ltr"> <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/Abakus_(ra%C4%8Dunanje)" title="Vidi stranicu sadržaja [c]" accesskey="c"><span>Stranica</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Razgovor:Abakus_(ra%C4%8Dunanje)&action=edit&redlink=1" rel="discussion" class="new" title="Razgovarajte o sadržini ove stranice (stranica ne postoji) [t]" accesskey="t"><span>Razgovor</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown " lang="sh-Latn" dir="ltr"> <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="Promijeni jezičnu varijantu" > <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">Latinica</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants" lang="sh-Latn" dir="ltr"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-varlang-0" class="selected ca-variants-sh-Latn mw-list-item"><a href="/w/index.php?title=Abakus_(ra%C4%8Dunanje)&variant=sh-latn" lang="sh-Latn" hreflang="sh-Latn"><span>Latinica</span></a></li><li id="ca-varlang-1" class="ca-variants-sh-Cyrl mw-list-item"><a href="/w/index.php?title=Abakus_(ra%C4%8Dunanje)&variant=sh-cyrl" lang="sh-Cyrl" hreflang="sh-Cyrl"><span>Ћирилица</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Teme"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" lang="sh-Latn" dir="ltr"> <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/Abakus_(ra%C4%8Dunanje)"><span>Prikaži</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Abakus_(ra%C4%8Dunanje)&veaction=edit" title="Uredite ovu stranicu [v]" accesskey="v"><span>Uredi</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Abakus_(ra%C4%8Dunanje)&action=edit" title="Uredite izvorni kod ove stranice [e]" accesskey="e"><span>Uredi kod</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Abakus_(ra%C4%8Dunanje)&action=history" title="Pogledajte prethodne verzije ove stranice [h]" accesskey="h"><span>Historija</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Pomagala"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" lang="sh-Latn" dir="ltr"> <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="Alatke" > <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">Alatke</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">Alati</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">premjesti na bočnu traku</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">sakrij</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Više mogućnosti" lang="sh-Latn" dir="ltr"> <div class="vector-menu-heading"> Radnje </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/Abakus_(ra%C4%8Dunanje)"><span>Prikaži</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Abakus_(ra%C4%8Dunanje)&veaction=edit" title="Uredite ovu stranicu [v]" accesskey="v"><span>Uredi</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Abakus_(ra%C4%8Dunanje)&action=edit" title="Uredite izvorni kod ove stranice [e]" accesskey="e"><span>Uredi kod</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Abakus_(ra%C4%8Dunanje)&action=history"><span>Historija</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" lang="sh-Latn" dir="ltr"> <div class="vector-menu-heading"> Opšte </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Posebno:%C5%A0to_vodi_ovdje/Abakus_(ra%C4%8Dunanje)" title="Pogledajte listu svih stranica koje vode ovamo [j]" accesskey="j"><span>Šta vodi ovamo</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Posebno:Povezane_izmjene/Abakus_(ra%C4%8Dunanje)" rel="nofollow" title="Prelistajte nedavne izmjene stranica koje su povezane s ovom [k]" accesskey="k"><span>Povezane izmjene</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Posebno:Posebne_stranice" title="Pregledajte listu svih posebnih stranica [q]" accesskey="q"><span>Posebne stranice</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Abakus_(ra%C4%8Dunanje)&oldid=42233567" title="Nabavite trajnu vezu do ove verzije stranice"><span>Trajna veza</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Abakus_(ra%C4%8Dunanje)&action=info" title="Pronađite više informacija o ovoj stranici"><span>Podaci o