Izingxenyana umlando izingxenyana zaso. Umlando ukuvela amafraktjhini

Omunye amagatsha nzima kakhulu wezibalo babonwa esingu namuhla. Umlando kwamafrakshini ezingaphezu kweyodwa yeminyaka. Ikhono ukwehlukana wonke ibe izingxenye iphutha endaweni waseGibhithe lasendulo neBabiloni. Kuyo yonke le minyaka, siye saba imisebenzi more xaka, wenziwa enamafrakshini, washintsha uhlobo ukurekhoda yabo. Ngamunye sezwe lasendulo kwadingeka izici zayo siqu kule "Ubuhlobo" nale legatsha wezibalo.

Kuyini ingxenyenamba?

Lapho-ke kwadingeka ukuba uhlukanise yonke ibe izingxenye ngaphandle umzamo owengeziwe, ngaleso sikhathi kuyoba khona ingxenyenamba. Umlando amafraktjhini abangu atehlukaniseki ukuze imisebenzi utilitarian. igama elithi "roll" ngokwalo elisuka Arabhu futhi lisuselwa egameni elisho "ukuba aphule, ukwehlukana." Kusukela ezikhathini zasendulo, ngalo mqondo, akukho okushintshile. Inchazelo yesimanje simi ngale ndlela: ingxenyenamba - kuyingxenye isamba izingxenye noma amayunithi. Ngakho, izibonelo enamafrakshini ukumela ukubulawa ezilandelanayo kwemisebenzi zezibalo kanye izingxenye izinombolo.

Namuhla, kunezindlela ezimbili zokuqopha kukhona. amafraktjhini Evamile futhi idesimali uvele ngezikhathi ezahlukahlukene: yangaphambili maningi lasendulo.

Bavela kudala

Ngokokuqala ngqá saqala ukuqhuba Ingxenyenamba eGibhithe naseBhabhiloni. Zezibalo indlela lamazwe amabili abe umehluko omkhulu. Nokho, ekuqaleni futhi kukhona futhi kukhona sabekwa ngendlela efanayo. Ingxenyana lokuqala kwaba nengxenye noma 1/2. Kwabe sekulandela isenzakalo esivelele ikota, yesithathu, nokunye. Ngokusho abavubukuli, umlando amafraktjhini has eminyakeni engaba ngu-5000. Ngokokuqala ngqá yisabelo ezitholakala papyrus yaseGibhithe kanye ezibhebheni zobumba waseBhabhiloni.

eGibhithe lasendulo

Izinhlobo amafraktjhini namuhla zihlanganisa okubizwa ngokuthi waseGibhithe. Ziyakwazi isamba imigomo eziningana ifomu 1 / n. Numerator - eyodwa njalo kanye zihilela - inombolo zemvelo. Kube ingxenyenamba enjalo, kungakhathaliseki ukuthi sinzima kangakanani ukuqagela eGibhithe lasendulo. Lapho kubalwa sonke sihlanganyela wazama ukurekhoda ngesimo izamba ezinje (isib 1/2 + 1/4 + 1/8). namagama ngamunye kwadingeka kuphela amafraktjhini 2/3 futhi 3/4, kanti bonke abanye zahlukaniswa imigomo. Kwakukhona amatafula ekhethekile lapho inani inombolo emelelwa isamba.

Ukukhuluma endala aziwayo njalo kwesimiso esinjalo butholakala Rhind Mathematical Papyrus, esukela ekuqaleni yesibili yeminyaka BC. Kuhlanganisa itafula kwamafrakshini nezinkinga zezibalo nezixazululo nezimpendulo, inikezwe njengoba tibalo kwamafrakshini. AbaseGibhithe wayekwazi engeza, uhlukanise futhi uphindaphinde inani share. Izingxenyana eSigodini saseNayile zalotshwa usebenzisa hieroglyphs.

Isethulo inani inombolo njengoba isamba ngokuya ifomu 1 / n, isici waseGibhithe lasendulo, esetshenziswa zezibalo, hhayi kuphela kuleli zwe. Kuze kube Ephakathi, ingxenyenamba baseGibithe babesebenzisa eGreece nakwamanye amazwe.

Ukuthuthukiswa wezibalo eBhabhiloni

Kungenjalo, ukubheka wezibalo we umbuso waseBhabhiloni. Umlando nesenzakalo zokusebenzisa izingxenyana zegazi kuhlobane ngokuqondile izici uhlelo inombolo, ngofuzo isimo basendulo balidla kumanduleli wawo, impucuko nesi-Akkad. Isisetshenziswa Settlement eBhabhiloni kwaba elula kakhudlwana futhi ephelele ezingaphezu kuka eGibhithe. Mathematics kuleli zwe ixazululwe ububanzi enkulu kakhulu imisebenzi.

AbaseBhabhiloni ukuba yahlulele ipumelelo namuhla kungenziwa walondoloza ezibhebheni zobumba cuneiform egcwele. Ngenxa izici of the impahla baye behlele kithi ngamanani amakhulu. Ngokwezazi ezithile ososayensi, zezibalo eBhabhiloni ngaphambi kokubhujiswa Pythagoras wavula theorem owaziwa, okuyinto ngokungangabazeki libonisa ukuthuthukiswa yesayensi isimo lasendulo.

