Mbiri ya nambala ziro. chiwerengero 0 ndani?

Kufunika ochuluka linaonekera munthu kuchokera pachiyambi cha mapangidwe a mtundu achikale. kachitidwe kawo n'zosangalatsa kumva, ndi mawerengero yeniyeni Buku, kupangidwa mu malo onse osiyana a chitukuko mu Iguputo ndi Babulo wakale, China ndi India, ndi American South amwenye Greece wakale. Masamu zachitika kwa chiwerengero yosavuta zinthu kuthetsa zovuta chiphunzitso mtunda. Pankhaniyi, nkhani ya ziro ali chochepa nthawi imeneyi.

Manambala ndi kanjedza

Kuchokera nullis Latin ( "ayi") anali mawu imodzi mwa mfundo zofunika kwambiri masamu. Pamafunikanso osati chizindikiro - chithunzi chimene chimapangitsa mphambu, mbiri masamu ntchito. Izi lingaliro lonse. Pakalibe alionse, kupanda, chiyambi ndi wopandamalire - maganizo nthanthi kuti mfundo izi zinali zosiyana mu Nthawi osiyana, mu machitidwe osiyana worldview.

Pamalo dongosolo chiwerengero

Mu nthawi ya mbiri isanayambe, kakyulasi thandizo kusunga zala ndi zala. manambala Gawani mu fives ndi makumi, magwero a decimal dongosolo chiwerengero likugwirizana izi. M'tsogolo, kuti atsogolere ntchito izi, mu maphunzirowa anali nicks nkhuni ndi nyama mafupa, serifs pa miyala, timiyala. zipolopolo ndi zinthu zina zazing'ono. Aliyense chinthu choterocho akuimira chiwerengero yeniyeni. chikhalidwe ofanana ndi othandiza kwambiri zitsanzo lapadera. kachitidwe amatchedwa Pamalo - manambala mtengo polemba manambala anatsimikiza ndi udindo wawo kapena kumaliseche.

Chitsanzo cha njira zosiyana, ndipo akugwiritsabe ntchito dongosolo ndi njira ya manambala kulemba watsikira kuyambira nthawi ya Roma. Mu kuti uzipereke mayunitsi, makumi, mazana ntchito zilembo za alifabeti Latin.

abacus

Kafukufuku bolodi, wopangidwa mwa maenje lolingana malo ena, amene anayikidwa timiyala kapena mikanda, ndi bwino kuti zikhalidwe za mitundu yosiyanasiyana ndi nyengo. Pali mitundu ina ya abaca - chingwe ndi mfundo kapena zingwe ndi mikanda. Siteji yotsatira chitukuko cha zipangizo zoterezi ambiri amene ntchito pamaso pa Kubwera kwa toŵerengera.

History chiwerengero cha ziro - ndiyo njira ya mapangidwe mfundo masamu ndi chiyambi cha ntchito chizindikiro, kusonyeza izo. Ndipo abacus, ndi makumi ali, tingati ndi njira zowonera ija lapadera. malo opanda kanthu mu recess chogwirizana kapena kusowa knuckle kupanga ndi mfundo umboni wa nkhani ziro bwino. Chizindikiro zikutanthauza kuti choyamba anaonekera masamu Babulo wakale ndi zakuthambo.

Babulo opanda chizindikiro

Mu chitukuko, anabadwa pakati pa mtsinje wa Tigirisi ndi Firate, Analeredwa ndi dongosolo n'zosangalatsa kumva anatengera kwa Sumerians wakale. Zinali Pamalo - manambala mtengo zimadalira malo poyerekezera ndi manambala ena. Anaikira 4-5 zikwi zaka BC. e., linamangidwa pa nambala 60. The masamu ntchito ndi zakuthambo Babulo wakale ndi akatswiri anayang'ana kwambiri choncho bulky ndi wovuta. Bwinobwino kusamalira manambala, kunali koyenera kuloweza kapena kusunga pamaso pa chulutsa manambala onse kuyambira 1 mpaka 60.

