KumiswaIsayensi

History of the inombolo. Ukuthuthukiswa lwati lwenombolo

Ukuthuthukiswa imibono mayelana inombolo kuyingxenye ebalulekile yomlando wethu. Kuyinto omunye eyisisekelo Tibalo.Sib, okuvumela ukuba baveze imiphumela izilinganiso noma izikweletu. I yekucala sebuningini eyeza nezazi zezinkanyezi ezikhuluma zezibalo inombolo umqondo. It is libuye lisetshenziswe Mechanics, i-physics, i-chemistry, ukufunda izinkanyezi, nezinye izinhlobo zesayensi eziningi. Ngaphezu kwalokho, ekuphileni kwansuku zonke sihlale usebenzisa izinombolo.

Ukuvela kwamadijithi

Abalandeli izimfundiso Pythagoras babekholelwa ukuthi izinombolo aqukethe essence ezingaqondakali of izinto. Lezi Abstraction zezibalo ukuhola izwe, ngokubeka oda kuwo. I Pythagoreans bazitshela ukuthi yonke imithetho ekhona emhlabeni ungaboniswa esebenzisa izinombolo. Kuyinto nemfundiso Pythagorean izinombolo waba nesithakazelo ososayensi abaningi. lezi zinhlamvu abhekwa ngesisekelo kulomhlaba, hhayi nje buyindlela uNkulunkulu abonisa ngayo umthetho-oda.

History of the inombolo ne-akhawunti uqalise nge yokuthi esiwusizo ngezindleko izinto, kanye ivolumu yizilinganiso evele nemigqa yadalwa.

Kancane kancane kwakheka umqondo izinombolo zemvelo. Le nqubo kube nzima lokuthi umuntu bakudala ayikwazanga uhlukane ukumelwa obuphathekayo abstract. Zezindleko ngenxa yalesi isikhathi ngempela kwahlala isikhathi eside ngempela. amanothi asetshenzisiwe, amatshe, izikhonkwane nokunye. N. Sasivame ngekhanda ke Izigaxana imiphumela nick nokunye. Ngemva kokusungulwa ukubhala umlando inombolo imakwe iqiniso lokuthi baqala ukusebenzisa izinhlamvu kanye nezimpawu ezikhethekile, eyayisetshenziselwa ukunciphisa isithombe lokubhala izinombolo ezinkulu . Ngokuvamile, ngiye ngizwe ukukhiqiza kabusha kule esephepheni ababebalelwa isimiso esifanayo ukuze ukuthi wasebenzisa ngolimi.

Kamuva, umbono ukubala amashumi, hhayi nje amayunithi. Ezilimini Indo-European, izihloko 100 ezahlukene izinombolo kusukela emibili kuya kweyishumi ezifanayo, njengoba amagama amashumi. Ngakho-ke, isikhathi eside, umqondo izinombolo abstract, ngisho nangaphambi lezi zilimi kwahlukaniswa.

On iminwe izindleko ekuqaleni ke kwakwandile, futhi lokhu kuchaza yokuthi iningi lezizwe kwetinhlavu zesi usesikhundleni nohlamvu olukhethekile olungu ngoba 10. I idesimali inombolo Uhlelo uya lapha. Nakuba zikhona ezehlukile. Ngokwesibonelo, 80 lihunyushwe kwelesiHeberu elithi isiFulentshi - "amane amabili" futhi 90 - ". Amane amabili plus eziyishumi" Ukusetshenziswa kwalesi iphindela akhawunti ye izinzwane nezandla. Kwahlelwa ngokufanayo netinombolo izilimi Isi-Abkhazian, isi-Ossetia kanye IsiDanishi.

I eko Georgian ngokusebenzisa ngokucace kakhudlwana. Ama-Aztec futhi Sumerians babekholelwa ekuqaleni ngakuhlanu. Kukhona futhi ongakhetha exotic ngaphezulu uphawule umlando inombolo. Ngokwesibonelo, izibalo isayensi AbaseBhabhiloni babesebenzisa sexagesimal uhlelo. Ngo okuthiwa izinhlelo "unary" isibalo ezakhiwe ukuphindaphindwa yesibonakaliso efanekisela iyunithi. Abantu lasendulo ka le ndlela esetshenziswa abantu kungathi izinkulungwane 10-11. BC. e.

