{"id":5651,"date":"2025-10-11T00:00:00","date_gmt":"2025-10-10T21:00:00","guid":{"rendered":"https:\/\/elmeistrai.lt\/?p=5651"},"modified":"2025-10-06T16:00:59","modified_gmt":"2025-10-06T13:00:59","slug":"abako-skaiciavimo-menas-seniausias-kalkuliatorius","status":"publish","type":"post","link":"https:\/\/elmeistrai.lt\/fr\/abako-skaiciavimo-menas-seniausias-kalkuliatorius\/","title":{"rendered":"Abako skai\u010diavimo menas: seniausias kalkuliatorius"},"content":{"rendered":"

Kai skai\u010diai dar netur\u0117jo ekran\u0173<\/h2>\n\n\n\n

\u017dinot, kartais pagalvoju, kaip mes i\u0161vis i\u0161gyvenome be skai\u010diuotuv\u0173 telefonuose. Bet dar labiau stebina, kaip \u017emon\u0117s prie\u0161 t\u016bkstan\u010dius met\u0173 sugeb\u0117jo valdyti sud\u0117tingus skai\u010diavimus be jokios elektronikos. Atsakymas paprastas \u2013 abakas. \u0160is senovinis \u012frankis, kur\u012f daugelis laiko paprastu \u017eaisleliu, i\u0161 tikr\u0173j\u0173 buvo tikra technologin\u0117 revoliucija savo laikais.<\/p>\n\n\n\n

Abakas \u2013 tai r\u0117melis su virvel\u0117mis ar strypais, ant kuri\u0173 u\u017emaunami karoliukai ar diskeliai. Skamba paprasta? Galb\u016bt. Bet \u0161is \u012frankis leido \u017emon\u0117ms atlikti sud\u0117tingus matematinius veiksmus grei\u010diau nei daugelis \u0161iuolaikini\u0173 \u017emoni\u0173 gali padaryti su popieriumi ir pie\u0161tuku. Kai kurie patyr\u0119 abako naudotojai net \u0161iandien gali lenktyniaoti su elektroniniais skai\u010diuotuvais paprastuose veiksmuose.<\/p>\n\n\n\n

Kelion\u0117 per am\u017eius ir \u017eemynus<\/h2>\n\n\n\n

Tiksliai niekas ne\u017eino, kur ir kada atsirado pirmasis abakas. Archeologai mano, kad pirmieji skai\u010diavimo \u012frankiai gal\u0117jo b\u016bti naudojami dar Mesopotamijoje ma\u017edaug prie\u0161 5000 met\u0173. Tiesiog \u012fsivaizduokite \u2013 kai egiptie\u010diai stat\u0117 piramides, ka\u017ekas jau stumd\u0117 karoliukus ant virveli\u0173.<\/p>\n\n\n\n

Seniausia fizin\u0117 abako forma, kuri\u0105 radome, yra Salamino plok\u0161t\u0117 i\u0161 Graikijos, datuojama ma\u017edaug 300 m. prie\u0161 Krist\u0173. Tai buvo marmuro plok\u0161t\u0117 su i\u0161rai\u017eytomis linijomis, ant kuri\u0173 d\u0117davo akmenukus ar metalo diskus. Rom\u0117nai v\u0117liau suk\u016br\u0117 savo versij\u0105, vadinam\u0105 „calculi” \u2013 nuo \u010dia, beje, ir kilo \u017eodis „kalkuliatorius”.<\/p>\n\n\n\n

Bet tikr\u0105j\u0105 abako \u0161lov\u0119 suk\u016br\u0117 Azija. Kinijoje apie II am\u017ei\u0173 atsirado „suanpan” \u2013 klasikinis kini\u0161kas abakas su dviem karoliukais vir\u0161uje ir penkiais apa\u010dioje. Japonai v\u0117liau \u0161\u012f dizain\u0105 patobulin\u0119 suk\u016br\u0117 „soroban” \u2013 kompakti\u0161kesn\u0119 versij\u0105 su vienu karoliuku vir\u0161uje ir keturiais apa\u010dioje. Rusijoje populiarus buvo „schoty” \u2013 abako versija su de\u0161im\u010dia karoliuk\u0173 kiekvienoje eilut\u0117je.<\/p>\n\n\n\n

