Umlando izinombolo. Umlando ukuthuthukiswa izinombolo zangempela

ngempucuko yesimanje akunakwenzeka ukuba ukucabanga ngaphandle izinombolo. Sihlangana nabo nsuku zonke, senza eziningi kubo, ngamakhulu nangezinkulungwane yezenzo esebenzisa amakhompyutha. Thina ngakho esetshenziswa ke ukuthi umlando izinombolo thina akanandaba, futhi okuningi zikuthola omane ngikucabange. Kodwa futhi kungesemehlweni esidlule ngeke ayiqonde okwamanje, ngakho-ke kufanele zizame siqonde umsuka.

Ngakho-ke yini umlando izinombolo? Lapho uvele njengoba umuntu waba yokudalwa? Sazise ngakho!

ukuthuthukiswa

Esifundweni sezibalo, akukho ingxenye ebaluleke kakhudlwana. Naphezu kwakho konke lokhu, nenani njengendlela mqondo uye savela ezinkulungwaneni zeminyaka akufani njengoba izingqondo ososayensi emhlabeni wonke baye akavumelananga okwamanje sendlela bayibheka.

Isicelo lokuqala isiyalo, okuyinto kakhulu yafuna ukuvela lo mqondo, ziye kuzolinyelwa, ukwakhiwa, futhi kugcinwa izinkanyezi. Ngakwelinye ihlangothi, ekutadisheni esibhakabhakeni kanye Ukwahlukaniswa zonke izilinganiso zibalulekile sokuthuthukiswa okuthumela ukuhwebelana kwamazwe omhlaba, ngaphandle okuyinto ke akakwazanga ukuthuthukisa noma isiphi isimo.

ifilosofi kancane

Ngisho izibalo bakudala kunazo abangu saveza futhi salethwa ingqondo evamile amakhulu amaningi eminyaka. Abaningi babo kwamiswa ngenxa a rethinking okudala amazwi noma izinhlamvu ngazinye. I Pythagoras edumile yathi izinombolo ziyimfihlakalo ngakho, amandla esikhashana, kwakhiwa kusukela lapho wonke umkhathi. Ngokuvamile, ngokuvumelana imiqondo yesimanje nesayensi, wayengumuntu kakhulu ilungelo.

AmaShayina ihlukaniswe ngenani ngezigaba ezimbili ezibanzi (zisekhona kuze kube namuhla):

• Ngakunye noma yang. Ngo nefilosofi yamaShayina yasendulo yayifanekiselani ezulwini auspiciousness.
• Ngakho, ngisho (Yin). Lo mqondo lifanekisela umhlaba futhi ukungazinzi.

Kusukela ezikhathini zasendulo ...

Mhlawumbe usuke kakade ukuyichaza ukuthi umlando izinombolo iqala ngophawu kusukela esikhathini endala. Ngaleso sikhathi, izinhlamvu ongaqondakali ezazitholakala kuphela ukuqonda nelungelo labapristi, owaba ngowokuqala emlandweni wethu zezibalo zomhlaba.

Izazi zemvelaphi nenhlalo yabantu kanye abavubukuli baye ayiqinise ukuthi umuntu ingathiwa usuvele Stone Age. Ekuqaleni, inombolo yekucala lisho inani elihlukile iminwe yakhe nezinzwani zakhe. Sasebenzisa kubo ukubala izinyathelo isizinda, izitha ... Ekuqaleni, abantu badinga izinombolo ambalwa nje elula, kodwa ekukhuleni komphakathi zidinga izinhlelo ngokuya eziyinkimbinkimbi. Lokhu akugcini nje kwaholela ekwakhekeni kwe-iziqalo wezibalo, kodwa futhi nomthelela ekuthuthukiseni impucuko zabantu bebonke, njengoba kudingwa yi-ukucindezeleka umsebenzi bokusungula.

Ngakho indaba ukuvela nentuthuko kuhlangene ngokungenakuhlukaniswa ngcono ingqondo isifiso wawobaba ukuzithiba ngcono. Lapho bebuka izinkanyezi, umcabango okwengeziwe regularities zezibalo (ngisho ezingeni bakudala) e elalibazungezile, abahlakaniphileyo baba.

umqondo enembile senombolo

Njengoba nje kwakukhona lapho enana lokuqala, abantu baqala ukutadisha ukuqhathanisa nenani ezinye izinto nezindinganiso ezifanayo imikhiqizo ahlinzekwa kuye. Imiqondo "ngaphezulu", "mbalwa kuna", "elilingana", "okuningi." Ulwazi kusheshe eyinkimbinkimbi ngoba ngokushesha kwaba khona isidingo uhlelo sibalo.