Kukhona futhi uhlelo nonpositional lapho amanani ezinombolo asetshenziswa ekulobeni izimpawu akuncikile endaweni yabo inombolo ikhodi. Isebenzisa kwalokho izinombolo.

oMdala

Ulwazi wezibalo eGibhithe lasendulo namuhla kusekelwe zebungu ezimbili, okuyinto usuku kusukela cishe 1700 ngonyaka BC. e. Imininingwane Mathematical obonakaliswe kubo, ubuyele emuva isikhathi ngaphezulu lasendulo, azungeze 3500 BC. e. AmaGibhithe ayesebenzisa leli isayensi ukubala isisindo kwemitimba yabohulumende, ivolumu wesitoreji okusanhlamvu kanye nosayizi kwezitshalo endaweni intela, kanye ezidingekayo ukuze kwakhiwe inani amatshe ezakhiwe. Nokho, endaweni eyinhloko isicelo wezibalo kwaba ukufunda izinkanyezi, ehambisana ne-izibalo ikhalenda. Ikhalenda kwakudingeka ukucacisa izinsuku ngamaholide enkolo ahlukahlukene, kanye nezibikezelo zokuphela Nile izikhukhula.

Ukubhala eGibhithe lasendulo yayisekelwe hieroglyphs. Ngaleso sikhathi, uhlelo inombolo ayithelanga vavilonyanskoy. AmaGibhithe ayesebenzisa nonpositional idesimali uhlelo lapho inani lemigqa mpo kuyinto inombolo-1 kuya 9. izinhlamvu ngamunye zaphathwa izinyathelo eziyishumi. Umlando yentuthuko waseGibhithe lasendulo baqhubeka kanje. ngokubhala hieratic (ie ngekuhlanganisa) laqanjwa nge ukuvela nge-papyrus. A nohlamvu olukhethekile olungu-isetshenziswa kuwo isho izinombolo 1 kuya ku-9 kanye isibuyabuyelelo se-10, 100 njalonjalo. D. Ukuthuthukiswa izinombolo okunengqondo ngenkathi kancane. Yalotshwa njengoba isamba zimbili izingxenye numerator lingana kuze fike.

Izinombolo in Ancient Greece

On ukusetshenziswa izinhlamvu ezahlukene zamagama yasungulwa by zesi-Greek. Umlando izinombolo zemvelo kuleli zwe kugcwele yokuthi baphuze 6-3 eminyaka BC. e. uhlelo ekamelweni ukuze ukhombise iyunithi zasebenzisa ibha mpo, futhi 5, 10, 100, nokunye. d. olubhalwe kusetshenziswa izinhlamvu zokuqala amagama abo ngesiGreki. I ionic uhlelo, kamuva, lisetshenziswa ekubhekiseleni kuyo izinombolo izinhlamvu 24 asebenzayo zamagama, kanye 3 zakudala. Nokho, njengoba 9 izinombolo zokuqala (1 kuya ku 9) babe zesi eziqokiwe 1000 kuya 9000, wabekwa ngesikhathi esifanayo emgqeni mpo phambi incwadi. "M" imelela amashumi ezinkulungwane (kusukela lesiGreki "mirioi"). Ngemva kufanele Unenani ngawo ukuze wande balandela 10,000.

EGrisi ku 3rd ekhulwini BC. e. kwakukhona uhlelo zezinombolo lapho uphawu ayo zamagama sifana idijithi ngayinye. AmaGreki kusukela ekhulwini lesi-6, njengoba izinombolo, baqala ukusebenzisa izinhlamvu zokuqala eziyishumi zamagama alo. Kuleli zwe hhayi kuphela ngenkuthalo ekuthuthukiseni umlando izinombolo yemvelo, kodwa futhi Mathematics eladabuka umqondo walo wanamuhla. Ngamanye uthi, ngesikhathi lasetshenziswa noma ukusetshenziswa okwejwayelekile, noma umuntu enze imicikilisho yokushiswa ezahlukene magic, ngokusebenzisa okuzokwenza wathola onkulunkulu (ukubhula ngezinkanyezi futhi m. P.).

zesi-Roman

ERoma lasendulo, ukuhlukanisa ngezinombolo esetshenziswa, okuyinto ngaphansi kwegama wamaRoma, kanye kwalondolozwa kuze kube namuhla. Sisebenzisa ukubhekisela kuwo wonke nemigubho, ubudala, amagama izinkomfa congresses, ababebalelwa amavesi inkondlo nobe sehluko. Ngokuphinda izinombolo 1, 5, 10, 50, 100, 500, 1000, lisho sazo ngokuhluka njengoba mina, V, X, L, C, D, M amarekhodi yonke integers. Uma inombolo enkulu kuphambi ezincane, basuke kwengezwe ndawonye, uma kunesidingo phambi ngaphezulu ezincane, mithandazo emholweni ke. Inombolo eyodwa ayikwazi ukubeka izikhathi ezingaphezu kwezintathu. Kwaphela isikhathi eside amazwe Western Europe esetshenziswa njengoba zesi-Roman eziyisisekelo.

izinhlelo positional

Lezi izinhlelo lapho amanani ezinombolo abalingiswa kuncike ezindaweni zabo inombolo ikhodi. Izinzuzo zabo eziyinhloko - lula enza imisebenzi izibalo ahlukahlukene, kanye nenani elincane izinhlamvu kudingeke ukuthi ubhale izinombolo.