stranici</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Posebno:Citiraj&page=Abakus_%28ra%C4%8Dunanje%29&id=42233567&wpFormIdentifier=titleform" title="Saznajte kako da citirate ovu stranicu"><span>Citiraj stranicu</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Posebno:Skra%C4%87iva%C4%8D_adresa&url=https%3A%2F%2Fsh.wikipedia.org%2Fwiki%2FAbakus_%28ra%25C4%258Dunanje%29"><span>Skrati 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%2Fsh.wikipedia.org%2Fwiki%2FAbakus_%28ra%25C4%258Dunanje%29"><span>Preuzmi QR kod</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" lang="sh-Latn" dir="ltr"> <div class="vector-menu-heading"> Štampanje/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:Kolekcija&bookcmd=book_creator&referer=Abakus+%28ra%C4%8Dunanje%29"><span>Napravi knjigu</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Posebno:DownloadAsPdf&page=Abakus_%28ra%C4%8Dunanje%29&action=show-download-screen"><span>Preuzmi kao PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Abakus_(ra%C4%8Dunanje)&printable=yes" title="Odštampajte ovu stranicu [p]" accesskey="p"><span>Odštampaj</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" lang="sh-Latn" dir="ltr"> <div class="vector-menu-heading"> Na drugim projektima </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/Abacus" hreflang="en"><span>Wikimedia Commons</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/Q12806" title="Pogledajte povezanu stavku u skladištu podataka [g]" accesskey="g"><span>Stavka na Wikipodacima</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="Pomagala"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Izgled"> <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">Izgled</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">premjesti na bočnu traku</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">sakrij</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">Izvor: Wikipedija</div> </div> <div id="contentSub" lang="sh-Latn" dir="ltr"><div id="mw-content-subtitle" lang="sh-Latn" dir="ltr"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="sh-Latn" dir="ltr"><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Boulier1.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Boulier1.JPG/220px-Boulier1.JPG" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Boulier1.JPG/330px-Boulier1.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/e/ea/Boulier1.JPG 2x" data-file-width="409" data-file-height="307" /></a><figcaption>Abakus</figcaption></figure> <p><b>Abakus</b> (lat.) ili <b>abak</b> (grč.) je prva poznata sprava za računanje starih <a href="/wiki/Egip%C4%87ani" title="Egipćani">Egipćana</a>, <a href="/wiki/Grci" title="Grci">Grka</a>, <a href="/wiki/Rimljani" class="mw-redirect" title="Rimljani">Rimljana</a>, <a href="/wiki/Kinezi" title="Kinezi">Kineza</a>. Računaljka je bila u obliku ploče. <a href="/w/index.php?title=Rimski_abak&action=edit&redlink=1" class="new" title="Rimski abak (stranica ne postoji)">Rimski abak</a> je bio ploča podeljena na pruge ili pravougaona polja, po kojima su se pomerali kamenčići ili žetoni. Prema položaju kamenčiću je pripadala određena <a href="/w/index.php?title=Mesna_vrednost&action=edit&redlink=1" class="new" title="Mesna vrednost (stranica ne postoji)">mesna vrednost</a>. Od latinskog izraza calculus - kamenčić nastalo je izraz calculare - računati. U Evropi se rimski abak mestimično upotrebljavao do <a href="/wiki/XVI_vek" class="mw-redirect" title="XVI vek">XVI veka</a>. <a href="/w/index.php?title=Kineski_abak&action=edit&redlink=1" class="new" title="Kineski abak (stranica ne postoji)">Kineski abak</a> je bio okvir sa napetim žicama na kojima su nanizane kuglice, svakoj žici, odgovarala je određena mesna vrednost. (Stariji korisnici se sećaju ovih računala sa prvih časova matematike u osnovnoj školi.) Od kineskog razvio se i japanski <a href="/w/index.php?title=Soroban&action=edit&redlink=1" class="new" title="Soroban (stranica ne postoji)">soroban</a> na kojem su unutar okvira na štapićima bili nanizani dvostruki čunjići (4+1 na svakom štapiću). Soroban se u <a href="/wiki/Japan" title="Japan">Japanu</a> i