Izingxenyana umlando amafraktjhini eBhabhiloni

uhlelo inombolo ibikade sexagesimal eBhabhiloni. isigaba ngasinye esisha ezahlukene kusukela odlule 60. Lesi simiso liyalondolozwa ukuhlangana nezwe lesimanje, isikhathi nama-engeli. Izingxenyana babe sexagesimal. Ukubhala usebenzisa imifanekiso ekhethekile. Njengoba eGibhithe, izibonelo enamafrakshini aqukethe izimpawu ezithile ukuze 1/2, 1/3 futhi 2/3.

uhlelo waseBhabhiloni azizange zinyamalale kanye isimo. Izingxenyana ebhaliwe ohlelweni 60-i-hexadecimal, esetshenziswa izazi zezinkanyezi zasendulo kanye Arab kanye zezibalo.

eGrisi lasendulo

Umlando kwamafrakshini okucetshiswe kancane kuka eGrisi lasendulo. Izakhamuzi Greece babekholelwa ukuthi wezibalo kufanele usebenze integers kuphela. Ngakho-ke, inkulumo ethi enamafrakshini e emakhasini azibhala yamaGreki asendulo cishe angakaze ayibone. Nokho, ezinye umnikelo oya kule legatsha wezibalo wenza Pythagoreans. Bayaqonda amafraktjhini njengecezu okungu noma ngezabelo, kanye kweyunithi indivisible yokucabanga. Pythagoras abafundi ejwayelekile theory kumafrakshini wafunda ukubamba zonke imisebenzi emine izibalo kanye ukuqhathanisa kumafrakshini nibakhulisa zifana.

Njengombusi woMbuso Ongcwele WamaRoma

Uhlelo Roman kwamafrakshini kwakuhambisana nezinga eliphansi elithile isisindo, ngokuthi "umpetha". It lahlukaniswa laba 12 nokwabelana. 1/12 umpetha ngokuthi i-ounce. Ukuze akhombise amafraktjhini, kwakukhona amagama 18. Nazi ezinye zazo:

• SEMIS - isigamu umpetha;

• sextant - lesithupha share umpetha;

• semiuntsiya - isigamu ounce noma 1/24 umpetha.

Ububi kwalesi simiso ukungakwazi amele inani njengoba ingxenyenamba ne zihilela 10 noma 100 wezibalo Roman unqobe ubunzima ngokusebenzisa amaphesenti.

Ukubhala letetayelekile

Endulo, ingxenyenamba isivele ajwayelekile kithi, thina wabhala lokhu: Inombolo bothile ngaphezu kobomunye. Nokho, ngesikhathi ngisemncane kwenzeka into umehluko ezinkulu. I numerator itholakala ngaphansi zifana. Ngokokuqala ngqá kusukela lokubhala amafraktjhini siqala eNdiya yasendulo. Indlela yesimanje Yilowo nalowo kithi waqala ukusebenzisa ama-Arabhu. Kodwa ayikho neyodwa kulezi izizwe ungazange usebenzise umugqa ovundlile ukuhlukanisa numerator kanye Iningi. Wayeqale livela ngemisebenzi Leonardo Pizanskogo, kangcono eyaziwa ngokuthi Fibonacci, e-1202.

China

Uma umlando ukuvela amafraktjhini waqala eGibhithe, idesimali siqala China. I Celestial Empire yayisetshenziswa kusukela mayelana BC III ekhulwini. Umlando aya ngalo yaqala ngala sezibalo Chinese Liu Hui, ngubani ezihlongozwayo ukusetshenziswa isizinda of izimpande sikwele.

Ekhulwini III BC aya e China ziye zasetshenziswa kulesi sibalo isisindo nevolumu. Kancane kancane, baqala zijule zidlule izibalo. Nokho, e-Europe, amafrakshini wedesimali yasetshenziswa ngemva kwesikhathi eside kakhulu.

Al-Kashi kusukela Samarkand

Kungakhathaliseki China ababengaphambi aya wavula sezinkanyezi al-Kashi kwedolobha Samarkand lasendulo. Waphila futhi owasebenza ngayo ekhulwini lokuthoma xv. inkolelo yakhe yokuziphendukela usosayensi wachaza e indatshana yakhe "Isihluthulelo Aritmethikhi," eyakhishwa ngo 1427. Al-Kashi ezihlongozwayo ukusebenzisa indlela entsha yokubhala izingxenyana zaso. Futhi wonke, futhi ayingxenye ingxenye manje abhalwe umugqa owodwa. Ukuhlukaniswa kubo kusukela Samarkand sezinkanyezi ungazange usebenzise ukhefana. Wabhala inamba futhi ayingxenye ingxenye imibala ehlukene, usebenzisa inki omnyama abomvu. Ngezinye izikhathi ukuhlukana Al-Kashi futhi wasebenzisa ibha mpo.