Kukhona impela eningi izinhlelo ezinjalo. Ngokwesibonelo, kanambambili, octal, kahlanu, idesimali, vigesimal, nabanye. Ngamunye has umlando walo.

Uhlelo ezazikhona Inca

Kip - lasendulo ngekhanda nokubala uhlelo ezazikhona Inca nabangaphambi zabo e-Andes. Akuve ehlukile. Lokhu ifindo eziyinkimbinkimbi futhi intambo Wreath Yenziwe noboya llama futhi alpaca, noma ukotini. Mhlawumbe inqwaba phezu imicu ambalwa ulenga phansi izinkulungwane ezimbili. Wayevame amakhuriya ukudlulisa imiyalezo endleleni yasebukhosini, kanye ezicini ezihlukahlukene umphakathi (njengoba uhlelo kwendawo, ikhalenda, ukulungisa imithetho nezintela, njll). Funda futhi ubhale inqwaba otolika oqeqeshiwe. Bona apotopotozwe Izigaxana iminwe, ngiphakamisa inqwaba. Okuningi kokwaziswa kuwo - izinombolo amelwe ohlelweni ledesimali.

izinombolo waseBhabhiloni

Ezibhebheni zobumba of we-cuneiform imifanekiso abaseBhabhiloni. Baye basinda kulokho eliningi eside (angaphezu kuka-500 eziyinkulungwane., Abangaba ngu-400 okuyizinto ezihlobene izibalo). Kufanele kuqashelwe ukuthi izimpande isiko abaseBhabhiloni babezitika ngofuzo ikakhulukazi Sumerians - counting indlela, we-cuneiform, njll ...

It kwakukukhulu kakhulu kunalokho waseGibhithe waseBhabhiloni nokubala uhlelo. AbaseBhabhiloni futhi Sumerians esetshenziswa positional 60-lekile okuyinto namuhla immortalized sokuhlukanisa kwesiyingi 360, kanye ihora ngomzuzu imizuzu 60 namasekhondi ngokulandelana.

I-Akhawunti e China Lasendulo

Ukuthuthukiswa umqondo inombolo kwenziwe China lasendulo. Kuleli zwe, izibalo ngokuthandana izinhlamvu ezikhethekile eziye zavela ecishe ibe yizinkulungwane 2. BC. e. Noma kunjalo, ekugcineni uphawu kuphela 3 ekhulwini BC. e. Futhi lezi zinhlamvu zisetshenziswa namuhla. Okokuqala kwaba indlela okuguquliwe zokuqopha. Inombolo 1946, isibonelo, kungenziwa emelelwa usebenzisa izinombolo zesiRoma esikhundleni sezinhlamvu njengoba 1M9S4H6. Kodwa umkhuba, izibalo enziwa ebhodini isikolo, lapho kwakukhona khona inombolo irekhodi - isikhundla, kokubili e-India hhayi idesimali, njengoba kwenza abaseBhabhiloni. izihlalo engenalutho esiqokiwe zero. mayelana 12 kuphela ekhulwini BC. e. manje uhlamvu esikhethekile kuye.

Umlando notation eNdiya

impumelelo ahlukahlukene futhi ububanzi wezibalo e-India. Leli zwe edlale indima enkulu ekuthuthukiseni nomqondo inombolo. Kulapha ukuthi idesimali isikhundla uhlelo yasungulwa, ajwayelekile kithi. AmaNdiya ahlinzekwa izinhlamvu ukubhala izinombolo ezingu-10, kanye nezinye izinguquko ekusebenziseni namuhla emazweni ngamazwe. Libuye usekela izibalo idesimali babekwa kulelizwe.

izibalo yamanje baka imifanekiso Indian, isitayela esasetshenziswa esikhangisweni se 1st ekhulwini BC. e. Ekuqaleni izinombolo Indian kwakwehla esiphundu. Okukushoyo ukuqopha izinombolo kwabayishumi ngezinga wamashumi omahlanu esetshenziswa ngesi-Sanskrit. izinombolo Okokuqala esetshenziselwa okuthiwa "amaSiriya nama-waseFenike" uhlelo, futhi ekhulwini lesi-6 BC. e. - "Brahmi", ne izinhlamvu ngazinye ngabo. Lezi mpawu, ngandlela-thile modified, babé izibalo yesimanje, ngokuthi ngesi-Arabhu namuhla.