Kaip \u0161itas dalykas i\u0161 tikr\u0173j\u0173 veikia<\/h2>\n\n\n\n

Pa\u017evelkime \u012f klasikin\u012f japoni\u0161k\u0105 soroban \u2013 jis puikiai iliustruoja abako logik\u0105. \u012esivaizduokite r\u0117mel\u012f su keliais horizontaliais strypais. Kiekvienas strypas atstovauja skaitmen\u0173 kategorij\u0105: vienetai, de\u0161imtys, \u0161imtai ir taip toliau. Strypas yra padalintas \u012f dvi dalis horizontalia skersine.<\/p>\n\n\n\n

Apatin\u0117je dalyje yra keturi karoliukai, kiekvienas rei\u0161kia „1”. Vir\u0161utin\u0117je dalyje \u2013 vienas karoliukas, kuris rei\u0161kia „5”. Kai karoliukas priartinamas prie skersin\u0117s, jis „aktyvuojamas” ir \u012fskai\u010diuojamas. Kai nutolina \u2013 jo vert\u0117 nebeskai\u010diuojama.<\/p>\n\n\n\n

Tarkime, norite parodyti skai\u010di\u0173 7. Paimate vienet\u0173 stryp\u0105, priartinate vir\u0161utin\u012f karoliuk\u0105 (tai 5) ir du apatinius karoliukus (dar 2). Sud\u0117j\u0119 gauname 7. Nor\u0117dami parodyti 23, vienet\u0173 stryp\u0105 nustatote \u012f 3 (trys apatiniai karoliukai), o de\u0161im\u010di\u0173 stryp\u0105 \u012f 2 (du apatiniai karoliukai).<\/p>\n\n\n\n

Sud\u0117tis ir atimtis abaku atliekama judant nuo de\u0161in\u0117s \u012f kair\u0119 arba atvirk\u0161\u010diai, priklausomai nuo tradicijos. Kai viename stryp\u0435 surenkate daugiau nei 9, „perkeliate” vien\u0105 karoliuk\u0105 \u012f kit\u0105 stryp\u0105 \u2013 kaip mes ra\u0161ydami perkeliame skai\u010di\u0173 \u012f kit\u0105 skilt\u012f. Daugyba ir dalyba reikalauja daugiau praktikos, bet principas lieka tas pats \u2013 tai serija sud\u0117\u010di\u0173 ir atim\u010di\u0173.<\/p>\n\n\n\n

Kod\u0117l pir\u0161tai \u010dia svarbiausi<\/h2>\n\n\n\n

\u0160tai ko daugelis nesupranta apie abak\u0105 \u2013 tai ne tik mechaninis \u012frankis. Tai savoti\u0161ka s\u0105saja tarp fizinio judesio, vizualinio suvokimo ir protinio skai\u010diavimo. Patyr\u0119 abako naudotojai i\u0161vysto tai, kas vadinama „mentaliniu abaku” \u2013 jie gali \u012fsivaizduoti abak\u0105 savo galvoje ir atlikti skai\u010diavimus be fizinio \u012frankio.<\/p>\n\n\n\n

Japonijoje ir Kinijoje vaikai mokyklose vis dar mokomi naudoti abak\u0105. Tyrimai rodo, kad tai stiprina ne tik matematines, bet ir bendras kognityvinius geb\u0117jimus. Vaikai, mokantys naudoti abak\u0105, da\u017enai geriau suvokia skai\u010di\u0173 santykius, grei\u010diau atlieka skai\u010diavimus ir turi geresn\u0119 koncentracij\u0105.<\/p>\n\n\n\n

Pir\u0161t\u0173 judesiai ant abako tampa automatiniais, kaip klavi\u0161\u0173 spausdinimas klaviat\u016broje ne\u017ei\u016brint \u012f j\u0105. Kai kurie ekspertai gali atlikti sud\u0117tingus skai\u010diavimus tiesiog judindami pir\u0161tus ore, tarsi liest\u0173 nematomo abako karoliukus. Tai primena tai, kaip muzikantai gali „groti” muzik\u0105 galvoje, judindami pir\u0161tus.<\/p>\n\n\n\n

Nuo prekybos aik\u0161\u010di\u0173 iki kosmoso program\u0173<\/h2>\n\n\n\n

Per istorij\u0105 abakas buvo naudojamas visur, kur reik\u0117jo skai\u010diuoti. Viduram\u017ei\u0173 pirkliai j\u012f ne\u0161iodavosi kaip mes \u0161iandien ne\u0161iojam\u0117s telefonus. Bankai naudojo abak\u0105 pinig\u0173 skai\u010diavimui. Mokes\u010di\u0173 rink\u0117jai \u2013 pajam\u0173 apskai\u010diavimui. Net statybininkai naudojo j\u012f med\u017eiag\u0173 kiekiui apskai\u010diuoti.<\/p>\n\n\n\n