danas ponegde upotrebljava. Abak sličan kineskm i japanskom mnogo se do nedavno upotrebnjavao i u <a href="/wiki/Rusija" title="Rusija">Rusiji</a> (SSSR). </p><p>Danas je teško zamisliti brojanje i računanje bez pisanih brojeva, ali nekada nisu ni postojali pisani brojevi. Ono na čemu se najranije računalo bili su prsti na rukama. Međutim za potrebe trgovine bilo je nužno smisliti neko pomagalo koje će moći da prebroji i izračuna veće vednosti. Jedno od takvih pomagala je bio abakus. Abakus je prosta i istorijski stara sprava za računanje. U narodu je poznat kao sprava (mašina) za računanje za decu ili kao harfa za ludake. I dan-danas je rasprostranjena i upotrebljava se u mnogim krajevima sveta. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Princip_rada">Princip rada</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abakus_(ra%C4%8Dunanje)&veaction=edit&section=1" title="Uredi odjeljak Princip rada" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abakus_(ra%C4%8Dunanje)&action=edit&section=1" title="Uredi kôd odjeljka Princip rada"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Abakus je najčešće napravljen od drveta. Sastoji se od okvira sa kuglicama ili kamenčićima koji su nabodeni na štapiće ili žicu, ili se kuglice povlače po izrezbarenim otvorima. Kuglice ili kamenčići svojim položajem predstavljaju vrednost određenog broja. Abakus omogućava i rešavanje malo komplikovanijih računskih operacija. Pored osnovnih računskih operacija (sabiranja, oduzimanja, množenja i deljenja) na njemu je moguće i korenovanje. <a href="/wiki/Rimski_brojevi" title="Rimski brojevi">Rimskim brojevima</a> nije bilo moguće vršiti komplikovanije operacije, tako da je ruski abakus bio nešto izmenjena verzija u odnosu na ostale vrste abakusa. </p><p>Bitno je naglasiti da, koliko god je abakus čoveku pomogao u računanju, to nije mašina koja je automatski rešavala operacije, već se to računanje vršilo u ljudskoj svesti. Abakus je bio samo mehaničko sredstvo, koje je služilo čoveku samo kao pomoć. </p><p>Na abakusu se računa tako što se kroz dodavanje pozitivnih ili negativnih brojeva, nova dobijena suma neposredno podešava kao rezultat. Pri učenju korišćenja abakusa najbitnijije je shvatiti kako za svaku početnu cifru podesiti cifru koja se sabira, odnosno koja se oduzima od nje. Kao posledica stalnog vežbanja prsti sami „shvate“ šta treba da rade tada je brojeve moguće uneti mnogo brže, nego na kalkulatoru. Ušteda vremena je postojana u operacijama sabiranja i oduzimanja. Množenje, deljenje i korenovanje su zasnovani na vižestrukom sabiranju i oduzimanju. </p> <div class="mw-heading mw-heading2"><h2 id="Istorijat">Istorijat</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abakus_(ra%C4%8Dunanje)&veaction=edit&section=2" title="Uredi odjeljak Istorijat" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abakus_(ra%C4%8Dunanje)&action=edit&section=2" title="Uredi kôd odjeljka Istorijat"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>O poreklu abakusa se raspravlja; zna se da su mnoge drevne civilizacije koristile abakus kao pomagalo u brojenju i računanju. Prvi abakusi su nastali na prostorima indo-kineskih kultura od perioda 1100. godine pne. Jedne od prvih civilizacija koje su koristile abakus su bile <a href="/wiki/Kina" title="Kina">Kina</a> i <a href="/wiki/Mesopotamija" class="mw-redirect" title="Mesopotamija">Mesopotamija</a>. Prva vrsta abakusa je bila zasnovana na ravnoj kamenoj ploči koja je bila posuta peskom ili prašinom, gde su jednim prstom ili perom upisivali slova i reči. Brojeve su dodavali uz pomoć kamenčića i tako izvodili računske operacije. Od tada su se razvile različite vrste abakusa; najpopularniji od njih su bili napravljeni da bi se na njima moglo računati u dekadnom brojnom sistemu. Upotreba reči abakus datira još od 1387. kada je engleski jezik kao pozajmicu uzeo reč iz latinskog jezika da bi tom rečju označili peščani abakus. Latinska reč potiče od reči abakos, što je oblik genitiva grčke reči abah (što znači tabla za računanje). Ova grčka reč je takođe imala značenje- tabla posuta peskom ili prahom