Esihlokweni esilandelayo uzofunda konke mayelana Ubani Osungule Izibalo, into etholakala njengamanje kukho konke okuthinta impilo yomuntu, ikakhulukazi ibhizinisi nomnotho womuntu, inkampani noma isizwe imbala. Thola ukuthi Ubani Osungule Izibalo?

Ubani-Osungule-Mathematics-1

Ubani Owasungula Izibalo?

Singagomela ngokuthi abaseGibhithe lasendulo baba abasunguli abakhulu besayensi yezibalo. Naphezu kweqiniso lokuthi, njengoba kuvame ukwenzeka ezimweni eziningi, akekho umuntu noma usuku olungasungulwa futhi olubonisa ukuthi Ubani Osungule Izibalo, ngoba le sayensi isiphenduke inguquko enengqondo yempucuko ngokuhamba kweminyaka.

Ngenxa yalesi sizathu, akunakwenzeka ukunikeza impendulo ecacile embuzweni othi Ubani Osungule Izibalo nokuthi isetshenziswa ngamuphi unyaka. Njengoba sesishilo, Ukwengeza kanye Nokukhipha sekuneminyaka eminingi kukhona. Kuthiwani, uma kungase kuqinisekiswe, ukuthi labantu basendulo I-Egypt waqala ukusebenzisa imisebenzi yezibalo ye-arithmetic yobunzima obuthile.

Ngokwesibonelo, bonke base beyazi kakade indlela ababengenza ngayo izibalo ezilula, njengoba kungase kuboniswe ngephepha le- papyrus abalishiya nezichasiselo zangaleyo nkathi futhi elivikelwe okwamanje emnyuziyamu.

Sengiphetha, ubani owasungula izibalo? Singathi njengoba sesike sachaza akekho umuntu othize noma umuntu obongwa ngokudala le sayensi yezibalo. Sithemba ukuthi lesi sihloko esithi Who Invented Mathematics singaba usizo olukhulu kuwe, sikumema ukuthi ufunde konke mayelana nezibalo. Umlando Womshini Wokubhala.

Iyini iMathematika?

Uma kukhulunywa ngezibalo, kubhekiselwa ochungechungeni lwezilimi ezisemthethweni, eziqala ku-axioms futhi zihlale zithobela lokho obekucatshangwa okunengqondo, zisebenze ukuhlela nokuxazulula izinkinga ezahlukahlukene, ngaphakathi kwaloluhlaka lwalokho okushiwo. izingqikithi.

Lokhu kumane kusho ukuthi izibalo ziqukethe uchungechunge lwemithetho ehlelekile, okusho ukuthi, i-abstract, enezela ezintweni ezisezingqondweni zabantu, ukuthi izinombolo zinjani, ama-engeli anjani, ukuthi izimo zejometri zinjani, phakathi kokunye. Isayensi yezibalo inesibopho salokhu:

  • Isakhiwo
  • I-oda
  • I-accounting
  • Isilinganiso noma Incazelo Yezinto

Nokho, akuwona umbuzo wokuthi ziyini, nokuthi zakhiwe ngani, noma ngisho nezinhlobo ezahlukene zezici zendawo yonke. Ucwaningo lwesayensi yezibalo lumane luqukethe lokho okuvame ukubandakanya konke okuhlobene nokuqonda izinombolo zesistimu yokucabanga okunzima, wathi uhlelo yilona oluhlanganisa kokubili ama-axiom kanye nama-theorems agcina ethathwe kuwo. bona.

Kucatshangwa ukuthi, kanye nolimi lomlomo, isayensi yezibalo imvamisa ingelinye lamathuluzi engqondo anamandla, abanzi kakhulu futhi ayinkimbinkimbi kakhulu achazwe ngumuntu. Konke lokhu kuwulwazi olubalulekile ukwazi ukuthi ubani owasungula izibalo.

Ingabe Isayensi?

Izibalo yilezo ezikhuluma ngezinto ezifanele hhayi izinto eziyiqiniso. Izibalo zifana nekilasi lesayensi elisemthethweni. Uma sikhuluma “ngokwakha” sisho ukuthi iphethe izinto ezifanele futhi, njengoba sishilo, hhayi izinto zangempela. Ezinye izinto ezifana nalezi:

  • Amafomu eJiyomethri
  • Izimpande zesikwele
  • Izinombolo, phakathi kwabanye

Ngokuvamile akuzona izinto umuntu angazithatha noma azinyakaze, kodwa kuyithuluzi lengqondo. Izibalo njengalezo zinengqondo uma zisohlelweni lwazo lokusebenza, okungukuthi, esimweni sazo esinikezwe sona sokuminyanisa.

Kodwa-ke, izibalo nazo ziwuhlobo lwesayensi olunembile, njengoba zisingathwa ngokunemba. Umphumela otholakala ekusebenzeni kokubala, ukunikeza isibonelo, uzofana ngaso sonke isikhathi uma wenziwa ngendlela efanele, kungakhathaliseki ukuthi ubani owenze, kuyiphi indawo futhi ngayiphi injongo. Konke lokhu kubalulekile ukwazi ukwazi ukuthi ubani owasungula izibalo.

Ubani-Osungule-Mathematics-3

Yiziphi Isayensi Esebenzisa Izibalo?

Imvamisa zonke isayensi yezenhlalo kanye neqondile ziphuma kwizibalo ukuze ziveze okwazo okuqukethwe kanye nobudlelwano. Kusukela emagatsheni we:

  • Ubunjiniyela
  • ibhayoloji
  • I-Chemistry
  • I-physics
  • Isayensi yezinkanyezi
  • Ikhompyutha

IMathematika iqukethe isisekelo esibalulekile futhi iyingxenye yohlobo olufanayo lolimi oluhlelekile, nangaphakathi kwalokhu:

  • Isayensi yezokuhlalisana kwabantu
  • Izakhiwo
  • Ukuma komhlaba
  • I-Psychology
  • Imidwebo yezithombe

Lapho beza ukuzodlala indima enqumayo neqondile emphakathini uwonke. Sithemba ukuthi le ndatshana yokuthi ngubani owasungula izibalo izoqhubeka nokukuthakasela, futhi sikumema ukuthi uvakashele indatshana yethu ethi The Umlando Wekhadi Lesikweletu.

Umlando Wezibalo

Konke okuhlobene nokuthi uyini umlando wezibalo kuqala ngengxenye yokuhlaziya ezimisweni zayo ekutholakaleni kwezibalo, kanye nasekutholeni izindlela ezehlukene zokuguquguquka kwamatemu futhi ngendlela efanayo kuyizinga elithile, bonke labo ngqondongqondo abakhulu bezibalo ezihlobene nayo.

Ukukhula kwezibalo emlandweni wesintu kuhlotshaniswa eduze nokuthuthukiswa kwegama lezinombolo, uhlobo lwenqubo eyenzeka ngokuqhubekayo emiphakathini eyahlukene yasendulo.

Naphezu kweqiniso lokuthi baba nekhono elithile lokulinganisa ubukhulu nobukhulu, kusukela ngaleso sikhathi babengenawo umbono wenombolo. Ngale ndlela, izinombolo ezingaphezu kuka-2 noma 3 zazingenalo igama njengoba zisebenzisa izinhlobo ezithile zezinkulumo ezilingana nokuthi "eziningi" ukuze zibhekisele kusethi enkulu kakhulu.

Isinyathelo esilandelayo kulolu hlobo lwentuthuko siwukuba khona kokuthile okusondele kakhulu kuthemu yenombolo, nakuba iyisisekelo kakhulu, nakuba kungesona isigaba sebhizinisi esingaqondakali, kodwa njengohlobo lwesakhiwo noma isici sesethi ethile. . Kamuva, ukuthuthukiswa kobunzima besakhiwo senhlalo kanye nobudlelwane baso kungabonakala kuboniswe kulokho okushiwo ukuthuthukiswa kwezibalo.

Izinkinga okufanele zixazululwe seziyinkimbinkimbi kakhulu futhi akusanele ngokwanele, njengoba kwakunjalo emiphakathini yakudala, kufanele nje ubale zonke izinto futhi uphathe ukuxhumana nabanye ngekhadinali yesethi e akubalwanga, kodwa ngendlela efanayo kwaba okuyisisekelo ukukwazi ukubala kwisethi enkulu kunazo zonke ngesikhathi ngasinye, ngesikhathi esifanayo ukulinganisa isikhathi, ukusebenza nezinsuku, ukunika amandla ukubalwa kokulinganisa kulokho okuyiyo. umhwebi.

Ubani-Osungule-Mathematics-5

Ngaphambi kokuthi kufike iNkathi Yesimanje kanye nokusabalala kolwazi emhlabeni wonke, izibonelo ezingatholakala zentuthuko yezibalo ziphakanyiswa izikhathi ezimbalwa kuphela. Imibhalo yezibalo emidala kakhulu engase itholakale yileyo ebonakala ibhalwe eThebuleni elenziwe Ngobumba Plimpton kusukela ngo-1900 ngaphambili Kristu, iyatholakala futhi:

  • El eMoscow papyrus kusukela ngonyaka we-1850 ngaphambili Kristu.
  • El i-papyrus kusukela ngonyaka we-1650 ngaphambili Kristu.
  • I-Los Imibhalo yeVedic Shulba Sutras kusukela ngonyaka wama-800 ngaphambili Kristu.

Ngokujwayelekile, sekucatshangwa ukuthi isayensi yezibalo isivele yavela ekupheleni kokwenza izibalo ngaphakathi kwezentengiselwano, ukuze ukwazi ukwazi isilinganiso soMhlaba futhi ngesikhathi esifanayo ukubikezela konke okuzayo kwesayensi yezinkanyezi. imicimbi. Uthe izidingo ezi-3 zingahlotshaniswa ngandlela thize kulokho okuhlukaniswa iziqephu okubanzi kwezibalo ngaphakathi kocwaningo lwesikhala, ushintsho kanye nesakhiwo.