Kufanele kukhunjulwe ukuthi umlando izinombolo empeleni yaqala nge ukubukeka wokuqala Umuntu ocabangelayo. Yena intuitively wayazi ukuthi ukuqhathanisa isibalo sabantu, izilwane, izinto, namanje ayengawazi nhlobo ngisho izibalo elula. Kodwa lokho yinto eyinqaba kwaba: iyiphi into okungase kuthintwe, futhi abaningana kubo futhi ingabe eligoqiwe kalula endaweni inqwaba.

Izinombolo ezichaza izakhiwo zalezi zinto ezifanayo ezikhona, kodwa uthinte noma ukuqhathanisa kubo kwakungenakwenzeka. Le mpahla liye laholela abantu bekhexile, bathi ukuba izinombolo imilingo, izinga kwemvelo.

Kunebufakazi imibono eyayisinesikhathi

Sekuyisikhathi eside ososayensi bazitshela ukuthi ekuqaleni ezintathu kuphela abantu baye basebenzisa welithi "omunye", "ngazimbili" 'eziningi ". Lo mbono is lolungenamaphutsa kusekelwa yiqiniso lokuthi ngezilimi eziningi basendulo ababenayo ncamashi ezintathu izinhlobo (ngesiGreki, isibonelo): ayiveli elimbaxambili futhi ubuningi. Ngemva nje kancane kwalokho, abantu bafunda ukuhlukanisa, isibonelo, Buffaloes ezimbili kusukela ezintathu. Ekuqaleni, amaphuzu kwakuhambisana nezinga iyiphi isethi ethile lezinto.

Kuze kube muva nje, abantu base-Australia zomdabu kanye basePolynesia babe Izinombolo ezimbili kuphela: "omunye" futhi "ezimbili", kanye nazo zonke ezinye izinombolo zabantu zathola ngokuhlanganisa kubo. Ngokwesibonelo, isibalo amathathu - ababili kwathi omunye ezine - zimbili ndawonye. Kuyinto ngokuphawulekayo nezosuku uhlelo kanambambili sibalo, manje okuyinto usebenzisa ubuchwepheshe bama-computer! Nokho, ukuphila okuhlukumezayo ngalezo zikhathi baphoqeleka ukuba bafunde, futhi bakudala ngakho ngokushesha yaphenduka isayensi zezibalo.

IBhabhiloni nabaseMesophothamiya

Ngo iBhabhiloni lasendulo wezibalo ezakhiwa ikakhulukazi kahle, ngoba kule wombuso ukudala omkhulu, izakhiwo eyinkimbinkimbi kakhulu ukuthi akukho izibalo ukuthi kwakungeke kwenzeke ukwakha. Isimanga siwukuthi kodwa abantu baseBhabhiloni akazange ukondla amadlingozi ekhethekile izinombolo, ukuze umlando nomqondo inombolo ngomqondo ebanzi izwi waqala ngokunembile nabo.

AbaseBhabhiloni abehlelwa besikhathi sakhe ukuthi Ungarekhoda inombolo enkulu lezinto, abantu noma izilwane isethi okungenani izinhlamvu. Bona uhlelo positional yethulwa okokuqala, okusikisela ehlukile inani lenombolo izibalo efanayo, bangazihluphi izikhundla ezahlukene umongo yezinombolo.

Ngaphezu kwalokho, uhlelo kwabo ukubala yayisekelwe sexagesimal nesilinganiso indlela, lapho abaseBhabhiloni ososayensi lokucabanga, lathathwa impucuko nesi. Ungacabangi ukuthi, nakuba kulendawo umlando nomqondo stop. Thina namanje ukusebenzisa umqondo imizuzu 60, imizuzwana 60, 360 ka esimeningcondvo nesilinganiso selilonke.

silindele Pythagoras

Ababhali basendulo eBhabhiloni kakade eyaziwa kahle izakhiwo onxantathu kwesokudla. Ngaphezu kwalokho, benza ukubala umthamo iphiramidi ufushanisiwe. Namuhla kuyaziwa ukuthi umlando ukuthuthukiswa izinombolo okunengqondo kuvela ngokunembile kusukela ngaleso sikhathi: eMesophothamiya neBhabhiloni wezibalo hhayi kuphela ngenkuthalo esetshenziswa izingxenyana zegazi, kodwa ndlela kungakusiza ngisho inkinga yabo, nge angaziwa bebathathu!