na kojoj se crtaju geometrijske figure. Neki lingvisti tvrde da ova reč: ili ima semitski koren, ābāq, hebrejska reč za - pesak, ili feničanski koren, abak, sa značenjem pesak, takođe. </p> <div class="mw-heading mw-heading3"><h3 id="Grčki_abakus"><span id="Gr.C4.8Dki_abakus"></span>Grčki abakus</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abakus_(ra%C4%8Dunanje)&veaction=edit&section=3" title="Uredi odjeljak Grčki abakus" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abakus_(ra%C4%8Dunanje)&action=edit&section=3" title="Uredi kôd odjeljka Grčki abakus"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Tabla pronađena na ostrvu <a href="/wiki/Salamina" title="Salamina">Salamina</a> 1846. datira iz 300. godine pne, što je najstarija otkrivena ploča namenjena samo računaju. Za ovu tablu se pretpostavlja da je prvobitno služila za igru. On se sastojao od table i belih mermernih kamenčića, dužine 149 cm, širine 75 cm i debljine 4,5 cm. U sredini table je bio set od pet paralelnih urezanih linija podjednakog razmaka između vertikalnih linija koje ih dele. Ispod ovih linija se nalazi širok prostor sa horizontalnom linijom. Ispod ove linije je druga grupa od jedanaest paralelnih linija, opet podeljenih u dva dela sa linijom koja je normalana sa njima, ali sa polukrugom na vrhu preseka; treća, šesta i deveta od ovih linija su obeležene krstićem gde se nalazi presek sa vertikalnom linijom. </p> <div class="mw-heading mw-heading3"><h3 id="Rimski_abakus">Rimski abakus</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abakus_(ra%C4%8Dunanje)&veaction=edit&section=4" title="Uredi odjeljak Rimski abakus" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abakus_(ra%C4%8Dunanje)&action=edit&section=4" title="Uredi kôd odjeljka Rimski abakus"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><div class="noprint relarticle mainarticle"><i>Glavni članak: <a href="/w/index.php?title=Rimski_abakus&action=edit&redlink=1" class="new" title="Rimski abakus (stranica ne postoji)">Rimski abakus</a></i></div></dd></dl> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:RomanAbacusRecon.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/RomanAbacusRecon.jpg/200px-RomanAbacusRecon.jpg" decoding="async" width="200" height="159" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/b/b5/RomanAbacusRecon.jpg 1.5x" data-file-width="300" data-file-height="239" /></a><figcaption>Rimski abakus</figcaption></figure> <p>Postojale su dve vrste rimskog abakusa: kalculi i ručni abakus, koji su pravljeni od kamena ili metala. Abakus iz <a href="/wiki/Anti%C4%8Dki_Rim" title="Antički Rim">Rimskog carstva</a> sastoji se od osam dužih proreza u kojima se nalazi po pet kuglica i osam kraćih proreza koji su ili sa po jednom kuglicom, ili su bez kuglica. Prorez obeležen sa I označavao je jedinice, prorez označen sa X označavo je desetice i tako dalje do miliona. Kuglice u kraćem prorezu označavaju pet jedinica, pet desetica itd, veoma značajano za bi-kvinarni sistem, najverovatnije povezano sa rimskim ciframa. Kraći prorezi sa desne strane mogli su da se koriste za pravljenje rimskih mernih jedinica. </p><p>Računanje je bilo zasnovano na vrednostima kuglica koje su se povlačile gore-dole po prorezu da bi označile vrednost svake kuglice. </p> <div class="mw-heading mw-heading3"><h3 id="Kineski_abakus">Kineski abakus</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abakus_(ra%C4%8Dunanje)&veaction=edit&section=5" title="Uredi odjeljak Kineski abakus" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abakus_(ra%C4%8Dunanje)&action=edit&section=5" title="Uredi kôd odjeljka Kineski abakus"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Pre otkrića kineskog abakusa za računanje i prebrojavanje koristile su se razne sprave: štapovi za računanje, kosti na kojima su urezivali količinu, ili meru nečega. Suanpan (suànpám), kako su ga Kinezi i nazivali, u osnovi je bio sličan rimskom abakusu, samo sa malo drugačijom konstrukcijom, koja je bila namenjena dekadnom i heksadekadnom brojnom sistemu. Njegova visina je bila oko 20 cm (8 inča), a širina