Kokubili izibalo zaseBabiloni kanye nezaseGibhithe yizona ezapheleliswa kakhulu yisayensi yezinombolo zamaGreki uqobo, lapho zonke izindlela zingachazwa, ikakhulukazi ukuthi kuyini ukufakwa kokuqina kwezibalo ebufakazini obuhlukene kanye nokuqukethwe kwesayensi eshiwoyo nakho. enwetshiwe. Konke lokhu kuyingxenye yomlando kanye nokuthi Ubani Osungule Izibalo.

I-Evolution yayo ngesikhathi

Ukweqa okukhulu kokuziphendukela kwemvelo kanye nolwazi lwezibalo kwenziwa impucuko yamaGreki ngezikhathi ze Ama-Pythagoras ikakhulukazi phakathi kweminyaka engama-569 kuya kwengama-475 ngaphambili Kristu. Isihluthulelo salokhu kungenxa yokuthi baqala ukufunda izinombolo njengezinhlobo zezinto ezingabonakali futhi abazange bakwenze lokho njengesigaba sokumelela izinto zangempela. Uma unentshisekelo esihlokweni sethu esithi Who Invented Mathematics, sikumema futhi ukuthi ufunde mayelana Umlando wezinombolo.

Kwakunezinhlobo zemithetho okwakuyizona ezaziphethe yonke into engumhlaba wezinombolo futhi le mithetho yayikwaziwa. Lapho bekubona, kwethulwa umhlaba omkhulukazi owawungase uhlolwe. Kwakuwumkhathi ongabonakali, nokho, wawuwusizo kakhulu lapho ubuyela ekuphileni kweqiniso.

Cishe ngesikhathi esifanayo, okwakuyikhulu lesihlanu ngaphambili Kristu, amaNdiya nawo ayehlanganyela ekuthuthukisweni okukhulu kanye nezibalo. Kodwa, ngesikhathi esifanayo, bazithola sebelwa nemiqondo efana nenombolo ethi Pi “π” noma endabeni yokungapheli “∞”, izinto ezazingaphezu kwezibalo ezilula ezenziwa abanye abathengisi.

Nokho, ngemva kokuphila isikhathi sodumo olumangalisayo, izibalo zahlala zimile cishe iminyaka eyinkulungwane. Ngaphandle kwempucuko yama-Arab kanye nentuthuko eza ukuzoyenza ku-algebra, ezifundeni zase-Europe izibalo zazilinganiselwe kulezo ezazitholwe amaGreki Asendulo futhi zaqhubeka ngale ndlela kwaze kwaba yisikhathi seRenaissance. Lokhu kubalulekile ukwazi ngokuthi ubani owasungula izibalo.

Umlando wokuqala

Esikhathini esidlule sobufakazi obuyinhloko bemibhalo, kunezinhlobo ezithile zezibalo okuyizona ezibonisa uhlobo oluthile lolwazi lwezibalo eziyisisekelo kanye nesilinganiso sesikhathi esimiswa ezinkanyezini zendawo yonke.

Ukwenza isibonelo, ochwepheshe abaziwa ngokuthi ama-Paleontologists bakwazile ukuthola amatshe e-ocher ngaphakathi I-Blombos Cave etholakala ezifundeni zaseNingizimu Afrika ezisukela eminyakeni eyizinkulungwane ezingama-70 edlule, ezihlotshiswe ngohlobo oluthile lwemifantu enomumo wamaphethini wejometri.

Ubani-Osungule-Mathematics-7

Ngokufanayo, ezinye izinhlobo zezinto zobuciko zemvelaphi yangaphambi komlando zachazwa ezifundeni zaseFrance nase-Afrika, ezineminyaka engaphezu kwezinkulungwane ezingama-35 nezingama-20 ubudala ngaphambili. Kristu, ezisikisela nokuba abanye bazame ukulinganisa isikhathi. Kunobunye ubufakazi bokuthi abesifazane beza ukuzosungula indlela yokugcina uhlobo lwerekhodi lomjikelezo wanyanga zonke ngale ndlela elandelayo:

Cishe amamaki angama-28 noma angama-30 enziwa etsheni noma ethanjeni, kwase kwenziwa uphawu olukhethekile kulo. Ngaphezu kwalokho, abelusi nabazingeli babevame ukusebenzisa imiqondo ka-1 no-2 nabaningi, kanye nomqondo wokuthi akekho noma u-zero (0), lapho bekhuluma ngemihlambi yezilwane.

El Ishango Bone, esitholwe eduze kwe Umfula iNayileikakhulukazi enyakatho-ntshonalanga ye Congo, ingase ibe nobudala obungaphezu kweminyaka eyizinkulungwane ezingu-20 ngaphambili Kristu. Uhlobo lokuhumusha oludumile ukuthi leli thambo liza ukuze sicabange uhlobo lobufakazi obudala kakhulu obungaziwa mayelana nokulandelana kwezinombolo zokuphindaphinda ngokuphinda kabili kanye nezinombolo eziyinhloko. Sithemba ukuthi lesi sihloko mayelana nokuthi ngubani owasungula izibalo sizokuthakasela. Sikumema ukuthi ubone isihloko sethu ku- Umlando Webhalbhu Lokukhanya.

Ukuguga

Izibalo zaseBabiloni, ezibizwa nangokuthi i Izibalo zase-Asiriya-iBabiloni Ziqukethe iqoqo lolwazi lwezibalo oluze lwathuthukiswa ngabantu base-Peoples of Mesopotamia, okumanje Iraq, kusukela empucukweni yokuqala yaseSumeri kuya kulokho okwaba ukuwa kwesikhulu IBabiloni ngonyaka wama-539 ngaphambili Kristu.

Isayensi yezibalo yaseBabiloni ayizange ibe khona emlandweni wezibalo phakathi nalokho okwaba inkathi yamaGreki. Kusukela ngaleso sikhathi izibalo zabo zahlanganiswa nesayensi yamaGreki kanye neyabaseGibhithe ukuze ngaleyo ndlela kusungulwe isayensi yezinombolo yamaGreki.

Esikhathini esithile kamuva, ngesikhathi sombuso wama-Arab, izifunda ze Mesopotamia, indawo ye-hegemonic yophenyo lwale sayensi. Imibhalo yabaseBabiloni ngokwezibalo ivamise ukuba mikhulu kakhulu futhi ihlelwe kahle kakhulu; Lezi zingahlukaniswa zibe izinhlobo ezi-2 zezikhathi okuyizi:

  1. olumayelana ne I-Antigua IBabiloni phakathi neminyaka ka-1830 kanye no-1531 ngaphambi kokuzalwa kukaKristu.
  2. Okuphathelene ne I-Seleucid yekhulu lokugcina lama-3 noma ama-4 ngaphambili Kristu.

Ngokuqondene nokuthi uyini umongo, kukhona ukuqhathanisa okumbalwa okuhlukile phakathi kwamaqoqo ama-2 wemibhalo. Izibalo zabaseBabiloni zahlala zingashintshile, ngokokuqukethwe kanye nomlingiswa, cishe iminyaka eyi-2. Uma kuqhathaniswa nemithombo ephansi yezibalo yabaseGibhithe, ulwazi lwamanje lwezibalo lwabaseBabiloni luvela ezibhebheni ezingaba ngu-400 ezenziwe ngobumba, ezambiwa ngonyaka ka-1850.

Zazilandelelwa ngombhalo we-cuneiform, izibhebhe zaziqoshwa ubumba lusamanzi, bese luqiniswa ngokulufaka kuhhavini noma ngokulufudumeza elangeni.

Ubufakazi bokuqala bezibalo obabhalwa phansi yibo obubuyela emuva kumaSumer asendulo, okungabantu abasungula impucuko yokuqala Mesopotamia. Laba bantu baseSumeri babenomthwalo wemfanelo wokwakha uhlobo lwesistimu eyinkimbinkimbi ye-metrology kusukela ngonyaka wezi-3.000 ngaphambili. Kristu.

Ubani-Osungule-Mathematics-14

Kusukela cishe ngonyaka wezi-2.500 ngaphambili Kristu, Kusukela ngaleso sikhathi kuqhubeke, impucuko yaseSumeri yafika izobhala lokho okwaziwa ngokuthi amatafula wokuphindaphinda anyatheliswe etafuleni elenziwe ngobumba futhi ngesikhathi esifanayo bazama ukufeza izinkinga zejometri kanye nokuzivocavoca kokuhlukanisa. Izibonelo zakuqala zezinombolo zaseBabiloni yilezo nazo ezangesikhathi esifanayo. Ngakho-ke ngubani owasungula izibalo ziyingxenye eyisisekelo yabantu abaningi.

I-Egypt

Lezi zibalo yizona ezakha into eyaziwa ngokuthi yigatsha elathuthuka kakhulu ngezikhathi ze- IGibhithe lasendulo nangolimi lwabo.

Kusukela kulokho okwakuyinkathi yobuGreki, ulimi lwesiGreki lwaba olwalandelayo olwathatha indawo yaseGibhithe njengolimi olwaqala ukubhalwa ochwepheshe baseGibhithe futhi kusukela ngaleso sikhathi, izibalo zabo zahlanganiswa nezamaGreki futhi neyabaseBabiloni ukuze ikwazi ukuzala amaGreki.

Ucwaningo lwezibalo ezifundeni zase-Egypt lwaqhubeka kamuva ngaphansi kwalokho okwakuyithonya lama-Arabhu njengengxenye yezibalo ze-Islamic, lokhu kwenzeka ngesikhathi lapho ulimi lwesi-Arabhu lukwazi ukuba ulimi lokubhala kakhulu lwazo zonke izingane zesikole zaseGibhithe. .