Intaneti ziro kapena chizindikiro, kuti zikuonetsa analandira Ababulo kumaliseche anaonekera awiri akonzedwa angled mphero kapena muvi. chizindikiro Izi zakhala mbali yofunika kwambiri ndipo sanali nawo ntchito masamu - kuwonjezera kapena kuchulukitsa ndi izo sizinali.

ziro kunja

Kaya masamu anu Mesopotamia ziro anayambitsa Amwenye a ku Central America - Maya ndi Ainka. Common kachitidwe chiwerengero onse anali kuti iwo sanali kukhala ndi lingaliro la ziro monga angapo.

Drevneamerikanskaya chitukuko wasiya dziko kwambiri mwa zinthu mu dera aluntha. Zovuta Mayan dongosolo kalendala ndi Ainka - chifukwa cha zaka zambiri kuzipenya zakuthambo ndi zovuta masamu. Koma osati maikwezhoni awo, chiwerengero ziro palibe chiwerengero cha kulimbikitsa chifukwa cha ntchito masamu.

zosowa zakale tione

Zotsatira waukulu wa masamu wakale Greek anali zipambano zawo mu Masamu ndi zakuthambo. Manambala mu ulaliki wawo - ndi zigawo kuti chiyambi, mathero ndi kutalika anakonzeratu. Ziro - angapo kuti palibe mu nkhani iyi, ndi yothandiza. Gawo ndi ziro yaitali masamu wakale ndi nzeru sizimatanthauza.

Imodzi mwa mfundo zikuluzikulu za chiphunzitso Aristotle ndi mawu Natura abhorret zingalowe - "Nature amadana ndi kuyamwa." Osawerengeka, kanthu, si kuli - siyana izi sizikugwirizana mu chilengedwe wakale. Choncho tanthauzo ano funso "kodi chiwerengero 0" sanali zotheka kwa Archimedes, Pythagoras kapena Euclid, ngakhale ofanana ndi chizindikiro ziro opezeka mu magome a zakuthambo kwambiri Ptolemy. Letter "Omicron" (kalata yoyamba mu mawu οὐδέν - "kanthu"), iye adzawonekera mu maselo kanthu.

Dziko ziro - India

masamu Kodi Indian anatulukira? Mahavira (850), Brahmagupta (1114), Aryabhata (476) - woyambitsa lonena, amene kwakukulukulu inkayenda dongosolo yamakono ya manambala kulemba ndi malamulo a zikuluzikulu masamu. Mbiri yakale amakhulupirira kuti dongosolo decimal wakhala anaitenga ku Amwenye Chinese, ndi chikhalidwe cha malo ake - kwa Ababulo. Amakhulupirira kuti chizindikiro ziro anali anabwereka ndi Amwenye ntchito ya Ptolemy.

The masamu woyamba amene anakonza wathunthu dongosolo n'zosangalatsa kumva, limene liri liziyenda bwino ndipo amakhala ochuluka anthu, anali Mohammed nkhokwe Musa Khwarizmi (787-850), amene ankakhala Baghdad. "Buku la nkhani Indian" naini mawerengero Arabic zafotokozedwa mwatsatanetsatane ndipo muyankhe funso ili: "Kodi chiwerengero cha 0?" Tchulani ziro m'buku lino amaona woyamba. Chilatini lomasuliridwa ntchito imeneyi, wakhala wotchuka mu Europe m'zaka XII ndipo anaika maziko a kufala kwa chidziwitso kum'mawa masamu.

Mosiyana ndi azungu, wamuyaya, anthu kum'mawa zachititsa mantha. Choncho, ziro mu maikwezhoni asayansi wakale Indian ali osati kukhala chizindikiro chachikulu cha kupanda mayunitsi ali lolingana, komanso nambala zachilengedwe, okhudza chifukwa cha mawerengedwe a. Kuwonjezera ziro, kuchulukitsa ndi 0 - zonsezi yapeza phindu zogwira ntchito masamu.

Nkosafuna kulemba manambala 1 0 chapeza maonekedwe komaliza komanso kuyamika wakale Indian Mfundo masamu, ndi zilembo, chomwe mu Arabic ku Ulaya, Aluya otchedwa Indian.