Ongaziwa sezibalo Indian cishe ngonyaka ka-500 BC. e. Nguye owasungula isimiso esisha amarekhodi - a positional ledesimali. Yenza imisebenzi ehlukahlukene izibalo kwaba ngokungenamkhawulo kulula kunakwezinye. AmaNdiya asetshenziswa ngemuva kwalokhu ngokubala ibhodi, okuyinto aguqulelwe libeke ukurekhoda. Baye basungula algorithm for izibalo imisebenzi, kuhlanganise yokwamukela izimpande cubic kanye sikwele. Indian sezibalo Brahmagupta, owaphila ekhulwini lesi-7 nelesi, waqamba izinombolo engemihle. AmaNdiya isihambile algebra kahle. Kufanekisa kubo bacebe kakhulu Diophantus, nakuba amazwi kancane zaphazamisa.

Ukuthuthukiswa zomlando izinombolo eRussia

I izinombolo yilona imfuneko esiyinhloko ilwazi leembalo. Yena kwakufanele a look ezahlukene ngesikhathi izizwe ezihlukahlukene endala. Ukuvela kanye nokuthuthukiswa luqondane ekuseni ezingxenyeni ezahlukene zomhlaba. Okokuqala bazo zonke izizwe babe esiqokiwe namantombazane ku izinti, ngokuthi tags. Lokhu indlela ukuqopha izintela noma izikweletu esetshenziswa abantu abangakwazi ukufunda nokubhala zomhlaba. Nisike ku induku kwakuhambelana nokuka nenani lentela noma umsebenzi. Khona-ke esehlukanisa ezimbili, kusale uhhafu we lokukhokha komunye oyedwa noma okweletayo. Enye yayigcinwe endaweni yengcebo noma yomuntu obolekisayo. Bobabili neengcezu at ukukhokhelwa eqinisekisiwe ngu alo.

Izibalo abonakala ukuvela lokubhala. Yayikhumbuza namantombazane kuqala ku izinti. Kwakukhona amabheji esikhethekile ezinye zazo, ezifana 5 no-10 Zonke ababebalelwa ngaleso sikhathi awazange positional, futhi zifana wamaRoma. ERussia yasendulo, kuyilapho emazweni Western Europe esetshenziswa netinombolo roman, zamagama asetshenziswa, efana esiGrekini, kusukela ezweni lakithi, njengabanye Slavic, njengoba yaziwa, itholakala inkhulumomphendvulwano amasiko yoMbuso WaseByzantium.

I izinombolo kusuka 1 kuya 9, bese eziningi kanti kunamakhulu izinombolo Old ukuboniswa izinhlamvu Slavic zamagama (Cyrillic, langena ekhulwini lesishiyagalolunye).

Ezinye Okuhlukile umthetho. Ngakho, hhayi designated 2 "beech", ibhange wesibili e zamagama, kanti "abaholayo" (eyesithathu), njengoba incwadi W e Starorusskaya ngocansi umsindo "a". Ingabe ekupheleni zamagama, "Ukulingana" libhekisela 9 "isibungu" - 90. izincwadi ngamunye azisetshenziswa. Ukubonisa ukuthi uphawu Nanku umumo, hhayi incwadi, wabhala ngaye phezu uphawu, elibizwa ngokuthi "Tittle", "~". "Ubumnyama" libizwa ezinkulungwane. Wababiza ngokukokelezela izimpawu amayunithi. Amakhulu ezinkulungwane babizwa ngokuthi "amabutho." imibuthano zabo zazinesithombe nge amachashazi ozungeza izimpawu amayunithi. Izigidi - "leodry". Lezi zinhlamvu abangu uchazwa ngokuthi azungeza in nemibuthano amakhoma noma imisebe.

ukuqhubeka izinombolo yemvelo iphutha ekuqaleni kwekhulu nesikhombisa, lapho Indian izibalo waziwa eRussia. Kuze ngekhulu weshumi nesishiyagalombili, lalisetshenziswa Russian izinombolo Slavic. Ngemva kwalokho kuthiwa lathathelwa indawo yi-yesimanje.

Umlando izinombolo eziyinkimbinkimbi

Lezi zinombolo bathola ngokuqondene yokuthi ifomula kuhlaziywa izimpande ezothando cubic wayehlala kude. Tartaglia, i sezibalo isiNtaliyane, kwaba engxenyeni yokuqala ka ngekhulu leshumi nesithupha, inkulumo ethi Ukubalwa izimpande kwesibalo ngokusebenzisa ezinye nemingcele, ukuthola ukuthi kwakudingekile ukuze usethe uhlelo. Nokho, kwatholakala ukuthi uhlelo kwakungesona ikhambi lakho konke zibalo cubic e izinombolo zangempela. Lesi simo esiyingqayizivele sibangelwa kuchazwe Rafael Bombelli ngo-1572, lapho empeleni ukwethulwa eqela. Nokho, imiphumela anesikhathi eside akholelwa bona ezingabazekayo ososayensi abaningi, futhi kuphela yekhulu nesishiyagalolunye, umlando eqela kwaphawulwa isenzakalo esibalulekile - khona kwabo emkhomba ngemuva ukubonakala imisebenzi uKarl F. Gauss.

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