Amaqhezu amaqhezu imbali. Imbali ukuvela amaqhekeza

Enye amasebe zinzima kwimathematika zithathwa ukuba shot namhlanje. Imbali amaqhezu ngaphezu kwiwaka elinye. Ukukwazi uwahlule lonke lezabelo kwenzeka kummandla waseYiputa yamandulo neBhabhiloni. Ukutyhubela iminyaka, siye saba imisebenzi ezinobunzima, wenziwa ngamaqhezu, batshintsha uhlobo nokurekhodwa kwazo. Nganye imeko yehlabathi lamandulo waba iimpawu zalo kwi "ulwalamano" nale isebe lemathematika.

Yintoni maqhezu?

Xa kuyimfuneko waba uwahlule lonke lezabelo ngaphandle kokusokola engaphezulu, ngoko kuya kubakho amaqhekeza. amaqhezu Imbali zaye kuhlangene kwimisebenzi ngevangeli. elithi "kuluhlu" kukodwa iingcambu Arabic kwaye livela intsingiselo yegama elithi "ukwaphula, ukwahlukanisa." Ukususela kumaxesha amandulo, kule ndlela, omncinane itshintshile. Le nkcazelo mihla ngolu hlobo lulandelayo: iqhezu - yinxalenye sum of iinxalenye okanye iiyunithi. Ngako oko, imizekelo ngamaqhezu zimele uphumezo ezilandelelana ngayo imisebenzi zezibalo ngamanani iindawo.

Namhlanje, kukho iindlela ezimbini zokurekhodisha. amaqhezu aqhelekileyo kunye wokugqibela wavela ngamaxesha ahlukeneyo: yangaphambili zinto zezakudala ngakumbi.

Beza ukusuka kudaladala

Ngokuba lixesha lokuqala saqalisa ukusebenza Iqhezu eYiputa naseBhabhiloni. Zezibalo indlela mazwe mabini abe umahluko omkhulu. Nangona kunjalo, isiqalo apho kwakukho wabeka ngendlela efanayo. Iqhezu yokuqala wawusele okanye 1/2. Kwafika ikota, wesithathu, njalo njalo. Ngokutsho ngabembi, imbali amaqhekeza unamalunga 5000 neminyaka. Kuba okokuqala isabelo inani ezifumaneka ngqangi yaseYiputa amacwecwe odongwe eBhabhiloni.

Egypt yamandulo

Iintlobo amaqhezu namhlanje ziquka njalo-ebizwa umYiputa. Bona sum of ngokoMthetho eziliqela ifom 1 / n. Kwinani - njalo omnye elingezantsi kunye nenani elingaphezulu - inani yendalo. Kukho iqhekeza ezinjalo, enoba kunzima kangakanani na ukuthelekelela eYiputa yamandulo. Xa kubalwa sonke isabelo wazama ukuba alobe ngohlobo loo mali (umz, 1/2 + 1/4 + 1/8). namagama ngamanye kuphela amaqhezu 2/3 kunye 3/4, kwaye abanye baye bohlulwa ngokwalo. Kwakukho iitafile ezizodwa apho umyinge inani amelwe inani.

Ukukhankanywa oludala inkqubo enjalo sifumaneka Rhind lweMathematika Papyrus, niyathandana ukususela ekuqaleni BC nkulungwane yesibini. Oku kuquka itafile amaqhezu kunye iingxaki zezibalo kunye nezisombululo kunye neempendulo, owawuboniswa izibalo zamaqhezu. AmaYiputa wayekwazi ukongeza indlela, uwahlule nande inani yesabelo. Amaqhezu kwi Valley umNayile zabhalwa kusetyenziswa eyayimela.

Ukuboniswa komyinge inani njengoko lodibaniso ngokoMthetho fom 1 / n, uphawu eYiputa mandulo, esetyenziswa zezibalo, hayi nje kuphela kweli lizwe. Kude kube eMiddle Ages, iqhezu waseYiputa esetyenziswa Greece kunye namanye amazwe.

Uphuhliso kwemathematika eBhabhiloni

Kungenjalo, khangela imathematika zobukumkani eBhabhiloni. Imbali isenzeko amaqhezu ezinxulumene ngqo iimpawu kwenkqubo inombolo, ilifa urhulumente bamandulo balidla ilifa owayephambi layo, lo Impucuko-isiAkkadia. Equipment Settlement eBhabhiloni kwaba lula ngakumbi umhle ngaphezu eYiputa. Mathematics kweli lizwe ingasombululwa uluhlu olubanzana kakhulu imisebenzi.

AmaBhabhiloni ukuba bagwebe impumelelo namhlanje ugcinwe kumacwecwe zomdongwe ngoonobumba kuhluthiswa. Ngenxa awohluke zezinto ukuba bahlile beza kuthi ngamanani amakhulu. Ngokutsho kweminye izazinzulu, zezibalo eBhabhiloni phambi kaPythagoras wavula theorem ezaziwayo-kakuhle, nto leyo ngokuqinisekileyo kubonisa uphuhliso inzululwazi sikarhulumente yamandulo.