Ubani-Osungule-Mathematics-9

Imibhalo yezibalo emidala kunayo yonke yaba yileyo etholakala ku-a eMoscow papyrus, ezinomlando olinganiselwe woMbuso izindlela de I-Egypt, phakathi neminyaka engu-2.000 no-1.800 ngaphambili Kristu. Njengenani elikhulu lemibhalo yakudala, equkethe lokho okwamanje okwaziwa ngokuthi:

  • izinkinga zamagama
  • izinkinga ngomlando

Ukuthi banenhloso eyodwa kuphela yokuzijabulisa. Sekucatshangwa ukuthi i-1 yalezi zinkinga ezibaluleke kakhulu futhi ebaluleke kakhulu ngoba kufanele inikeze uhlobo lwendlela yokuthola umthamo we-trunk, yiyona ethi:

“Uma kufanele bakutshele: Ngokuba nephiramidi elisikiwe elingu-1 (elinesisekelo esiyisikwele) elingu-6 ubude elinesakhiwo esiqondile, ngo-4 esisekelweni (sikhuluma ngesisekelo esingezansi, okungukuthi, ingxenye engezansi) futhi okungu-2 phezulu (sisho isisekelo esiphezulu). Kuphi:

  • Uthola ukwenza isikwele sika-4 futhi siphumela ku-16.
  • Bese uphinda u-4 bese uthola u-8.
  • Bese wenza isikwele sibe ngu-2 futhi kufanele sibe ngu-4.
  • Bese wengeza u-16, futhi 8 futhi kamuva 4 bese uthola 28.
  • Bese uthatha 1/3 kokungu-6 futhi lokhu kuphumela ku-2.
  • Manje ubamba ama-28 cishe izikhathi ezi-2 futhi umphumela uba ngu-56.

Ekugcineni, yonke le nkinga iholele ku-56. Ngakho-ke uthole into efanele kule nkinga”

Ngaphakathi kwayo le Papyrus yilapho kunesethi yemithetho esebenza ukuze ikwazi ukunquma umthamo noma ubukhulu bento efana nebhaluni. Manje kukhona enye into ethathwa njengobufakazi bezibalo zasendulo ezibalulekile futhi sikhuluma ngayo i-papyrus kusukela ngonyaka we-1650 ngaphambili Kristu. Lolu wuhlobo lwe-geometry kanye ne-arithmetic imiyalelo yemiyalelo.

Sengiphetha, leli thuluzi yilona elenza kube lula izinyathelo zokuthola isisombululo sezindlela kanye nezindawo zokuphindaphinda ezindaweni ezahlukahlukene. Ngendlela efanayo, yiyona enobufakazi bolunye ulwazi lwezibalo lwabaseGibhithe, okuhlanganisa:

  • Izinombolo Eziyinhloko Nezihlanganisiwe
  • I-Arithmetic Mean
  • ijiyomethri
  • i-harmonica
  • Ukuqonda Okulula kwe Imfumbe ka-Eratosthenes
  • Theory of Perfect Numbers "ukwazi, inombolo 6".

Le papyrus futhi ikhombisa ukuthi kungenzeka kanjani ukuxazulula lezo zibalo zomugqa we-oda loku-1, kanye nochungechunge lwejometri nochungechunge lwe-arithmetic. Sithemba ukuthi lesi sihloko esithi Who Invented Mathematics siyakuthakasela, sikumema ukuthi uvakashele isihloko sethu mayelana I-Historia de Microsoft.

Greece

Iqukethe izibalo eziye zabhalwa ngolimi lwesiGreki kusukela ngonyaka ka-600 ngaphambili Kristu kuze kube unyaka wama-300 ngemva kwalokho Kristu. Izazi zezibalo zamaGreki zazihlala ezindaweni noma abantu abahlakazeke kuzo zonke izifunda ze IMedithera NOMAempumalanga, kusukela ezindaweni ze Italia kuze kube I-North Africa, nokho, babehlanganiswe ulimi olufanayo nayisiko elivamile.

Lonke uphenyo olukhona lwezibalo zangaphambi kwe-Hellenistic luza ukuze lubonise ukuthi kuyini ukusetshenziswa kwe-inductive reasoning, lokhu kusho ukuthi kuwukubhekwa okuphindaphindiwe okusetshenziselwa ukumisa imithetho evamile.

Izazi zezibalo zamaGreki, ngokungafani nalezo ezandulele, zasebenzisa lokho okuwukucabanga okunciphisayo. Izibalo zamaGreki zasebenzisa ingqondo ukuze zikwazi ukudonsa eziphethweni, noma izithiyori, ezincazelweni nama-axiom. Umbono olula wezibalo njengohlobo lwenethiwekhi yethiyori ukuthi zisekelwa ama-axiom acacile ezinhlobonhlobo ezahlukahlukene. Izakhi zika-Euclid kusukela ngonyaka wama-300 ngaphambili Kristu.

Ngokuvamile kunenkolelo yokuthi izibalo zamaGreki zaqala ngabakhulu nabaziwayo Amazwi de IMilethu cishe ngonyaka wama-624 noma wama-546 ngaphambili Kristu, futhi futhi Ama-Pythagoras eminyakeni engama-582 no-507 ngaphambili Kristu. Nakuba kungase kuxoxwe ngazo ngohlobo lobubanzi bethonya labo, ziye zafana, ngokunokwenzeka zikhuthazwa izibalo ezihlukahlukene zabaseGibhithe, kanye namaNdiya nabaseMesophothamiya.

Ngokwenganekwane exoxwayo, le ndoda okuthiwa uPythagoras yafika ukuze izovakashela izifunda zaseGibhithe ukuze ifunde izibalo, isayensi yezinkanyezi kanye ne-geometry kubo bonke abapristi baseGibhithe.

UThales waseMilethu wayengumuntu owayesebenzisa i-geometry ukuze akwazi ukuxazulula izinkinga ezahlukene njengezinxushunxushu zokubala ubude bemibhoshongo kanye nebanga imikhumbi enalo ukusuka ogwini. Omunye umlingiswa kuthiwa, njengoPythagoras, isigaba sokuqala sokuboniswa kwethiyori enegama lakhe ngokuqondile, naphezu kokuthi isitatimende sethiyori sinomlando omkhulu.

Okubhalwe kumazwana owenziwe ngu I-Euclid,kukhale indoda I-Proclus nguye othi omunye umlingiswa uqanjwe igama Ama-Pythagoras wafika ekuvezeni inkolelo-mbono ebizwa ngegama lakhe futhi yiyona eyakha i-algebra ye-Pythagorean kathathu ngaphambi kokuba ibe ngokwejometri. I Plato's Academy njalo nginesiqubulo esithi:

"Makungadluli muntu ongayazi iGeometry"

Okubizwa ngokuthi AmaPythagoreans babenomthwalo wemfanelo wokufakazela ukuba khona kwezinombolo ezingenangqondo. Kwakukhona indoda eyakhula phakathi neminyaka engama-408 kuya kwengama-355 ngaphambili Kristu indlela ebizwa ngokuthi exhaustive method eyenziwa ngu I-Eudoxus, okwaba umgqugquzeli obaluleke kakhulu wokuhlanganiswa kwesimanje.

Ubani-Osungule-Mathematics-13

Okukhulu I-Aristotle phakathi neminyaka engama-384 kuya kwengama-322 ngaphambili Kristu, waba ngumuntu wokuqala ukuyithatha kalula imithetho yengqondo emlandweni wesintu. Kamuva, kwakukhona umuntu owafika ngaphambili kakhulu ukuzonikeza isibonelo sendlela yezibalo esetshenziswa namuhla futhi lokhu kwakungeyona into futhi akukho okuncane kunalokho. I-Euclid, ukwenze nge:

  • I-Axioms
  • Amathiyori
  • Izincazelo
  • Izikhombisi

Ngokunjalo, weza ukuzokwenza izifundo ze-conic mathematics. Incwadi ka I-Euclid enesihloko "Izinto” yiyona eqoqa zonke izibalo ezihlobene naleso sikhathi. Kule ncwadi yeIzinto” izinhlobo ezihlukahlukene zezinkinga zezibalo ezibalulekile zivame ukubhekwana nazo, naphezu kweqiniso lokuthi ngaso sonke isikhathi kwenziwa ngaphansi kwesigaba solimi lwejometri. Ngakolunye uhlangothi, ngaphezu kwezinkinga ezahlukene zejometri, iphinde ibhekane nezinkinga ze-arithmetic, algebraics futhi, ekugcineni, ukuhlaziywa kwezibalo ngokujwayelekile.

Ngakolunye uhlangothi, ngaphandle kwama-theorems ajwayelekile abhekisela ku-geometry, njengecala lika Umbono kaPythagoras, the Izinto (incwadi) ihlanganise nohlobo lobufakazi bokuthi impande yesikwele ka-2 imane iyinombolo engenangqondo futhi enye imayelana nokungapheli kwezinombolo eziyinhloko. Umbhalo ka-Eratosthenes othi Sieve phakathi nonyaka ka-230 ngaphambi kukaKristu, wasetshenziswa kulokho kamuva okwaba ukutholakala kwezinombolo eziyinhloko.

I-Gran Bretaña

Izikhumbuzo ezinkulu ze-megalithic ezifundeni ze E-England futhi ku IScotland, phakathi nalokho okwakuyinkulungwane yesithathu ngaphambili Kristu, yizona ezingahlanganisa imibono eminingi yejometri njengendaba yendilinga, Ellipses futhi i I-Pythagorean kathathu ekuchazeni kwayo. Kulezi zifunda, futhi, abaningi babezibuza ukuthi ubani owasungula izibalo.

China

Umbusi odumile we China kubizwa UQin shi huang wayengumuntu owayala phakathi nonyaka ka-212 ngaphambi kukaKristu ukuthi zonke lezo zincwadi ezingakhishwanga umbuso Qiniso zashiswa. Lesi sinqumo asizange samukelwe yibo bonke abantu, nokho, ngenxa yalokhu, kuncane kakhulu okwaziwayo mayelana nezibalo ezifundeni zezifunda. IsiShayina sasendulo.