Azijoje abakas i\u0161liko populiarus net elektronini\u0173 skai\u010diuotuv\u0173 eroje. Japonijos parduotuv\u0117se ir \u0161iandien galite matyti pardav\u0117jus, naudojan\u010dius soroban. Kinijos turgaviet\u0117se prekiautojai vis dar greitai stumd\u0117 karoliukus, skai\u010diuodami kainas ir gr\u0105\u017e\u0105. Kod\u0117l? Nes jiems tai grei\u010diau ir patikimiau nei spaudin\u0117ti skai\u010dius \u012f skai\u010diuotuv\u0105.<\/p>\n\n\n\n

\u012edomus faktas \u2013 1946 metais Tokijuje \u012fvyko var\u017eybos tarp japono su soroban ir amerikie\u010dio su elektromechaniniu skai\u010diuotuvu. Japonas laim\u0117jo keturis i\u0161 penki\u0173 test\u0173. Tai buvo simbolin\u0117 akimirka, parod\u017eiusi, kad sena technologija ne visada yra prastesn\u0117 u\u017e nauj\u0105.<\/p>\n\n\n\n

Mokslinis po\u017ei\u016bris \u012f karoliuk\u0173 st\u016bmym\u0105<\/h2>\n\n\n\n

\u0160iuolaikiniai neuromokslininkai susidom\u0117jo abaku kaip \u012frankiu smegen\u0173 tyrimams. Funkcin\u0117s magnetinio rezonanso tomografijos (fMRI) tyrimai rodo, kad abako naudojimas aktyvuoja kitas smegen\u0173 sritis nei \u012fprastas skai\u010diavimas. Patyr\u0119 abako naudotojai labiau aktyvuoja vaizdin\u0117s atminties ir erdvinio m\u0105stymo sritis.<\/p>\n\n\n\n

Yra teorija, kad abakas padeda i\u0161vengti „darbo atminties perkrovos”. Kai skai\u010diuojame galvoje, turime laikyti atmintyje tarpines vertes, o tai apkrauna smegenis. Su abaku \u0161ios vert\u0117s yra fizi\u0161kai reprezentuojamos karoliukais, tod\u0117l smegenys gali sutelkti d\u0117mes\u012f \u012f pa\u010di\u0105 skai\u010diavimo logik\u0105.<\/p>\n\n\n\n

Kai kurie tyrimai rodo, kad vaik\u0173, mokan\u010di\u0173 naudoti abak\u0105, IQ rodikliai gali pager\u0117ti. Nors tai dar diskutuotina tema, akivaizdu, kad abako treniruot\u0117 stiprina daugel\u012f kognityvini\u0173 funkcij\u0173: d\u0117mes\u012f, koncentracij\u0105, atmint\u012f, erdvin\u012f m\u0105stym\u0105 ir net k\u016brybi\u0161kum\u0105.<\/p>\n\n\n\n

Kaip prad\u0117ti mokytis \u0161io senovinio meno<\/h2>\n\n\n\n

Jei jus sudomino abakas, prad\u0117ti mokytis niekada ne per v\u0117lu. Pirmiausia reikia \u012fsigyti pat\u012f \u012frank\u012f. Rekomenduo\u010diau japoni\u0161k\u0105 soroban su 1-4 karoliuk\u0173 sistema \u2013 jis paprastesnis nei kini\u0161kas 2-5 variantas. Galite rasti nebrangi\u0173 plastikinio abako variant\u0173 internete u\u017e 10-20 eur\u0173.<\/p>\n\n\n\n

Prad\u0117kite nuo papras\u010diausi\u0173 dalyk\u0173. I\u0161mokite, kaip reprezentuoti skai\u010dius nuo 0 iki 9 viename stryp\u0435. Praktikuokit\u0117s, kol tai taps automati\u0161ku. Tada pereikite prie dvi\u017eenklio skai\u010di\u0173, trij\u0173 \u017eenki\u0173 ir taip toliau. Nesiskubinkite \u2013 geriau gerai \u012fsisavinti pagrindus nei skub\u0117ti \u012f sud\u0117tingesnius dalykus.<\/p>\n\n\n\n