Amaqhezu amaqhezu kumlando eBhabhiloni

Inkqubo nombolo sexagesimal eBhabhiloni. udidi ngalunye entsha ezahlukeneyo ukusuka edlulileyo 60. Le nkqubo igcinwe ehlabathini namhlanje, kuba ixesha kunye engile. Amaqhezu baba sexagesimal. Ukubhala usebenzisa icon ezizodwa. Njengoko eYiputa, imizekelo ngamaqhezu eziqulathe iisimboli ezithile 1/2, 1/3 kunye 2/3.

inkqubo waseBhabhiloni azizange zithi shwaka kunye norhulumente. Amaqhezu ezibhaliweyo kule nkqubo 60-njengokom, esetyenziswa yi izazi zamandulo Arabhu kunye zezibalo.

Greece yamandulo

Imbali amaqhezu natyetyiswa kancinane eGrisi yamandulo. Abahlali of Greece wayekholelwa ukuba imathematika kufuneka isebenze integers kuphela. Ngoko ke, eli binzana amaqhezu amaphepha azibhala zamandulo zamaGrike phantse sibonane. Noko ke, abanye igalelo kweli sebe yemathematika Wenza Pythagoreans. Bona ukuqonda amaqhezu ngokulinganayo kwemali okanye ibonwe ngaphambili, kwakunye iyunithi ayahlukahlukenanga nasengcamangweni. KaPythagoras abafundi ukuba amaqhezu theory jikelele bafunda ukubamba yonke imisebenzi ezine yokalo emileyo namaqhezu uthelekiso ngokuzisa ukuba zifana.

ANgcwele bamaRoma

Inkqubo yamaRoma zamaqhezu edityaniswa ngomlinganiselo ubunzima, ebizwa ngokuba "ace". Kuye yahlulwe nezabelo-12. 1/12 ace ebizwa ounce. Ukuze ubonise amaqhezu, kwakukho amagama-18. Nazi ezinye zazo:

• Semis - isiqingatha ACE;

• kwesextant - sixth share ACE;

• semiuntsiya - isiqingatha ounce okanye 1/24 ACE.

Engxakini kule nkqubo kukungakwazi ukumela inani njenge iqhezu kunye nedinomineyitha 10 okanye 100 imathematika baseRoma ukoyisa ubunzima ngokusebenzisa ekhulwini.

Ukubhala amaqhezu aqhelekileyo

Kwamandulo, iqhezu sele eziqhelekileyo kuthi, thina wabhala oku: Inombolo omnye phezu komnye. Noko ke, kwakukho omnye umahluko enkulu. Elingezantsi ibekwe phantsi kwinani elingezantsi. Kuba ixesha lokuqala ukusukela ngokubhala amaqhezu baqala e-India yamandulo. Indlela yanamhlanje kuthi baqalisa ukusebenzisa Arabhu. Kodwa akukho nanye yezi zizwe zange asebenzise umgca oxwesileyo zokwahlula njengenani eliphezulu nenani eliphantsi. Yena kuqala livela imisebenzi uLeonardo Pizanskogo, eyaziwa ngokuba Fibonacci, ngo-1202.

China

Ukuba imbali ukuvela amaqhekeza baqalisa eYiputa, kuqala kwesishumi wabonakala China. UMbuso Iinkwenkwezi ukuba isetyenziswe ukususela malunga BC kwinkulungwane III. needesimali Imbali yaqala yezibalo Chinese Liu Hui, owoyiswayo kukulawula ukusetyenziswa nezokukhupha kweengcambu square.

Kwinkulungwane III needesimali BC e China ziye zasetyenziswa ekubaleni ubunzima kunye nomthamo. Ngokuthe ngcembe, baqala ukungena nzulu kwizibalo. EYurophu, Noko ke, iincindi wokugqibela zasetyenziswa kakhulu kamva.

Al-Kashi evela Samarkand

Kungakhathaliseki ababengaphambi needesimali eTshayina wavula ngeenkwenkwezi al-Kashi esixeko samandulo Samarkand. Wayehlala waza wasebenza ngenkulungwane XV. imfundiso yakhe ISAZINZULU kuchazwa wakhe othi "I Undoqo Izibalo," nto leyo yakhululwa 1427. Al-Kashi ecetywayo ukusebenzisa indlela entsha zamaqhezu yokubhala. Kwaye lilonke, yaye inxalenye iqhezu ngoku ibhalwe line olulodwa. Ukuze abahlule Samarkand ngeenkwenkwezi zange usebenzise isiphumlisi. Wabhala kwinani kunye inxalenye iqhezu imibala eyahlukeneyo, ngokusebenzisa i-inki emnyama kunye ebomvu. Ngamanye amaxesha ukwahlulwa Al-Kashi naye wasebenzisa ibha nkqo.