Incwadi yezibalo endala kunazo zonke eyasinda kulesi simemezelo esishisayo yileyo enesihloko esithi "I Ching”, okuyilona elisebenzisa ama-trigrams kanye nama-hexagrams anenjongo yefilosofi, kanye nezibalo futhi ekugcineni angaqondakali. Lezi zinto zezibalo zihlanganiswa emigqeni ephelele noma ehlukene ebizwa ngokuthi "Yin” okuyingxenye “yowesifazane” kanye “Yang” okuyingxenye yesilisa, ngokulinganayo.

Emidala kunayo yonke ekhuluma ngejiyomethri ezifundeni ze China kuba yilokho okuvela ku-a I-Mohist Philosophical Canon, kusukela ngonyaka wama-330 ngaphambili Kristu, eyaqoqwa yi ama-acolyte de Mozi phakathi neminyaka engama-470 nama-390 ngaphambili Kristu. Okuthiwa Mo Jing nguye owachaza izici eziningi zemikhakha ehlukahlukene ehlotshaniswa nesayensi yezemvelo kanye nalowo owanikeza isilinganiso esincane sezibalo.

Ngemva kokushiswa kwezincwadi, inzalo ebusayo phakathi neminyaka engu-202 ngaphambi kukaKristu neyama-220 ngemva kukaKristu, yaqala ukuchaza izincwadi ezihlukahlukene eziphathelene nalezi zihloko ze-algebra okungenzeka zazigcwele imisebenzi okwafinyelelwa kuyo.

Esinye sezigqame kakhulu esakhiqizwa yileso esinesihloko esithi “Izahluko Eziyisi-9 Zobuciko Bezibalo”, isihloko saso esiphelele savela phakathi nonyaka ka-179 ngemva kwalokho. Kristu, nokho, kwakukhona ezinye izihloko zeminye imisebenzi ngaphambi kwalokho ezansi. Lo msebenzi yilowo obhekana nezinhlobo zezinkinga ezingaba ngu-246 ezivame ukubandakanya imikhakha efana nale:

  • Ezolimo
  • Ibhizinisi

I-Geometric Isebenzisa ukuze ukwazi ukusungula ubukhulu obuhlukene be:

  • AmaPagoda
  • Ubunjiniyela
  • ukuhlola

Imibono emayelana "Nonxantathu Wakwesokudla" kanye "Ne-Pi". Okunye okusetshenzisiwe yilokhu okubizwa Isimiso sikaCavalieri emiqulwini engaphezu kweminyaka eyi-1.000 ngaphambi kwayo Knights Bengizoyibumba ezindaweni ze ENtshonalanga.

Kamuva, kwavezwa ubufakazi mayelana nalokhu Umbono kaPythagoras kakade uhlobo lwenqubo yezibalo ekuqedeni Gauss-Jordan. Kwafika umuntu ezosho okuthile ngalo msebenzi phakathi nekhulu lesithathu leminyaka, lo muntu wabizwa U-Liu Hui. Konke lokhu kuyingxenye yalabo abasungula izibalo.

Sengiphetha, imisebenzi yezibalo yesazi sezinkanyezi u-Han nomsunguli oqanjwe ngaye UZhang Heng phakathi nonyaka wama-78 no-139 ngemva kukaKristu, yiyona eyayiqukethe isigaba sokwakheka kwe-“pi” ngendlela efanayo, okuyiyona eyahluka ngezibalo zayo siqu. U-Liu Hui.

Ubani omunye owasebenzisa ifomula yakhe ethi "pi" ukuze akwazi ukwenza izibalo ezihambisanayo. Kwatholakala nezincwadi ezabhalwa abadumile Jing Fang phakathi nonyaka wama-78 – 37 ngaphambili Kristu; ngokusebenzisa ukhefana wePythagorean, kanjalo I-Jing wakwazi ukubona ukuthi izingxenye zesihlanu eziphelele ezingaba ngu-53 zazicishe zibe yisishiyagalombili.

Yilokhu kamuva okwakuyoholela ekutholakaleni okukhulu kwesimo somoya, njengoba nje sahlukanisa esesishiyagalombili sibe izingxenye ezilinganayo ezingu-53, futhi sasingeke sibalwe kabusha ngokunemba okukhulu kwaze kwaba phakathi nekhulu le-XNUMX, indoda eyaziwayo yomdabu waseJalimane okuthiwa. Nicholas Mercator. Kulezi zifunda kwaphakama umbuzo omningi: Ubani owasungula izibalo? Njengoba ongoti abaningi bethi kuqhamuka kuleli zwe abathi isayensi yaphuma.

India

Izibalo zase-Indian noma izibalo zamaHindu zizuze ukubaluleka okukhulu kusiko laseNtshonalanga langaphambi kweNkathi Yenguquko ngefa lezinombolo zalo, okuhlanganisa uziro wenombolo (0), ukukhombisa ukungabikho kweyunithi ekubhalweni kwendawo.

Izibalo zokuqala ezaziwa emlandweni waseNdiya yilezo ezisukela ngonyaka wezi-1 - 3.000 ngaphambili. Kristu, etholakala ku I-Indus Valley Culture okungokwempucuko Harappa etholakala enyakatho ye India futhi of Pakistan Njengamanje.

Lolu hlobo lwempucuko lwaluphethe ukuthuthukisa uhlobo lwesistimu yezilinganiso kanye nezisindo ezifanayo ezazisebenzisa lokho okuyisimiso sedesimali, ubuchwepheshe obuthuthuke kakhulu obunezitini ezithile ezimelela izilinganiso, njengemigwaqo ehlelwe ngama-engeli aphelele futhi aqondile futhi. isethi yomumo wejometri kanye nomklamo, ohlanganisa:

  • Cuboid
  • Imiphongolo
  • Izigaxa
  • Amasilinda
  • Imiklamo Yendilinga
  • Idizayini ye-Concentric kanye ne-Secant Triangles.

Izinto zezibalo ezisetshenziswayo zafinyelela ekuhlanganiseni umthetho wedesimali ogcina isikhathi onezinhlobo ezithile zokuhlukaniswa okuncane nokunembayo, kanye nezinhlobo ezithile zezakhiwo ezisebenza ukukala kusukela ezingxenyeni eziphelele eziyi-8 kuye kweziyi-12 zomkhathizwe kanye nesibhakabhaka futhi ngokufanayo. indlela ithuluzi elisebenzela ukukalwa kwezindawo zazo zonke izinkanyezi eziqashelwa ukuzulazula.

Ukubhalwa kwamaHindu ngokunokwenzeka akukakahunyushwa kuze kube manje, yingakho luncane kakhulu ulwazi mayelana nezindlela ezilotshwe futhi eziphathelene nezibalo Harappa. Kunobufakazi bemivubukulo obenze ososayensi abaningi basola ukuthi le mpucuko yasebenzisa uhlobo lwesistimu yezinombolo enesisekelo se-octal futhi yayinenani lophawu u-Pi (π), okuyisizathu esiphakathi kobude bomjikelezo nokuthi buyini ububanzi bayo.

Nokho, kwaba phakathi nenkathi yakudala esukela ekhulwini lokuqala kuya kwelesi-XNUMX lapho izazi zezibalo zaseNdiya zikhula. Ngaphambi kwalesi sikhathi, abantu abangamaHindu bahlangana ngandlela thize nezwe lamaGreki. Ukuxoshwa kwe Alejandro Magno mayelana nezifunda ze India kwenzeka phakathi nekhulu lesine ngaphambili Kristu.

Ngakolunye uhlangothi, ukusabalala kweBuddhism ezifundeni ze China futhi lokho kwezwe lama-Arabs yikho okwandise amaphuzu okuxhumana kwezifunda ze India ngengaphandle. Nokho, izibalo zamaHindu yizona ezathuthukiswa endizeni yokuqala, zithembele kakhulu ekubalweni kwezinombolo kunokuqina kokudonswa kwemali.

Intuthuko ehlukahlukene eyenziwe eNdiya kwizibalo ngemuva kwe suba sutras imvamisa I-Siddhantas, okuyimibhalo ethile yezinkanyezi yangaleso sikhathi I-Gupta Ikhulu lesi-XNUMX nelesi-XNUMX ngaphambili Kristu, okumane kubonise ithonya elikhulu lamaGreki kubo.

Lezi zibaluleke kakhulu ngoba ziqukethe isibonelo sokuqala sobudlelwane be-trigonometric obusungulwa ngohlobo lwe-semi-chord, njengaku-trigonometry yanamuhla, esikhundleni sohlobo lwe-chord egcwele, njengoba kunjalo.

Ikholi ISuria - sidhanta phakathi nonyaka wama-400 nguye owangena emisebenzini ye-trigonometric ye i-cosine, webele y i-arcsine futhi ngesikhathi esifanayo weza ukumisa imithetho ukuze kusungulwe imikhondo yazo zonke izinkanyezi ezihambisana nezindlela zazo zamanje esibhakabhakeni.

Leli klasi lomsebenzi lahunyushwa lisuka olimini lwesi-Arabhu layiswa olimini lwesiLatini phakathi nesifundo Iminyaka ephakathi. AmaHindu ayingxenye yabasunguli bezibalo, ngakho embuzweni wethu othi Ubani owasungula izibalo? AmaHindu nawo ayeyingxenye ebalulekile yawo. Bheka isihloko sethu kuUbani Owasungula Ikhampasi?

Inca

Izibalo zempucuko ye-Inca noma ezaziwa kangcono ngokuthi Tawantinsuyu Yilawo abhekisela kusethi yolwazi lwezinombolo kanye nejometri futhi, ngaphezu kwakho konke, kumathuluzi athuthukiswe futhi asetshenziselwa isizwe sama-Inca ngokwawo ngaphambi kokufika kwezifiki zaseSpain.