je mogla da bude različita, što je zavisilo od njegove namene. Uglavnom su kineski abakusi bili podeljeni na dva dela od po sedam redova. Svaki red u gornjem delu table je imao po dve kuglice, a u donjem delu redovi su imali po pet kuglica prilagođeno i za dekadni i za heksadekadni brojni sistem. Kuglice su bile pravljene od drveta. Računalo se njihovim pomeranjem gore-dole. Kineski abakus je korišćen i u druge svrhe. Za razliku od običnih dečijih računaljki, kineskim abakusom je moglo da se vrši množenje, deljenje i kvadratni i kubni koren. </p><p>Veza između suanpana i rimskog abakusa postoji. Verovatno je jedan uticao na nastanak drugog. Uz to postoje i dokazi da su ova dva carstva sarađivala u trgovini. Međutim, može da se desi da je veza između ove dve sprave slučajna. Bilo kako bilo, oba su svoje računanje zasnivala na računanju sa deset prstiju. Rimski abakus je imao 4+1 kuglicu za svaku decimalnu poziciju (kao i japanski abakus), a kod kineskog abakusa je bilo 5+2 kglice do decimalnoj poziciji, što je dozvoljavalo da se rešavaju malo složenija računanja i aritmetički algoritmi u <a href="/wiki/Heksadecimalni_sistem" title="Heksadecimalni sistem">heksadecimalnom sistemu</a>. U kineskom i japanskom abakusu kuglice se pomearaju po žici, a kod rimskog proreze u kojima su smeštene kuglice (ili kamenčići), što je usporavalo računanje. Zato je rimski abakus upotrebljavan samo za prostije računske radnje. 12. novembra 1946. u takmičenju između kineskog abakusa i tadašnjeg <a href="/wiki/Kalkulator" title="Kalkulator">kalkulatora</a>, abakus je pobedio sa 4:1. </p> <div class="mw-heading mw-heading3"><h3 id="Japanski_abakus">Japanski abakus</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abakus_(ra%C4%8Dunanje)&veaction=edit&section=6" title="Uredi odjeljak Japanski abakus" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abakus_(ra%C4%8Dunanje)&action=edit&section=6" title="Uredi kôd odjeljka Japanski abakus"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Soroban.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Soroban.JPG/300px-Soroban.JPG" decoding="async" width="300" height="88" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Soroban.JPG/450px-Soroban.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/72/Soroban.JPG/600px-Soroban.JPG 2x" data-file-width="629" data-file-height="184" /></a><figcaption>Soroban</figcaption></figure> <p>Soroban je japanski abakus, modifikovana verzija kineskog suanpana. Ovaj abakus je nastao oko 1600. godine, tada se pojavljuje još i u <a href="/wiki/Koreja" title="Koreja">Koreji</a>. Japanski abakus, u odnosu na kineski, eliminisao je po jednu kuglicu iz svake kolone, a kasnije još po jednu iz svake kolone iz donjeg dela table i tako ga načinili samo za <a href="/wiki/Decimalni_sistem" class="mw-redirect" title="Decimalni sistem">decimalni sistem</a>. Japanci su takođe eliminisali i Quichu (kineska tabla za deljenje), ali kineska tabla za deljenje je i dalje nastavila da se korsti. Zatim dolazi do borbe između table za množenje i table za deljenje. 1920. kao „pobednik “ u škole ulazi tabla za množenje. Broj štapića po kojima su nizane kuglice su sa 21 porasle prvo na 23, 27, sve do 31. Ovo je omogućilo predstavljanje više različitih brojeva i više cifara u isto vreme. </p><p>Soroban se izučavao kao lekcija iz matematike u osnovnim školama, zato što je tako bilo najlakše predstaviti dekadni sistem vizuelno. Soroban je bio oko 8cm visok. Kuglice na sorobanu su obično bile spojene u grupe od po dve, da bi se olakšalo njihovo pomeranje. U osnovnim školama učenici mogu da koriste dve vrste sorobana: prvi je imao po jednu kuglicu na svakoj žici u gornjem delu table, a u donjem po pet kuglica na svakoj žici; drugi je imao po jednu u gornjem delu, a donjem po četiri kuglice na svakoj žici. Bez obzira na prednost ručnih kalkulatora, neki roditelji pre šalju decu u one škole gde će računanje prvo učiti na sorobanu, zato što je ovaj način računanja blizak <a href="/w/index.php?title=Mentalna_aritemetika&action=edit&redlink=1" class="new" title="Mentalna aritemetika (stranica ne postoji)">mentalnoj aritmetici</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Ruski_abakus">Ruski abakus</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abakus_(ra%C4%8Dunanje)&veaction=edit&section=7" title="Uredi odjeljak Ruski abakus" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abakus_(ra%C4%8Dunanje)&action=edit&section=7" title="Uredi kôd odjeljka Ruski abakus"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Schoty_abacus.