Esikhathini esidlule yamuva, nesifundo sezibalo zanamuhla bamangala ukufunda ukuthi ababengaphambi zabo lasendulo kuphumelele imizamo square nje kuphela, kodwa ngisho impande cube. Baqala nokuqaphela eduze definition of Pi, cishe ukuqoqa phansi kuya kwemithathu. Kufanele kuqashelwe ukuthi amaGibhithe ke bakwazi ukubala okuningi ngokunembe kakhudlwana ukubaluleka (3.16).

izinombolo yemvelo

Ayikho lasendulo kancane umlando ukuthuthukiswa inombolo zemvelo. Manje babekholelwa ukuthi ukusetshenziswa lokuqala leli gama emibhalweni yakhe isazi esingumRoma Boethius (480-524 GG.), Kodwa esikhathini eside ngaphambi kokuba Nicomachus ka Gerazy wabhala ezincwadini zakhe phezu zemvelo, uchungechunge engokwemvelo izinombolo.

Nokho, ngomqondo wesimanje ukuthini igama elithi "inombolo wemvelo" lisetshenziswa kuphela D'Alembert (1717-1783 GG.). Kodwa akufanele quibble: isifundo ngokwayo akhawunti e ukuqala nabo. Phela, kungokwemvelo ukuthi inombolo 1, 2, 3, 4, ...

Nge ukubukeka kwabo kwaba yisinyathelo esibalulekile ekufezeni ukuvela wezibalo ne-Aljibhra ngesimo lapho siwazi namuhla. nesifundo sezibalo zanamuhla ngokuqiniseka ekhuluma uchungechunge esingapheliyo izinombolo zemvelo. Yiqiniso, ezikhathini zasendulo, abantu babengazi ngakho. Inani ukuthi abantu nje abakwazi ukucabanga, okhonjiswe igama elithi "ubumnyama" "ULegiyona, *", "iqoqo", njalo njalo. Ngakho ukuthi umlando inani lemigqa kuyinto endala kakhulu ...

Setha theory

Okokuqala, izinombolo zemvelo bebumfishane kakhulu. Kodwa-Archimedes abadumile (III. BC. E.) Ingabe ukwazi kakhulu ukwandisa lo mqondo. Wayekhipha yona le usosayensi edume wabhala umsebenzi "Isihlabathi ningi," okuyinto besikhathi sakhe uvame ukubizwa ngokuthi "Ukubalwa zesihlabathi." He bala ngokunembile inani ezinhlayiyeni ezincane, okuyinto kwakuthiwa kungathatha wawuqeda wonke lo mqulu we-sithombe ne ububanzi 15.000.000.000.000 amakhilomitha.

Ngaphambi Archimedes amaGreki bakwazi ukufika inombolo 10.000.000 inqwaba. Nokho, inqwaba, babiza inombolo at 10 000. kakhulu Igama livela esiGrekini "Miros", okuyinto zihunyushelwe izindlela Russian "ngokungenamkhawulo enkulu", "sikhulu omkhulu". Archimedes futhi gone okwengeziwe: waqala ukusebenzisa izibalo zayo inkulumo ethi 'amashumi ezinkulungwane aphindwe ngamashumi ezinkulungwane,' kamuva bamyisa ukudala siqu, uhlelo ukubala kombhali yakhe.

Inani esiphezulu ezingase ukuchaza Usosayensi othile iqukethe amaqanda 80.000.000.000.000.000. Uma uzitholele le nombolo ende iphepha itheyiphu ke kungenzeka ukuba uhlanganise wonke umhlaba enkabazwe izikhathi abayizithulu abangaphezu kwezigidi ezimbili.

Ngakho, kuzo zonke integers omuhle kukhona imisebenzi emibili emikhulu:

• Abakwazi lungachazwa inani nanoma yiziphi izinto.
• Ngosizo lwabo uchaze izimfanelo lezinto ochungechungeni inombolo.

reals

Kodwa kuthiwani umlando ukuthuthukiswa izinombolo yangempela? Phela, izibalo hlala endaweni kubaluleke! Okokuqala, uvuselele inkumbulo. Igama langempela kungaba yisiphi omuhle, negative, futhi zero. Iningi labo zihlukaniswe okunengqondo engenangqondo.