Ingabonakala, empeleni, ngamandla ayo amakhulu okubala emkhakheni wezomnotho. Okuthiwa yupanas futhi i I-Quipus zingenye yezinkomba ezibaluleke kakhulu izibalo ezikwazile ukuzifinyelela kulokho okuwukuphathwa kombuso we Inca.

Lokhu kwaba enye yezibalo ezilula, nokho, eziphumelela kakhulu, ngezinjongo zokubala, ezisekelwe ohlelweni lwedesimali; ababazi ngayo u-ziro (0) futhi ekugcineni baphumelela:

  • Ukwengeza
  • Bamba
  • Ukuphindaphinda
  • Isigaba

Ubani-Osungule-Mathematics-21

Iphinde yaba nesigaba sabalingiswa abasebenzayo abavelele emisebenzini yokulinganisa, izibalo nokuphatha. Okwakukude kakhulu nohlelo luka-Euclid lwezibalo njengohlobo lweDeductive Corpus. Okunamandla ngokuphelele futhi kunenzuzo ezidingweni zokuphatha okumaphakathi kwempucuko.

Ngakolunye uhlangothi, ukucaciswa kwemisele, imigwaqo kanye nezikhumbuzo, njengoba kwenzeka ekuhlelweni kwamadolobha nezinqaba, kwadingeka ukuba kuthuthukiswe isigaba seJiyomethri Esiwusizo, esasibalulekile ekukalweni kwezindawo nobude, ngaphandle nje kokuthi umklamo wezakhiwo. Ngesikhathi esifanayo, bahlakulela amandla abalulekile kanye nezinhlelo zokulinganisa ubude, ezathatha izingxenye zomzimba womuntu njengesigaba sereferensi.

Ngaphandle kwalokhu, beza ukuze basebenzise kahle izinto noma izenzo ezingavumela umphumela ngenye indlela, noma kunjalo, esebenzayo futhi efanelekile. Konke lokhu yikho obekuyingxenye yomlando wezibalo futhi owasungula izibalo.

Maya

Basebenzise uhlobo lwendlela yokubala ye-vigesimal esekelwe ku-20 wempande ehlanganisiwe, iyafana nezinye izakhamuzi zaseMesoamerica. Indlela eyasetshenziswa yenani lamachashazi namadashi, eyayivame ukwakha isisekelo salokho okuyizinombolo zamaMayya, yayisetshenziswa kusukela ngonyaka ka-1.000 XNUMX ngaphambili. uKristu; amaMaya kamuva azokwamukela Late Preclassic, bese wengeza uphawu lukaziro (0).

Lokhu yikhona okungenzeka kube isenzakalo sokuqala nesaziwa kakhulu segama lenombolo enguziro (0) elicacile emhlabeni wonke, nakuba kungenzeka ukuthi landulelwa uhlelo lwaseBhabhiloni. Ukusetshenziswa kokuqala kwegama elithi "0" kwakungenkathi liqoshwa ezikhumbuzo ezinosuku lonyaka wama-357 ngemva kukaKristu.

Ekusetshenzisweni kokuqala kwalokhu, inombolo ethi "0" yayisebenza njengohlobo lwe-positional notation, okusho ukuyekwa kohlobo oluthile lokubala lwekhalenda. Kamuva, ngokuvamile lakhula laba inani elalingase lisetshenziswe ekubaleni, futhi laze lanezelwa emibhalweni ehlukahlukene ye-glyphic phakathi neminyaka engaphezu kuka-1.000 XNUMX, kwaze kwaba yilapho ekugcineni ukusetshenziswa kwalo kushabalala kusetshenziswa iSpanishi.

Ohlotsheni lwendlela yokufaka izinombolo eziyisisekelo, lokho okwaziwa ngokuthi iyunithi imelelwa yiphuzu elingu-1, bese kuthi u-2 (..), 3 (...) no-4 (....) amaphuzu asebenze ngenhloso yokuchaza izinombolo , Ezintathu nezine, kanti kulena enomugqa ovundlile, iyona esebenza ukuze imele inombolo yesi-5.

Phakathi nenkathi ye-Postclassic, uphawu olunesimo segobolondo noma umnenke lumele inombolo "0"; phakathi nenkathi ye-Classic kwasetshenziswa ezinye izinhlobo zama-glyphs. Abantu baseMeya bakwazi ukubhala noma yiluphi uhlobo lwenombolo ukusuka ku-0 kuye ku-19, besebenzisa uhlobo lwengxube yezimpawu ezishiwo.

Inani elinqunyiwe lenombolo yilelo elimiswa ngokuma kwayo mpo; lapho ukhuphuka indawo, inani elibalulekile leyunithi liphindaphindwa ngenombolo engu-20. Ngale ndlela, uphawu oluphansi kakhulu yilolo oluzomelela wonke amayunithi esisekelo, uphawu olulandelayo yilo olusendaweni yesi-2, olumele ukuphindaphinda ngo-20 kweyunithi ngokwayo, futhi uphawu olusendaweni yesi-3 yilolo olumele ukuphindaphinda ngo-400 njalonjalo ngokuphindaphindiwe.

AmaMayya ayimpucuko eyingxenye ebalulekile yabasunguli noma labo abasebenzisa izibalo kusukela ezikhathini zasendulo, ngakho-ke uma uzibuza ukuthi ubani owasungula izibalo? AmaMeya ayingxenye yalokhu.

Iminyaka ephakathi

Ake sibheke kancane ngezibalo kulokho okwakukhona Iminyaka ephakathi, isikhathi lapho ochwepheshe abaningi besayensi babezibuza ukuthi ubani owasungula izibalo nokuthi yaziwa kanjani, nokho, kuseyinto enkulu engaziwa emhlabeni wonke.

izwe lamaSulumane

Izibalo ze-Islam, nazo zaziqashelwa njengama-Arabhu noma njengamaSulumane, zanda ngokuqhubekayo njengoba amaSulumane ngokwawo ethatha isikhundla ezindaweni ezintsha.

Ngejubane elikhulu elingavamile, umbuso wamaSulumane wanwetshwa kuyo yonke indawo ehlelwe ngasogwini lolwandle. IMedithera, kusukela ezifundeni ze iPheresiya uyini umsinga I-Iran kuze kufinyelele Pyrenees. Naphezu kokunqotshwa, waba neqhaza elikhulu ekusizeni izibalo ngekhulu lesi-8.

Njengoba kungase kucatshangwe, ingxenye enkulu yemibhalo yamaSulumane ephathelene nesayensi yezibalo yabhalwa ngolimi lwesi-Arabhu futhi akuyona yonke eyabhalwa ama-Arabhu ngokwawo, njengoba, ngendlela efanayo ulimi lwesiGreki olwafika ngalo. ukuze lisetshenziswe izwe lamaGreki, ulimi lwesi-Arabhu lwaqala ukusetshenziswa njengohlobo lolimi olubhalwayo yizazi ezinkulu ezazingezona ezendabuko yama-Arab kuwo wonke umhlaba omkhulu wamaSulumane ngaleso sikhathi.

https://www.youtube.com/watch?v=M1bpyd-vRXE

Ezinye izazi zezibalo zamaSulumane eziningi zabaluleka kakhulu kanye nama-Arabhu, njengamaPheresiya. Phakathi nekhulu lesishiyagalolunye, indoda eyaziwa ngokuthi I-Al-Juarismi Nguye owafika ezobhala izincwadi ezihlukahlukene ezibaluleke kakhulu mayelana nezinombolo zesi-Arabhu kanye nezindlela ezihlukahlukene zokuxazulula izibalo zezibalo.

Incwadi yakhe, ebhekisela ekubaleni kwama-Arabhu, yabhalwa phakathi nonyaka ka-825, kanye nomsebenzi womunye umlingiswa ogama lakhe lingu. Al Kindi, okwaba amathuluzi abantu okwenza kwaziwe zonke izibalo zesi-Arabhu kanye nalokho okwaziwa ngokuthi izinombolo zesi-Arabhu ezifundeni ze ENtshonalanga.

Igama elithi algorithm yilelo elivela kuLatinization yegama layo, elithi "algoritmi", futhi igama elithi "algebra" lisuselwa esihlokweni somunye wemisebenzi yawo.

Okusho ukuthi ekuhumusheni kwayo "Iqoqo lokubala ngokuqedela nokuqhathanisa". I-Al-Juarismi Waqanjwa ngokujwayelekile waphinde wathathwa ngokuthi "Ubaba we-algebra", lokhu kungenxa yeqhaza lakhe elikhulu nelibalulekile kulo mkhakha ofanayo. Yena ngokwakhe uzele ukuzonikeza umfanekiso ocophelela kakhulu ngesixazululo sezibalo ze-2nd degree ezinezimpande ezinhle, futhi le ndoda yaba ngowokuqala ukwazi ukufundisa abanye i-algebra kanjalo ngendlela yayo ngayinye eyisisekelo.

Ubephinde abe ngumuntu oze ukuzokwethula ukuthi iyiphi indlela ebalulekile ethi "Balance" kanye "nokunciphisa", ebhekisela ekwengezweni kwezakhi ezikhishiwe ezazikolunye uhlangothi lwezibalo, lokhu kusho, ukwesulwa kwemibandela efana nalena. ngakolunye uhlangothi lwe-equation.

Lolu hlobo lokusebenza lwaze lwachazwa kakhulu yi- Al-Jarismi kanye ne i-al-jabr. Okwabaningi kwakumayelana:

“Iqoqo lezinkinga ezingazange zixazululwe, kodwa kunalokho ohlotsheni lokuchazwa oluqala ngezimo ezindala ezivame ukunikezwa kuzo zonke izinhlobo zezibalo ezingenzeka ngeqoqo lezingoma, kusukela kulokho Ngesikhathi esifanayo, i-algebra into yokufunda.