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Schoty_abacus.jpg/200px-Schoty_abacus.jpg" decoding="async" width="200" height="232" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Schoty_abacus.jpg/300px-Schoty_abacus.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Schoty_abacus.jpg/400px-Schoty_abacus.jpg 2x" data-file-width="919" data-file-height="1064" /></a><figcaption>Ruski abakus</figcaption></figure> <p>Ruski abakus, sčёtы, sastoji se od jednog okvira u kom se nalaze žice na koje je nanizano po deset kuglica(osim jedne na kojoj se nalaze po četiri kuglice). Ruski abakus se postavlja vertikalno sa žicama sleva na desno. Računaljka se dovodi u početno stanje kada su sve kuglice usmerene u desno. </p><p>Dok se vrši operacija množenja, kuglice se pomeraju na levo. Za lepši pregled dve kuglice (peta i šesta) u sredini svake žice su uglavnom drugačije obojene od ostalih kuglica. Isto tako leva kuglica na jednoj od hiljade žica (ili milion, zavisi koliko ih ima može takođe biti različite boje). Ruski abakus se i danas koristi u trgovini, u prodavnicama širom bivšeg <a href="/wiki/Sovjetski_Savez" title="Sovjetski Savez">Sovjetskog Saveza</a>, iako se u mnogim školama više ne uči na njemu. </p> <div class="mw-heading mw-heading3"><h3 id="Drevni_američki_abakus"><span id="Drevni_ameri.C4.8Dki_abakus"></span>Drevni američki abakus</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abakus_(ra%C4%8Dunanje)&veaction=edit&section=8" title="Uredi odjeljak Drevni američki abakus" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abakus_(ra%C4%8Dunanje)&action=edit&section=8" title="Uredi kôd odjeljka Drevni američki abakus"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Neki izvori pominju i korišćenje abakusa po imenu <b>nepohualtzintzin</b> u drevnoj <a href="/wiki/Asteci" title="Asteci">astečkoj</a> kulturi. <a href="/wiki/Carstvo_Inka" title="Carstvo Inka">Inke</a> su koristile spravu koja je imala ime quipu. Kipu je imao kanap koji je bio postavljen horizontalno i viseću užad. Užad su bila različith boja, razmak između čvorova je bio različit. Svaka boja je imala svoje značenje, svako uže je bilo namenjeno za određeni pojam ili stvar. Ali on je pre imao namenu za beleženje nekih događaja ili za brojčani popis stvari jednog domaćinstva, nego kao alatka za računanje. Neki naučnici tvrde da to nije bio najraniji oblik numeričke sprave, već jedan od najranijih oblika pisanja. Kao takav oblik zapisa po naučniku Grau Urton-u, kipu je bio jedan oblik koda, slični <a href="/wiki/Binarni_sistem" title="Binarni sistem">binarnom kodu</a> u <a href="/wiki/Ra%C4%8Dunar" class="mw-redirect" title="Računar">računarima</a>. Inke su za računanje koristile uupana, koji je korišćen i posle osvajanje <a href="/wiki/Peru" title="Peru">Perua</a>. Princip računanja na ovoj spravi bio je nepoznat sve do 2001. Upoređujući nekoliko uupana zaključeno je da je računanje bilo kao i kod <a href="/wiki/Leonardo_Fibona%C4%8Di" class="mw-redirect" title="Leonardo Fibonači">Fibonačijevog</a> niza: 1,1,2,3,5,8… </p> <div class="mw-heading mw-heading3"><h3 id="Školski_abakus"><span id=".C5.A0kolski_abakus"></span>Školski abakus</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abakus_(ra%C4%8Dunanje)&veaction=edit&section=9" title="Uredi odjeljak Školski abakus" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abakus_(ra%C4%8Dunanje)&action=edit&section=9" title="Uredi kôd odjeljka Školski abakus"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Kugleramme.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Kugleramme.jpg/200px-Kugleramme.jpg" decoding="async" width="200" height="214" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Kugleramme.jpg/300px-Kugleramme.