Amadesimali eYurophu

A hlobo olusha amafraktjhini kwaqala ukubonakala imisebenzi zezibalo European kusukela ngekhulu XIII. Kumele kuqashelwe ukuthi umsebenzi al-Kashi, kanye kokusungulwa Chinese babengesibo ajwayelekile. amafrakshini wedesimali okwakubhalwe ka Jordanus de Nemore. Basuke-ke lisetshenziswe XVI ekhulwini Fransua Viet. Isazi-French wabhala "I zezibalo uhlu lwezincwadi zeBhayibheli", eyayinekheli amatafula Trigonometric. Bona Viet aya. Ukuze kuhlukaniswe inamba futhi ayingxenye ingxenye usosayensi isicelo umugqa oqondile, futhi usayizi ezahlukene wefonti.

Nokho, lezi kuphela ezithile ukusetshenziswa kwesayensi. Ukuze imisebenzi yansuku zonke aya e-Europe waqala zisetshenziswe kamuva. Lokhu kwenzeke sibonga usosayensi Dutch Simon Stevin ekupheleni kwekhulu XVI. Wanyathelisa zezibalo umsebenzi "Weshumi" e 1585. Kuyo usosayensi wachaza ukuthi imfundiso yokuziphendukela usebenzisa izibalo idesimali, ohlelweni yemali ukucacisa izilinganiso.

Point, iphuzu, ukhefana

Stevin futhi ungazange usebenzise ukhefana. Ngombana bekumnyama tshu yoke amafraktjhini amabili usebenzisa i-zero zizungezwé kumbuthano. ukhefana Okokuqala ukuhlukanisa izingxenye ezimbili ingxenyenamba yedesimali kuphela ngo-1592. Nokho, e-England, laqala ukusetshenziswa ingasetshenziswa esikhundleni iphuzu. E-United States namanje aya ukubhala ngaleyo ndlela.

Omunye initiators ukusetshenziswa kokubili izimpawu zokubhala, ukuze zehlukanise phakathi inamba futhi ayingxenye ingxenye kwaba sezibalo Scottish Dzhon Neper. Waveza isigwebo sakhe 1616-1617 GG. Khomba futhi bejabulela usosayensi German Iogann Kepler.

Izingxenyana e Rus

On umhlabathi Russian sezibalo lokuqala, kubekwe esigabeni sika-wonke ibe izingxenye, Novgorod baba indela Kirik. Ngo 1136, wabhala umsebenzi, lapho ezibekwe indlela "iminyaka Isisekelo sesistimu yezinombolo." Kirik abasebenze kwezikhathi nekhalenda. Encwadini yakhe ethi Wangenisa, kuhlanganise division amahora zibe izingxenye ezimbili: owesihlanu, amabili nanhlanu, nokunye share.

Kwehlukanisa wonke ibe izingxenye esetshenziswa kubalwa Usayizi intela xv-XVII eminyaka. imisebenzi asetshenzisiwe wokuhlanganisa, ukukhupha, ukwahlukana futhi ukubuyabuyelela nge izingxenye wamaqhuzu.

Igama elithi "dubula" uvele Russia ekhulwini VIII. Kuqhamuka Isenzo "ukuze akuqede, uhlukanise zibe izicucu." Ukuze bewutjho amafraktjhini okhokho bethu wasebenzisa amazwi ekhethekile. Ngokwesibonelo, 1/2 yakhethwa njengoba ngengxenye noma poltina 1/4 - chet, 1/8 - polchet, 1/16 - polpolchet nokunye.

A theory ephelele kwamafrakshini, ukungathandi namuhla, ukuthi ebekwe ebhukwinitifundvo kuqala ku izibalo, abhalwe 1701, Leontiem Filippovichem Magnitskim. "Aritmethikhi" yayinama izingxenye eziningana. Mayelana nomlobi ekutshela amafraktjhini imininingwane "Ngo izinombolo eliphukile noma ukwabelana" sigaba. Magnitsky kuholela imisebenzi 'ukubhidliza "izinombolo, namagama abo ehlukene.

Namuhla namanje phakathi kwamagatsha nzima kakhulu wezibalo okuthiwa izingxenyana zaso. Umlando amafraktjhini wayebuye akulula. abantu abahlukile kwezinye izikhathi ngokuzimela, ngezinye izikhathi ngokuphindwe zokweboleka isipiliyoni ngaphambili, wakubona kudingekile ukwethula, isungule futhi isebenzise inani nokwabelana. Njalo efundisa kwamafrakshini zamila kokuma esiwusizo futhi sibonga izinkinga ngokucindezela. Kwakudingekile ukuba kwahlukaniswe isinkwa, uphawu ezweni alinganayo, ukubala intela, ukukala isikhathi nokunye. Izici isicelo kwamafrakshini futhi imisebenzi zezibalo nabo kwakuxhomeke ohlelweni inombolo isimo kanye nezinga jikelele ekuthuthukisweni wezibalo. Noma kunjalo, breaking iminyaka engaphezu kwenkulungwane, esigabeni algebra enikelwe amasheya izinombolo, kwakhiwa, kwakhiwa futhi kwasetshenziswa izingxube ngempumelelo namhlanje ezihlukahlukene izidingo kokubili ezingokoqobo futhi theory.