Mbiri ya nambala "ziro" kumaonekera etymology wa Kunena mwachidule masamu. Mawu "chithunzi" ali mizu Arabic ndi anachokera ku mawu akuti "al-Sifre," kutanthauza "kanthu, ziro." English "ziro" zingaoneke zofananako "marshmallow" - mphepo kuchokera kummawa - ndi ku East Europe anabwera kutsirizitsa, zomveka ndi yabwino dongosolo chiwerengero.

mawerengero Arabic mu Europe

Mmodzi wa ochirikiza yaikulu ya Arab dongosolo European digito anali wotchuka wa ku Italy masamu Leonardo Fibonacci. ntchito yake "Liber Abaci" (1202) anayambitsa asayansi European ndi zizindikiro ndi malamulo oti Aluya kulemba ntchito masamu. Mayiko woyamba ndi rationality kum'mawa masamu chitsanzo waife amene anazolowera mankhwala tsiku ndi manambala - ndi osunga ndalama ndi amalonda. Mwamsanga anatengedwa ndi amalonda Arab analipo dongosolo ndi kulemba manambala. Koma mwambo wa sayansi ku Europe kudziwa izi ndi zolimba kudzera m'ma 4, m'malo kukhazikitsidwa kwa masamu European a dongosolo wakale.

Iwo chapeza kufunika ndi kumayambiriro ziro mu ntchito sayansi amakona anayi ndi ntchito dongosolo, akufuna mu XVII m'ma Mnazareti Descartes. Zero ali oyenerera pakati, mtengo anapeza zooneka ndi zowoneka zomveka kutchula mfundo za nkhwangwa atatu.

Mu Russia anayambitsa ziro khama mchitidwe Leontiya Magnitskogo, wotchuka wolemba buku "masamu, ndiko kunena kuti sayansi numeral" (1703).

katundu ziro

Ziro, amene demarcates manambala zabwino ndi zoipa, ali wapadera katundu masamu. Ndi chiwerengero osati inteja kukhala chizindikiro positive. Kuwonjezera ndi wochotsera ndi ziro ziro sikumangotikhudza chiwerengero ndi kuchulukitsa ndi 0 amapereka ziro. Division ndi ziro imatengedwa opaleshoni phindu, lomwe nkhani ya kuphedwa mwina amavutitsa kwambiri dongosolo mu kompyuta.

Zinali pofuna kugawanitsa ndi 0 anasonyeza kuti walephera mfundo mu kompyuta dongosolo la US Navy cruiser "Yorktown" kumene kunachitika mu kugwa kwa 1997 ndipo zinachititsa kuti shutdown kosaloleka dongosolo zosagwiritsa. Molakwika zokhudzana ndi chiwerengero, kutanthauza "kanthu", kwapangitsa warship wamphamvu njakata chandamale n'kupuma.

Mtengo wa nambala iyi kwambiri chinawonjezeka ndi chitukuko cha sayansi. Zero amapezeka m'madera a mwangwiro osati masamu. Kumva pakhomo mu zowulutsira amakhala 0. uti nambala pa chiyambi cha sikelo ya zipangizo zambiri choyezera, wodziwika ndi sukulu: 0 pa Celsius - ndi yozizira koopsa mfundo ya madzi, chiyambi cha kuwerengera longitude - ziro meridian ndi zina zotero ..

Bayinare numeration, amene anali ngati maziko kwa chilengedwe cha zipangizo zamakono kompyuta ndi Pamalo chiwerengero dongosolo ndi tsinde awiri. Izi zikutanthauza kuti deta onse adalowa dongosolo computer, ndi ndiyotengera ndi osakaniza zilembo ziwiri - wina ndi ziro.

Udindo mu dziko yamakono ya makompyuta akukhala motsimikiza kuti mbali zonse za moyo, choncho mbiri ya nambala ziro, popanda zomwe maonekedwe awo sizikanatheka kukanakhala, akupitiriza.