Needesimali eYurophu

A uhlobo olutsha zamaqhezu baqalisa ukuba avele imisebenzi zezibalo yaseYurophu ukususela ngenkulungwane XIII. Kufuneka kuqatshelwe ukuba bayalazi umsebenzi al-Kashi, kwakunye kokusungulwa Chinese. Amaqhezu ezishumi uvele kwimibhalo Jordanus de Nemore. ke zisetyenziswa ngenkulungwane XVI Fransua Viet. umphengululi French wabhala: "Le zemathematika Canon", aqulathe iitafile netrigonometri. Bona Huy needesimali. Ukwahlukanisa elipheleleyo kunye inxalenye iqhezu ISAZINZULU isicelo umgca nkqo, kwaye ubungakanani befonti eyahlukileyo.

Nangona kunjalo, ezi kuphela kwiimeko ezithile nokusetyenziswa zenzululwazi. Ngokuba imisebenzi yemihla ngemihla needesimali eYurophu waqalisa ukuba isetyenziswe kamva. Oku kwenzeka ngenxa sisazinzulu Dutch uSimon Stevin ekupheleni kwenkulungwane XVI. Wapapasha umsebenzi "lweShumi" zemathematika ngo-1585. Kulo nzulu wachaza imfundiso kusetyenziswa izibalo wokugqibela, kwinkqubo lemali yaye zijongisise iintsimbi kunye namanyathelo.

Point, ingongoma, ikoma

Stevin zange usebenzise isiphumlisi. Kwakhe amaqhezu amabini usebenzisa zero ezijikeleze kwisangqa. isiphumlisi kuqala ukwahlula iinxalenye ezimbini a iqhezu wokugqibela kuphela ngo-1592. ENgilani, Noko ke, oko waqala izakusetyenziswa endaweni yencopho. EUnited States nangoku ngenani leshumi ukubhala ngaloo ndlela.

Enye lwabasunguli ukusetyenziswa kwazo zombini iziphumlisi ukohlula elipheleleyo kunye inxalenye iqhezu yaba yezibalo Scottish Dzhon Neper. Wothuka isigwebo sakhe ngo 1616-1617 gg. Khomba yaye sisazinzulu waseJamani Iogann Kepler.

Amaqhezu e Rus

Kumhlaba Russian sezibalo yokuqala, ebekwe kwisahlulo lonke lwagabuka, Novgorod waba indela Kirik. Ngowe-1136, wabhala msebenzi, apho amise indlela "iminyaka radix." Kirik babesebenza maxesha kunye nekhalenda. Xa umsebenzi akhe, kuquka ngokwahlulwa iiyure zibe iinxalenye ezimbini: lweyesihlanu, sesihlanu-amabini, njalo njalo isabelo.

Balani yonke lezabelo ezisetyenziswa ukubala ubungakanani irhafu XV-XVII eminyaka. imisebenzi Used of Ukongeza, ukuthabatha, icandelo kunye phindo kunye namalungu fraction.

Kwabonakala Igama elithi "shot" eRashiya ngenkulungwane VIII. Lisuka isenzi 'ukuba awadubadube, ezahlulwe ziingceba. " Ukuze amaqhezu igama ookhokho bethu kusetyenziswa amagama ezikhethekileyo. Ngokomzekelo, 1/2 labekwa njengenye-isiqingatha okanye poltina 1/4 - chet, 1/8 - polchet, 1/16 - polpolchet njalo njalo.

Ingcamango epheleleyo ngamaqhezu, hayi ngokungafaniyo namhlanje, nesacaciswa kule ncwadi yokuqala arithmetic, abhalwe 1701 Leontiem Filippovichem Magnitskim. "Izibalo" yayiba ungamalungu amaninzi. Malunga umbhali usixelela amaqhezu iinkcukacha "Ngomhla amanani eyaphukileyo okanye izabelo" kwicandelo. Magnitsky kukhokelela imisebenzi ukuba 'ukwaphula "amanani, izihionipho zabo ezahlukeneyo.

Namhlanje ngxi phakathi kwamasebe zinzima kwimathematika ekuthiwa amaqhezu. Imbali amaqhezu nalo akuzange kube lula. abantu abahlukahlukeneyo ngamanye amaxesha ngokuzimeleyo, maxa wambi xa uboleka ngamava ngaphambili, wakufumanisa kuyimfuneko ukwazisa, ukuphuhlisa ukusebenzisa inani lezabelo. Soloko kokufundisa amaqhezu bakhula ngaphandle nimana esebenzayo ngenxa iingxaki ngokucindezela. Kwafuneka ukuba ayahlule isonka, phawula umhlaba ngokulinganayo, ukubala irhafu, ukulinganisa ixesha njalo njalo. Iimpawu isicelo amaqhezu kunye imisebenzi zezibalo kunye nabo kwakuxhomekeke kwindlela manani kwi karhulumente kunye nomgangatho ngokubanzi kuphuhliso lwemathematika. Kunjalo, beqhekeza kwiminyaka engaphezu kwewaka, icandelo algebra eyahlulelwe ukuba izabelo amanani, kwasekwa, yaye isetyenziswe ngempumelelo namhlanje ngenxa yezizathu ezininzi ezahlukeneyo iimfuno zombini ABRSM, kwakunye nemiqathango.