IYurophu ngeNkathi Ephakathi

Ekuhambeni kwe Iminyaka ephakathi ukusetshenziswa kwe-algebra emikhakheni yamabhizinisi, kanye nokuba nekhono kwezinombolo, yikho okwaholela ekusetshenzisweni njalo izinombolo ezingenangqondo, okuwuhlobo lwesiko olube seludluliselwa ezifundeni ze Europa. Ngendlela efanayo, izimpendulo ezingezinhle ku:

  • Izinkinga Ezithile
  • Amanani Acatshangwayo
  • Izibalo zeDegree 3.

Ubani-Osungule-Mathematics-23

Ukuthuthukiswa kwezibalo ngokuhamba kwesikhathi Iminyaka ephakathi wakhuthazwa njalo yilokho okwakuyinkolelo yohlobo oluthile "I-oda Natural”; kwabiza indoda Boethius yiyona eyawabeka ngaphakathi kohlelo lwezifundo, phakathi nekhulu lesithupha, ngokufaka umqondo wokuthi I-Quadrivium ngoba bekuyini isifundo semethodical:

  • izibalo
  • I-geometry
  • Isayensi yezinkanyezi
  • Umculo

Kwakuyini eyakheI-arithmetica yesikhungo”, uhlobo lokuhumusha lwe uNicomachus, phakathi kwezinye izincwadi ezaba isisekelo sezibalo kwaze kwaba yilapho sezitholakele zonke izincwadi zezibalo zamaGreki nama-Arabhu.

Ngesikhathi sekhulu leshumi nambili, ikakhulukazi ezifundeni ze Italia futhi ku España, baqala ukuhumusha imibhalo ethile eyayibhalwe ngesi-Arabhu futhi yilapho izibalo zamaGreki zaphinde zatholakala khona. Umlingiswa owaziwa ngokuthi Toledo Iguqulwa ibe uhlobo lwesikhungo samasiko futhi iphinde ibe isikhungo sokuhumusha; izazi zemvelaphi yaseYurophu zathuthela ezifundeni ze España futhi nasezindaweni ze Sicilia ukuze ukwazi ukusesha izincwadi zesayensi zama-Arabhu ezihlanganisa:

"I-Calculus Compendium Ngokuqedwa Nokuqhathanisa"

Yenziwe ngu al-Khwarizmī, futhi babefuna nenguqulo ephelele yencwadi ethi "The Elements" eyabhalwa abadumile I-Euclid, eyahunyushelwa ezinhlotsheni eziningi zezilimi yiqembu lamadoda elibizwa ngokuthi:

  1. Adeleard of Bath
  2. UHerman waseCarinthia
  3. UGerard waseCremona

Ukukhula kwezohwebo nomnotho okwaziwayo ezifundeni ze Europa, ngokufakwa kokuvulwa kwemizila emisha ebheke endaweni esempumalanga yamaSulumane, yilokho okuvumela ngendlela efanayo abathengisi abaningi abahlukene ukuba bakwazi ukuzivumelanisa namasu adluliswa ama-Arabhu ngokwawo. Yonke imithombo emisha iyona ethuthukisa izibalo zalezi zikhathi.

Kwafona indoda I-Fibonacci ungumlingiswa obhala i-"Liber Abaci" yakhe phakathi nonyaka we-1202, owaphinde wakhishwa ngonyaka we-1254, lo ngumbhalo okwazi ukukhiqiza intuthuko yokuqala ebalulekile ngokwezibalo ezifundeni zalo lonke elaseYurophu. ngokwethulwa kohlelo lwezinombolo lwaseNdiya olwaziwayo, njengoba negama libonisa, kwakungeyamasiko amaNdiya ahlanganisa uhlelo lokuphawula ngedesimali, kanye nokuma kanye nokusetshenziswa okukhulu okuvamile kwenombolo enguziro.

Ubani-Osungule-Mathematics-25

Lena kwakuyithiyori eyafika ukufundiswa ku I-Quadrivium, nokho, ngendlela efanayo eyayihloselwe umkhuba wokuhweba. Lolu hlobo lokufundisa lusakazwa ngezingcingo "i-botteghe d'abbaco" ezaziwa ngokuthi "izikole ze-abacus", lapho “amaestri” (othisha) ayephethe ukufundisa:

  • izibalo
  • I-geometry
  • Izindlela zokubala

Kubo bonke labo bathengisi besikhathi esizayo bezikhathi ezizayo, ngezinkinga zokungcebeleka, ezazaziwa kakhulu ngenxa ye-"Algebra Treatises" othisha ngokwabo abebeyishiya kuwo wonke umlando wezibalo. Nakuba i-algebra kanye negatsha le-accounting kuyizo ezihamba ngezindlela ezihlukene, ekwenzeni izibalo eziyinkimbinkimbi ngokuvamile ezihlanganisa inzalo ehlanganisiwe, ukuphatha okuhle kakhulu kwe-Arithmetic kwaziswa kakhulu abaningi.

Konke lokhu kuyingxenye yomlando wezibalo futhi owasungula izibalo njengoba zazisetshenziswa imiphakathi eminingi emandulo. Sithemba ukuthi le ndatshana emayelana nokuthi ngubani owasungula izibalo ikusiza ekutholeni ulwazi olusha, sikumema futhi ukuthi ubone indatshana yethu ephathelene nezibalo. umlando womsakazo.

I-European Renaissance

Kukhona intuthuko enkulu endaweni yezibalo phakathi nekhulu leshumi nane, njengoba kunjalo nge-dynamics of movement. Kwafona indoda Thomas Bradwardine ungowokuqala ukuphakamisa ukuthi ijubane linyuswe ngesilinganiso se-arithmetical njengesizathu sokuthi amandla okumelana akhuphuka ngesilinganiso sejometri, futhi uyaqhubeka nokubonisa imiphumela yakhe ngesethi yezibonelo ezithile, njengoba i-logarithm yayingakafiki. ukucabanga.

Ucwaningo lwakhe luyisibonelo esihle sokuthi indlela yezibalo esetshenziswa ngayo al-Kindi futhi Vilanova ngaleso sikhathi. Izazi zezibalo zangaleso sikhathi, zingenayo imigomo yokubala okuhlukanisayo noma umkhawulo wezibalo, ziyaqhubeka nokuthuthukisa eminye imibono njengoba kunjalo, isibonelo, yokulinganisa isivinini esisheshayo kanye ne:

"Indlela (umzimba) ebingawulandela ukube... ibihanjiswe ngokufanayo ngezinga elifanayo lejubane elivame ukuhanjiswa ngalo ngaleso sikhathi."

Noma kungenzeka ukunquma uhlobo lwendlela embozwe umzimba ongaphansi komfaniswano kanye nokunyakaza okusheshisiwe (njengamanje lokhu kuxazululiwe ngosizo lwezindlela zokuhlanganisa). Leli qembu elifanayo, elakhiwe ngabantu abafana:

  • Thomas Bradwardine
  • UWilliam Heytesbury
  • Richard Swineshead
  • UJohn Dumbleton

Impumelelo yabo enkulu wukudala lokho okubizwa I-average Velocity Theorem ukuthi kamuva, kusetshenziswa ulimi lwe-kinematic nolimi olwenziwe lula, yilona oluzofika ukuzobhala isisekelo salokho okwaziwa namuhla ngokuthi "umthetho wemizimba ewayo”, ephakanyiswe ngabakwa UGalileo Galilei.

Ubani-Osungule-Mathematics-27

Enye indoda enkulu okuthiwa Nicholas Oresme okungeye- Inyuvesi yaseParis ngokubambisana nesiNtaliyane Giovanni di Casali, kwakuyibo abayinhloko abahlinzeka ngokuzimele uhlobo lokuboniswa kwesithombe sobudlelwano obalulwe ngenhla. Ngesikhathi kuvuselelwa abeLungu, abaningi babezibuza ukuthi ubani owasungula izibalo, abanye bazi ukuthi owasungula izibalo zazingakaze zibonakale ngaphambili kodwa kwakungama-Arab, amaGibhithe namaGreki ayezisebenzisa kakhulu endulo.

Ikhulu le-XNUMX kuya kwelama-XNUMX

Manje, sizofunda kancane ngomlando wezibalo nokuthi njengoba sesike sachaza, akwaziwa kahle ukuthi ngubani owasungula izibalo, kodwa kuyaziwa ukuthi zavela eqenjini lempucuko eyayisebenzisa isikhathi eside. futhi lokho kwavela phakathi nekhulu le-XNUMX kuya kwelama-XNUMX.

Ukutholwa Kwezibalo Zesimanje 

Phakathi nekhulu leshumi nesikhombisa, ulwazi abantu abanalo ngomhlaba kanye nomhlaba wonke lwaqala ukusheshisa futhi ngenxa yalokhu kwakudingeka ukuba kube namathuluzi ezibalo ayengavumela ukuguqulwa kwezinto ezintsha ezitholakalayo ezazizokwenzeka. Kodwa-ke, kwethulwa ibhomu lesibili lesayensi. Ngaleso sikhathi imigomo ye:

  • I-Logarithm
  • I-Infinitesimal Calculus
  • I-Calculus of Probabilities

Futhi nakho konke okwamanje okuhlobene nesisekelo sezibalo zesimanje. Zingaba izinto abantu abaningi ezibonakala zingaqondakali kakhulu, nokho, zingatholakala phansi kwezibalo ukuze zikwazi ukwakha izakhiwo, kanye nokwenza izindiza zindize, ngendlela efanayo ezikhonza ngayo ukuthumela ulwazi ngezindlela ye-inthanethi noma ukuze kuthathwe i-akhawunti yokuthi ungakanani umthamo womuthi okufanele usetshenziswe.