Uma ufundisisa isihloko, ungase ukuqagela ukuthi umlando ukuthuthukiswa izinombolo yangempela iqala ukuntwela isintu. Njengoba umqondo weguncu ngokokuqala (ukwaziswa okwengeziwe noma ngaphansi okunokwethenjelwa) washayelwa ngonyaka 876 ngemva kokufa kukaKristu, futhi yethulwa e-India, ungakwazi uphawu lolu suku njengoba eliphakathi nendawo.

Njengoba for amagugu negative, okokuqala siwachaza Diophantus (Greece) e lesithathu AD leminyaka, kodwa "ibhaliswe ngokomthetho", babesanda India, cishe ngasikhathi sinye nge umqondo wegama elithi "u-zero".

Kufanele kukhunjulwe ukuthi umlando izinombolo mathematics kudinga ukuba khona eGibhithe lasendulo ngenxa izibalo kuthiwa Ngokuvamile ubonakaliswa isimo sengqondo. Nawa nje ngesikhathi babebhekwa 'ezingenakwenzeka' zenzeke futhi "ungenangqondo", nakuba ngezinye izikhathi asetshenziswa njengoba amanani Intermediate.

izinombolo okunengqondo

Khumbula ukuthi inombolo okunengqondo kuyinto ingxenyenamba. Ngo ngesimo numerator inamba elisetshenziswa kuyo, kanye nezenzo zifana njengoba inombolo zemvelo. Asazi ukuthi nini futhi kuphi lo mqondo Kuvezwe okokuqala, kodwa ngenkuthalo esetshenziswa Sumerians kakade minyaka eyizinkulungwane ezimbalwa BC. Isibonelo sabo kwalandelwa amaGreki futhi abaseGibhithe.

izinombolo eziyinkimbinkimbi

Kodwa abazitholile esanda kutholakala, ngokushesha ngemuva kokukhomba izindlela ukubala izimpande ezothando cubic. Ngakwenza lokhu Italian Niccolò Fontana Tartaglia (1499-1557 GG.) Mayelana ekuqaleni kwekhulu leshumi nesithupha. Wabe esethola ukuthi ukuxazulula izinhlobo ezahlukene izinkinga kuyenzeka zingayitholi ukusebenzisa izinombolo kuphela langempela.

Ukuchaza lokhu into eyinqaba kwaba kuphela ngo-1572. Kwenze ayengakwenza Rafael Bombelli, kusukela oqala indaba ukuthuthukiswa eqela. Kodwa imiphumela yakhe isikhathi eside kubhekwa "ezisungulwe quack, 'futhi uyena kuphela ekhulwini le-19, isazi sezibalo esikhulu Carl Friedrich Gauss wafakazela ukuthi eyandulela wakhe okude kwaba ngokuphelele kwesokudla.

omunye umbono

Abanye abacwaningi bathi amagugu lokuqala ngengqondo oshiwo kudala njengoba 1545. Kwasekusithi Amakhasi odumile ngesikhathi zomsebenzi "art Omkhulu, noma Algebra Imithetho", owabhala Gerolamo Cardano. Wabe esezama ukuthola izinombolo ezimbili ikhambi, okuyinto lapho siphindwe 10 Phanini futhi banda value abo ukukhuphuka 40.

Kwaphela isikhathi eside ngaphambi ngu zezibalo kwaba umbuzo ukuthi kungaba khona eziningi kubo ivaliwe ngokuphelele. Ake uchaze: is imisebenzi ku amagugu eziyinkimbinkimbi kuholele eziyinkimbinkimbi Imiphumela yangempela nje noma olunye ucwaningo kungaholela ekutholakaleni into entsha ngokuphelele? Nokho, ikhambi lale nkinga ungaphakathi imisebenzi ka-Abrahama de Moivre (bathi usukela emuva 1707), kanye emibhalweni Roger Côtes, okuyinto yashicilelwa 1722.

Yilokho sonke umlando inombolo. Kafushane, yebo, kodwa sihloko usawucubungula lo mlando ezinkulu zocwaningo kule ndawo.