Sud\u0117\u010diai ir atim\u010diai yra konkre\u010dios taisykl\u0117s ir pir\u0161t\u0173 judesi\u0173 sekos. YouTube pilna mokom\u0173j\u0173 vaizdo \u012fra\u0161\u0173, kurie tai demonstruoja. Rekomenduoju ie\u0161koti japon\u0173 mokytoj\u0173 \u2013 jie turi \u0161imtme\u010di\u0173 patyrim\u0105, perduodam\u0105 i\u0161 kartos \u012f kart\u0105. Praktikuokit\u0117s kasdien bent 15 minu\u010di\u0173. Kaip ir bet koks \u012fg\u016bdis, abako naudojimas reikalauja nuoseklaus kartojimo.<\/p>\n\n\n\n

Kai \u012fvaldysite sud\u0117t\u012f ir atimt\u012f, galite pereiti prie daugybos ir dalybos. Tai sud\u0117tingiau, bet principas tas pats. V\u0117liau galite mokytis „mentalinio abako” \u2013 vizualizuoti abak\u0105 galvoje ir atlikti skai\u010diavimus be fizinio \u012frankio. Tai auk\u0161\u010diausias abako meistri\u0161kumo lygis.<\/p>\n\n\n\n

Kai karoliukai tampa filosofija<\/h2>\n\n\n\n

Galiausiai, abakas yra daugiau nei tik skai\u010diavimo \u012frankis. Jis yra tiltas tarp praeities ir dabarties, tarp fizinio ir mentalinio, tarp paprasto ir sud\u0117tingo. \u0160is senovinis i\u0161radimas primena mums, kad technologin\u0117 pa\u017eanga ne visada rei\u0161kia sud\u0117tingesn\u0119 elektronik\u0105.<\/p>\n\n\n\n

Kartais pati papras\u010diausia id\u0117ja \u2013 karoliukai ant virveli\u0173 \u2013 gali b\u016bti ne\u012ftik\u0117tinai galinga. Abakas i\u0161gyveno t\u016bkstantme\u010dius ne d\u0117l to, kad nebuvo geresni\u0173 alternatyv\u0173, o d\u0117l to, kad jis puikiai atlieka savo funkcij\u0105. Jis greitas, patikimas, nereikalauja baterij\u0173 ar elektros, niekada neu\u017esikarsta ir nesul\u016b\u017eta nuo kritimo.<\/p>\n\n\n\n

\u0160iandien, kai m\u016bs\u0173 telefonai gali atlikti milijonus operacij\u0173 per sekund\u0119, abakas vis dar turi savo viet\u0105. Jis mokomas mokyklose, naudojamas parduotuv\u0117se ir tyrin\u0117jamas mokslininkuose. Jis primena mums, kad kartais seniausios technologijos yra geriausios ne tod\u0117l, kad jos senos, o tod\u0117l, kad jos veikia.<\/p>\n\n\n\n

Galb\u016bt verta i\u0161mokti naudoti abak\u0105 ne d\u0117l praktin\u0117s naudos \u2013 juk visi turime skai\u010diuotuvus ki\u0161en\u0117je. Bet d\u0117l to, k\u0105 tai moko apie skai\u010dius, apie koncentracij\u0105, apie ry\u0161\u012f tarp rank\u0173 ir proto. D\u0117l to, kad tai jungia mus su t\u016bkstan\u010diais kart\u0173 \u017emoni\u0173, kurie prie\u0161 mus st\u016bm\u0117 tuos pa\u010dius karoliukus, spr\u0119sdami tas pa\u010dias matematines problemas. Ir tai, ties\u0105 sakant, gana nuostabu.<\/p>","protected":false},"excerpt":{"rendered":"

Kai skai\u010diai dar netur\u0117jo ekran\u0173 \u017dinot, kartais pagalvoju, kaip mes i\u0161vis i\u0161gyvenome be skai\u010diuotuv\u0173 telefonuose. Bet dar labiau stebina, kaip…<\/p>","protected":false},"author":1,"featured_media":5678,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_uag_custom_page_level_css":"","footnotes":""},"categories":[7],"tags":[],"class_list":["post-5651","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-kompiuteriu-remontas-kompiuteriai-naujienos-patarimai","wpcat-7-id"],"yoast_head":"\nAbako skai\u010diavimo menas: seniausias kalkuliatorius<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/elmeistrai.lt\/fr\/abako-skaiciavimo-menas-seniausias-kalkuliatorius\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Abako skai\u010diavimo menas: seniausias kalkuliatorius\" \/>\n<meta property=\"og:description\" content=\"Kai skai\u010diai dar netur\u0117jo ekran\u0173 \u017dinot, kartais pagalvoju, kaip mes i\u0161vis i\u0161gyvenome be skai\u010diuotuv\u0173 telefonuose. 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