Manje, izibalo ngendlela eqondile azisafundelwa ukusebenza kwazo, kodwa zifundwa ngokuphelele ukuze kuhlolwe izindawo ezingaziwa. Akulona uhlobo lokuzijabulisa olungawenzi umqondo, ngoba ulwazi olutholiwe lukhomba ukuthi yonke intuthuko enkulu eyenziwe kuzibalo iyasebenza ngokushesha empilweni yangempela esiphila kuyo, kungakhathaliseki ukuthi ikude kangakanani futhi ingabonakali. izazi zezibalo zomlando zingavezwa.

Mhlawumbe, ingxenye enkulu yabantu izosala ingenandaba nokuthile engakakwazi ukuthola ukuthi i-hypothesis eyethulwa yindoda ibizwa ngokuthini. U-Riemann ngonyaka we-1859, okumayelana nohlobo lwesiphakamiso sezibalo esingacacile, lapho sikhuluma ngokufihlakala lokhu ngaphandle kwezazi zezibalo.

Kodwa-ke, kungamane kwanele ukwazi ukuthi ikusasa lezokuxhumana lizoncika kakhulu ekubonisweni okunjalo U-Riemann ukuze sikwazi ukwazisa isintu ukuthi izibalo ngaso sonke isikhathi zinohlobo lomphumela oqondile wokuthi buyini ubukhona bempilo yomuntu.

Futhi naphezu kweqiniso lokuthi abantu abaningi bakuthola kunzima ukuqonda konke lokhu, izibalo zisenalo uhlobo lobuhle bangaphakathi, obufana kakhulu nomsebenzi omkhulu wobuciko nezincwadi. Imigomo yobuhle nobuhle icacile kwisayensi yezibalo, futhi mhlazana ukuqaphela lokhu, umkhakha omusha wesipiliyoni uzovulelwa wena.

Sithemba ukuthi lesi sihloko esithi Who Invented Mathematics siyakusiza ukuba uthole ulwazi oluningi kakhulu kunalo onalo, futhi sikumema ukuthi wazi konke ngomlando we-¿Ubani Osungule Injini Ye-Steam? Njengoba lo mlingisi bekumele asebenzise izibalo eziningi ukuze ayidale.

Europa

Izibalo ziza ekuncikeni ezicini zezobuchwepheshe nezomzimba. Indoda eyaziwayo njengoba kwenzeka Isaac Newton futhi of UGottfried Leibniz Yibo abadale i-infinitesimal calculus, okuyisiqalo senkathi yokuhlaziywa kwezibalo ngalezo zikhathi, okuvela ekuhlanganisweni nasekubuyeni kwezibalo ezihlukene.

Lokhu kwenzeke ngenxa yesikhathi esinqunyelwe, esithathwa njengomqondo obaluleke kakhulu ngalesi sikhathi wezibalo. Kodwa-ke, ukwakhiwa okuqondile kwethemu lomkhawulo akuzange kukhiqizwe kuze kube ikhulu leshumi nesishiyagalolunye ngosizo lwe I-Cauchy.

Izwe elikhulu lezibalo lasekuqaleni kwekhulu leshumi nesishiyagalombili lingaphansi kwesibalo somuntu okuthiwa Leonhard Eulerkanye nangeqhaza lakhe elikhulu kuyo yomibili imisebenzi yezibalo kanye nemibono ehlukene yezinombolo, kanti omunye umlingisi oqanjwe igama lakhe Joseph-Louis ILagrange ngumuntu okhanyisa ingxenye yesi-2 yekhulunyaka mayelana nalokhu.

Ikhulu leminyaka elidlule likwazile ukubona ukuqaliswa kwe Ukubala okungenamkhawulo, obekuzovula indlela yokuthuthukiswa okukhulu kwesifundo sezibalo esisha esihlanganisa ukuhlaziya i-algebra, lapho yonke imisebenzi yakudala ye-algebra yengezwa ekuhlukaniseni nasekuhlanganisweni. Ingxenye ebalulekile yomlando wezibalo kanye nokuthi ubani owasungula izibalo eminyakeni yasendulo.

Japan

Izibalo ezithuthukiswa ezifundeni ze Japan phakathi nenkathi Edo phakathi kweminyaka ye-1603 kuya ku-1887, izimele ezibalweni zasentshonalanga.

Ngalesi sikhathi kukhona Seki Kowa, owayengumlingiswa obaluleke kakhulu kulokho okwaba yintuthuko ye wasan okubhekwa njengezibalo ezijwayelekile zaseJapan, futhi okutholwe kuyo ngaphakathi kwezindawo ezifana ne- integral calculus, kuhambisana ngokoqobo nochwepheshe bezibalo abakhulu banamuhla baseYurophu, njengoba kwenzeka komunye obizwa ngokuthi. UGottfried Leibniz.

Izibalo ze Japan kulesi sikhathi esifanayo wabe esegqugquzelwa yizibalo ze China, okuhloswe ngokuyinhloko ezinkingeni zejometri. Kwezinye izinhlobo zamaphilisi enziwe ngokhuni okuthiwa sangaku, ukuthi iziphakamiso zibekwe futhi lokho okubizwa ngokuthi "I-Geometric Enigmas" ixazululwa; kusukela kulelo gama ukuthi livela, isibonelo, owaziwayo i-sextet theorem Soddy.

Sithemba ukuthi uyayijabulela indatshana yethu yokuthi ngubani owasungula izibalo, sikumema futhi ukuthi uvakashele i-athikili yethu Umlando wefoni.

Ikhulu le-XIX

Phakathi naleli khulu leminyaka abaningi babezibuza ukuthi ubani owasungula izibalo futhi iqiniso liwukuthi phakathi nekhulu leshumi nesishiyagalolunye umlando wezibalo ubulokhu uthela kakhulu futhi uchichima. Kuleli khulu leminyaka, kwavela amanani amakhulu emibono emisha futhi umsebenzi owawuqalwe ngaphambili waqedwa.

Kuyinkathi lapho ukuqina kuqala ukubusa, njengoba kuvezwa "Ocwaningweni Lwezibalo" ngophenyo lwe I-Cauchy kanye nesamba sochungechunge, okuyilona elethulwa futhi ngenxa yejiyomethri, kanye neTheory of Functions futhi ngokwesici lokho okubhekisela ezisekelweni zokubala okuhlukile futhi okubalulekile kuze kube yilapho ukwazi ukususa yonke imibono emincane ngokungenakulinganiswa. bakwazile ukuzuza impumelelo ebaluleke kakhulu phakathi nekhulu leminyaka elidlule.

Ubani-Osungule-Mathematics-29

Ikhulu lamashumi amabili

Phakathi nekhulu lama-XNUMX futhi kwakunezinto eziningi ezazingaziwa mayelana nokuthi ubani owasungula izibalo, futhi iqiniso liwukuthi ngesikhathi saleli khulu leminyaka kungabonakala ukuthi izibalo zaba kanjani umsebenzi omkhulu kochwepheshe abaningi nochwepheshe besayensi ababethungatha impendulo umbuzo wokuthi ubani owasungula izibalo?

Unyaka ngamunye, odokotela abaningi bayaphothula, futhi izindawo zokusebenza zitholakala kakhulu kwezokufundisa kanye nezimboni. Amathiyori amathathu amakhulu okubusa aziwa ngokuthi:

  1. Ithiyori Yokungapheleli Godel.
  2. Ubufakazi Bokucatshangelwa Taniama–Shimura, okusho ukuthi ubufakazi bokugcina beTheorem kaFermat.
  3. Ubufakazi Beziqalo ngoba ngenye ingxenye Pierre Deligne.

Inani elikhulu lemikhakha emisha eyakhiwe noma eyazalwa iwuhlobo lokuqhubeka kwayo yonke imisebenzi ye I-Poincare noma iningi labo, futhi mayelana:

  • Amathuba
  • I-Topology
  • I-geometry ehlukile
  • Umqondo
  • Ijometri ye-algebraic
  • imisebenzi ye Grothendieck, phakathi kwabanye abaningi.

Konke lokhu kuvame ukuba yingxenye ebalulekile yesayensi yezibalo futhi ochwepheshe abaningi bavame ukuba nemibuzo ngokuthi ubani owasungula izibalo. Siyethemba ukuthi le ndatshana yokuthi ngubani owasungula izibalo iyakusiza ekufuneni kwakho ulwazi, siyakumema futhi ukuthi uvakashele isihloko sethu mayelana Umlando Wesibonakhulu.

Ikhulu lama-XXI

Ngonyaka ka-2000, isikhungo safona Clay Mathematics Institute Weza ukuzomemezela ukuthi zaziyini izinkinga eziyisi-7 zenkulungwane yeminyaka, kwathi ngonyaka ka-2003 ukubonakaliswa komcabango wendoda ebizwa ngokuthi. I-Poincare eyenziwe ngu Grigori Perelman obengumuntu owacabanga ukuthi angawemukeli umklomelo wale mpumelelo.

Ingxenye enkulu yamamagazini ezibalo anenguqulo ye-inthanethi kanye nenguqulo ephrintiwe, ngendlela efanayo inani elikhulu lokushicilelwe kwedijithali livame ukwethulwa. Kukhona ukukhula okukhulu kulokho okutholakala ku-inthanethi, okuthandwa ngabakwa I-ArXiv. Lolu ulwazi olubalulekile ukuze wazi Ubani Osungule Izibalo.

Umsuka Wezibalo

Ukuze wazi okwengeziwe mayelana nokuthi iyini imvelaphi yezibalo, okokuqala, kufanele ubuyele emuva ezinkulungwaneni zeminyaka ngokuhamba kwesikhathi. Singasho ukuthi namuhla akukho okungeke kwenzeke ngaphandle kokusetshenziswa kwezibalo zezibalo, noma kunjalo, ngaso sonke isikhathi lokhu akuzange kube njalo.