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Kugleramme.jpg/400px-Kugleramme.jpg 2x" data-file-width="1675" data-file-height="1793" /></a><figcaption>Školski abakus - Računaljka</figcaption></figure> <p>Širom sveta abakusi se koriste u predškolskim ustanovama i osnovnim školama, kao pomagalo u učenju osnovnih računskih radnji i aritmetike. U zapadnim zemljama okvir sa kuglicama sličan je ruskom abakusu, samo što oni imaju žice postavljene vertikalno. Abakus se koristi i kao igračka, koja se pravi ili od drveta, ili od plastike. Ova vrsta abakusa se koristi da predstavi brojeve bez dodeljivanja vrednosti pozicijama na kojima se nalazi kuglica. Svaka kuglica i svaka žica imaju istu vrednost i služe za predstavljanje brojeva do sto. Dok se množi kuglice se pomeraju u desno. Najveća edukativna prednost abakusa u odnosu na slobodne kuglice, jeste lakše učenje u brojenju i računanju, tako da učenici nauče da grupišu stvari po deset, što je osnova dekadnog brojnog sistema. </p><p>U srpskom jeziku se koristi termin - računaljka. </p> <div class="mw-heading mw-heading3"><h3 id="Abakus_kod_slepih">Abakus kod slepih</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abakus_(ra%C4%8Dunanje)&veaction=edit&section=10" title="Uredi odjeljak Abakus kod slepih" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abakus_(ra%C4%8Dunanje)&action=edit&section=10" title="Uredi kôd odjeljka Abakus kod slepih"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Abakus koriste i pojedinci koji ne mogu da vide. Oni ga korste da predstave matematičke funkcije kao što su množenje, deljenje, oduzimanje i sabiranje, kvadratni i kubni koren. Iza žica na kojima su kuglice stavlja se gumeni ili neki drugi meki materijal da se kuglice ne pomerale dok slepi dodirju prstima kuglice. </p><p>U skorije vreme, abakus je zamenjen električnim kalkulatorima sa zvukom, ali samo u onim zemljama, gde su pristupačni i gde mogu da se priušte. Međutim i onde gde je moguće priuštiti ove kalkulatore, slepi se pre odlučuju za abakuse. Slepa deca se u njihovim specijalnim školama uče prvo na ovim spravama da sabiraju, pa tek onda koriste kalkulatore, kao kod dece koja mogu da vide, prvo koriste računaljke, pa tek onda kalkulatore. </p> <div class="infobox sisterproject" style="width: 300px"> <div style="float: left;"><figure class="mw-halign-none" typeof="mw:File"><a href="https://commons.wikimedia.org/wiki/Category:Abacus" title="commons:Category:Abacus"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/15px-Commons-logo.svg.png" decoding="async" width="15" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/23px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a><figcaption></figcaption></figure></div> <div style="margin-left: 20px;"><i><b><a href="https://commons.wikimedia.org/wiki/Category:Abacus" class="extiw" title="commons:Category:Abacus">Abakus (računanje)</a></b></i> na <a href="https://commons.wikimedia.org/wiki/Glavna_stranica_-_%D0%93%D0%BB%D0%B0%D0%B2%D0%BD%D0%B0_%D1%81%D1%82%D1%80%D0%B0%D0%BD%D0%B8%D1%86%D0%B0" class="extiw" title="commons:Glavna stranica - Главна страница">Wikimedijinoj ostavi</a> </div> </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="" lang="sh-Latn" dir="ltr">Izvor: <a dir="ltr" href="https://sh.wikipedia.org/w/index.php?title=Abakus_(računanje)&oldid=42233567">https://sh.wikipedia.org/w/index.php?title=Abakus_(računanje)&oldid=42233567</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:Sprave" title="Kategorija:Sprave">Sprave</a></li><li><a href="/wiki/Kategorija:Ra%C4%8Dunanje" title="Kategorija:Računanje">Računanje</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" lang="sh-Latn" dir="ltr"> <ul id="footer-info"> <li id="footer-info-lastmod"> Ova stranica je posljednji put izmijenjena 19. novembra 2024. u 14:55.</li> <li id="footer-info-copyright">Tekst je dostupan pod licencom <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-ShareAlike</a>; mogu se primijeniti i dodatni uslovi. 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