Ekuqaleni kwakuyinto elula. Igama lenombolo laba yinto engenakuphikiswa kakhulu, naphezu kweqiniso lokuthi selivele limele uguquko olukhulu ezingeni lomqondo. Ukukhuluma iqiniso, kukhona idatha ethile esalibele ebonisa ukulandelana kwamamaki okungafanekisela izibalo ezivela eminyakeni engaphezu kuka-30.000 edlule. Futhi ngezibalo yilapho kwethulwa khona imisebenzi ye-arithmetic ebalulekile, okuyilezi:

  • Izibalo
  • Ukukhipha

Ngalokhu nje, umhlaba omkhulu wamathuba angenamkhawulo wawusuvele uvulekele sonke isintu. Uhwebo lwalungase lusungulwe, amabanga ayengalinganiswa, futhi amabutho nawo ayengase aqhathaniswe namanye.

Kamuva, ukuhlukana nokuphindaphindeka kwaqala ukuvela ngokushesha. Ukusabalalisa izinto nokwengeza amanani kuvame ukuba ezinye zezinto ezivame ukwenziwa nsuku zonke noma ezenziwa ngalezo zikhathi. Kungakhathaliseki ukuthi okwebhizinisi, okomlimi, umthelisi kanye nokuphila kwansuku zonke kwawo wonke umuntu. Lokhu kuyingxenye yendaba ethi Who Invented Mathematics, yona ngokwayo eyayingeyena umuntu oyedwa kodwa yayingabantu ngokwamarekhodi atholakele.

Amagatsha eMathematika

Cishe kuzoqashelwa amagatsha ezibalo angaba ngu-5, ngokuvamile aqoqwe abe yizinkambu zezibalo ezinkulu ezi-4 ezithathwa ngokuthi "Pure", futhi lokhu okulandelayo:

Ubungako: Kulo mkhakha yilapho izinombolo zikhona:

  • izinombolo
  • Izilinganiso
  • Ngokwemvelo
  • Izakhiwo
  • okunengqondo

Isakhiwo: Ngaphakathi kwalo mkhakha, izinombolo nobudlelwano kusetshenziswa ukuze ukwazi ukubala nokumela amasethi noma izimo ezifana nalezi:

  • I-Algebra
  • Ithiyori Yezinombolo
  • Ama-Combinatorics
  • I-Graphic Schema Theory
  • Ithiyori Yeqembu

Isikhala: Lapha kulapho izinombolo zilandelana khona ngesilinganiso sesikhala kanye nokubalwa kobudlelwane obungaba khona obuhlukahlukene phakathi kokumelwa kwendawo okuyilokhu:

  • I-geometry
  • I-Trigonometry
  • I-geometry ehlukile
  • I-Topology

I-Cambio: Yilapho izinombolo zisebenza khona ukuveza ubudlelwano obushintshayo, ukunyakaza, ukufuduka futhi ekugcineni ushintsho ngokujwayelekile, njengoba kwenzeka ku:

  • Ukubalwa
  • I-Vector Calculus
  • Amasistimu anamandla
  • Izibalo ezihlukile
  • Ithiyori yesiphithiphithi.

Ingxenye yamagatsha ezibalo yavela kumuntu owasungula izibalo, okungukuthi, isiko lasendulo elalilisebenzisa ngendlela enkulu. Siyethemba ukuthi le ndatshana yokuthi ngubani owasungula izibalo izoba usizo olukhulu kuwe, sikumema ukuthi uvakashele isihloko sethu mayelana Umlando Weselula.

Ubani-Osungule-Mathematics-32

Kungani Izibalo Zibalulekile?

Izibalo yiyona eyenza kube nokwenzeka ukuveza ngokubhala izinombolo kanye nezixhumanisi ezinhle nomhlaba wangempela, futhi yisayensi evula umnyango wazo zonke izindlela ezingabonakali kanye nezibalo eziyinkimbinkimbi kakhulu emhlabeni wonke. Kuyini inqubekelaphambili yabantu, yilokhu okwafika ekucabangeni ukwanda okukhulu kwamandla okukhipha kanye nokukwazi ukuphatha imibono eyinkimbinkimbi.

Nokho, phakathi nomkhakha wocwaningo owabonakala ungenalutho futhi uhlukanisiwe nalokho okuyikho ngempela ukuphila, intuthuko enkulu iye yahlukaniswa nayo nezinye izigaba zesayensi, kokubili ezobuchwepheshe nezimboni, njengoba Ngaphandle kwalokho, bebeyontula uhlobo oluthile lwesayensi ehlelekile. ulimi ukuze lukwazi ukuveza imisebenzi yezibalo. Lokhu kubalulekile ngoba noma ngubani owasungula izibalo wayazi kancane ngokubaluleka kwazo.

Yenzelweni iMathematics?

Izibalo zisetshenziswa nsuku zonke ukwenza izinhlobo ezahlukene zezilinganiso. Izibalo ziwuhlobo lwethuluzi lengqondo elinamandla kakhulu. Izibalo zivumela umuntu ukuthi akwazi ukwenza uchungechunge olukhulu noluyinkimbinkimbi lwemisebenzi enolunye ekuphileni kwansuku zonke, njengoba kwenzeka:

  • Incazelo kanye Nokuhlaziywa Kwezikhala
  • Ubudlelwano
  • Ubuningi
  • Qalisa
  • Izilinganiso
  • Ukuqiniseka

Ngaphandle kwanoma yikuphi kwalokhu, akunakwenzeka ukuba ukwazi ukubala, ukwazi ukulinganisa, noma ukukwazi ukunquma ngokunengqondo izinto ezibonakala nsuku zonke ekuphileni kwabo, ngakho bazisebenzisa ngaphandle kokucabanga ukuthi basebenzisa izisekelo eziyisisekelo. isigaba sesayensi esidala ngempela. Konke lokhu kungenxa yokubonga kunoma ngubani owasungula izibalo.

Izicelo Zezibalo

Ngaphandle komkhakha wezibalo othi “Pure” noma osemthethweni ngokuphelele, kunezinhlobo ezithile zezindawo lapho izibalo zinikezelwa khona ukuze kufundwe izici zeminye imikhakha yolwazi, ikakhulukazi leyo okuhloswe ngayo ukwakhiwa kwamathuluzi ocwaningo nokuxazulula izinkinga. zezinkinga zezibalo. Ezinye zalezi zindawo zokusetshenziswa kwezibalo yilezi:

Izibalo

Lezi izibalo ezivame ukusetshenziswa emathubeni kanye nasemakhonweni okubikezela izehlakalo ngezinga elilinganayo noma lephesenti, ukuze ukwazi ukwenza izinqumo ezifanele nezihlosiwe.

Amamodeli Wezibalo

Yilezo ezisetshenziselwa ukumelwa kwezinombolo njengendlela yokulingisa izici zeqiniso lansuku zonke, ukuze sizame ukubikezela noma ukuqonda ngokufingqiwe ubudlelwano obukhona kuzo. Kuzuzisa ngokukhethekile ukuthi iyini indawo yekhompyutha.

Izibalo Zezezimali

Kulokhu zisetshenziswa emhlabeni jikelele wezezimali, njengoba izibalo kulokhu zivame ukuboleka uhlobo lwayo lolimi oluhlelekile ukuze kuboniswe kokubili ubudlelwano bezentengiselwano nezomnotho okuyibo okuyibo abakha lo mkhakha obaluleke kakhulu emphakathini wamanje nowakudala njengoba kahle..

I-Mathematics Chemistry

Isayensi yekhemistri iyona esebenzisa izibalo ukuze ikwazi ukuveza ubudlelwano bengxenye evame ukwenziwa ngezindlela ezihlukahlukene nezingenzeka zokusabela kodaba olushiwo.

Izinhlobo Zokusebenza

Ngokusho I-Chevalard, a Bosch futhi ukuze i-gascon, uphethe ngokuthi bekukhona cishe izinhlobo ezi-3 zokuhlinza ezingenziwa ngezibalo:

Sebenzisa Izibalo Ezaziwa

Lokhu kuhlanganisa ukuthatha izinqubo ezidalwe ngabanye abantu futhi bazenze ezinkingeni zabo ukuze zikwazi ukuxazululeka, kuphela ukusebenzisa ingqondo eqoqiwe nolwazi lwezinombolo njengethuluzi.

Bafunde Futhi Bafundise

Lapho kukhona inkinga enzima, umuntu angaphendukela kochwepheshe bezibalo abakhulu kunabo bonke noma kwezinye zezincwadi zayo, ukuze akwazi ukufunda ukuphatha zonke izindlela ezingaziwa kuze kube manje futhi ngaleyo ndlela andise eyabo indawo yokugcina. babe.

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Dala Izibalo Ezintsha

Esimeni esinjalo lapho lingekho ithuluzi lezibalo elibasebenzelayo ukuxazulula inkinga ethile, umuntu angaqhubekela ekudaleni eyodwa, inqobo nje uma kuthatha njengesiqalo lezo esezivele zaziwa kuze kube yimanje.

Ochwepheshe bezibalo abadumile

Emlandweni wezibalo kuneqeqebana labantu abebethathwa njengezazi zezibalo ezidume kakhulu emhlabeni wonke kusukela emandulo kuze kube yimanje. Yiqiniso, akekho kubo owasungula izibalo. Phakathi kwazo kukhona okulandelayo:

  • UPythagoras waseSamos kusukela ngonyaka wama-570 - 495 ngaphambili UKristu.
  • Euclids yonyaka wama-325 - 265 ngaphambili UKristu.
  • ULeonardo Pisano Bigollo kusukela ngonyaka we-1170 - 1250.
  • URené Descartes kusukela ngonyaka we-1596 - 1650.
  • Leonhard Euler kusukela ngonyaka we-1707 - 1783.
  • Andrew Wiles kusuka ngonyaka we-1953

Sithemba ukuthi lesi sihloko esithi Who Invented Mathematics sibe nesithakazelo esikhulu kuwe nokuthi kungenzeka ukuthi uthole ulwazi oludingekayo ngomlando wayo, imvelaphi, lokho ezisetshenziselwa kona futhi ikakhulukazi owasungula izibalo.