Fibonacci izinombolo kanye isilinganiso segolide: ubudlelwane

Ngo yonke zisekhona eziningi eziyimfihlakalo ezingaxazululeki, ezinye zazo, ososayensi baye bakwazi phambili ngokubona begodu bahlathulule. Fibonacci izinombolo kanye isilinganiso segolide ziyisisekelo zokuthambekela emhlabeni, ukwakhiwa ezakheke kanye elikhulu womuntu okuqonda sibonwa, ngalo bangazizwa muhle futhi ube nobunye.

Golden Isigaba

Umgomo we segolide kwesigaba osayizi oluyisisekelo ukuphelela umhlaba wonke futhi izingxenye zalo e lokuphatselene nesakhiwo nemsebenti yayo, ukubonakaliswa yayo kungabonakala ezintweni zemvelo, ezobuciko kanye nobuchwepheshe. Imfundiso kaZiqu-isilinganiso golden iye ifakwe ngenxa izifundo izimfundiso bemvelo izinombolo lasendulo.

Kusekelwe imfundiso yokuziphendukela olinganise futhi okungu lenebudze yezigaba okwakwenziwe ukuze sefilosofi lasendulo nesazi sezibalo Pythagoras. Akabanga ukuthi ukuhlukana kwazo ingxenye yaba izingxenye ezimbili: X (ezincane) kanye Y (elikhulu), isilinganiso esikhulu ukuze elincane elilingana isilinganiso isamba (ubude):

X: Y = Y: X + Y.

Umphumela ezothando: x ² - x - 1 = 0, okuyinto ixazululwe x = (1 ± √5) / 2.

Uma sibheka ratio 1 / x ke elilingana 1.618 ...

Ubufakazi ukusetshenziswa ongqondongqondo isilinganiso golden lasendulo banikwa encwadini "Imisuka" Euclid sika, azibhalwanga kudala njengoba 3. BC, okuyinto isicelo mthetho ukwakha lesifanele 5-gon. I Pythagoreans, leli nani liphindeke njengengcwele ngoba kokubili ziyalingana futhi engalingani. Pentagram lifanekisela ukuphila nempilo.

Fibonacci izinombolo

Adume ncwadi Liber abaci sezibalo Leonardo Pizanskogo e-Italy, okuyinto kamuva eyaziwa ngokuthi Fibonacci, yanyatheliswa ngo 1202. Ngo-ke usosayensi wokuqala phambili iphethini izinombolo lapho inombolo ngayinye isamba inani 2 izinombolo odlule. Fibonacci ukulandelana simiswe ngalendlela lelandzelako:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, njll

Futhi, usosayensi kuye kwaholela inombolo kwemithetho:

• Noma iyiphi inombolo yemigqa yahlukaniswa okwalandela, kuyoba ulingana value okuyinto ivame ukuba 0.618. Futhi Fibonacci izinombolo zokuqala ungayeki inombolo enjalo, kodwa njengoba uthuthukela kusukela ekuqaleni wokulandelana, isilinganiso kuyoba oluqonde kakhulu.
• Uma thina bahlukanise inani lemigqa ku sangaphambilini ke umphumela sukela 1.618.
• Inombolo yokuqala ehlukaniswa kwesilandelayo, sizobonisa ukubaluleka ukuthi ivame ukuba 0,382.

Ukusetshenziswa zokuxhumana kanye amaphethini esigabeni segolide, Fibonacci izinombolo (0.618) zingatholakala hhayi kuphela kwi-mathematics, kodwa futhi ngokwemvelo, umlando, izakhiwo kanye nokwakhiwa, kanye neminye imikhakha yesayensi eziningi.

Kuvunguza Archimedean kanye isikwele segolide

Lemiklamo kuvamile kakhulu emvelweni, iye liphenywa Archimedes, okuyinto ngisho kwaholela kwesibalo wakhe. umumo Kuvunguza kusekelwe imithetho esigabeni segolide. Ubude bayo unwinding etholwe, okungase kusetshenziswe futhi olinganise Fibonacci izinombolo, isinyathelo ukwanda kwenzeka nombala.

Parallel phakathi kwezinombolo Fibonacci futhi esigabeni segolide, ungabona futhi ukwakha "isikwele osemqoka", ogama izinhlangothi ezilinganiselwe njengoba 1.618: 1. It yakhiwa, uya kusukela komncane kuya isikwele emikhulu ukuze ubude emaceleni kuyoba ulingana izinombolo yochungechunge. Ukwakhiwa kungenziwa oda reverse, eziqala isikwele "1". Uma uxhuma imigqa, amakhona konxantathu maphakathi nomgwaqo etholwe Fibonacci noma Kuvunguza logarithmic.

Umlando ukusetshenziswa ngezabelo igolide

Eminingi yasendulo Egypt esikhumbuzo yezakhiwo ezakhiwa usebenzisa ngezabelo igolide: abadumile Omkhulu Pyramid njll Architects Ancient Greece ispolzoval kubo kabanzi ekwakhiweni izinto lathumela, ezifana amathempeli, inkundla yemidlalo, izinkundla .. Ngokwesibonelo, ngezabelo ezinjalo ziye zasetshenziswa ukuba kwakhiwe le Parthenon lasendulo, yaseshashalazini Dionysos (Athens), kanye nezinye izinto abe wobuciko izakhiwo ezindala, ebabonisa ngokuvumelana, esekelwe njalo zezibalo.

Emakhulwini eminyaka alandela, isithakazelo esigabeni segolide kudamba, nemithetho ziye ukhohliwe, kodwa futhi waqala Yempucuko ngethi Franciscan indela L. Pacioli Di Borgo "Ingxenye Kwaphezulu '(1509). It nemifanekiso nge uLeonardo da Vinci senenziwe, futhi okuyinto kuvikelwe igama elisha "kwesigaba osemqoka". Kube tiphindze ngokwesayensi kungase kutholakale 12 izakhiwo isilinganiso segolide, umlobi sasixoxa ngakho ububonisa kanjani ngokwayo ngokwemvelo, kwezobuciko, walibiza ngokuthi "isimiso ekwakheni ukuthula nendalo."

SikaLeonardo Vitruvian Man

Figure ukuthi uLeonardo da Vinci ngo-1492 kuboniswe encwadini Vitruvius, ke ubonisa sibalo babantu 2-isikhundla ngezandla ohlukanisile ezinhlangothini. Isibalo alotshiwe kumbuthano futhi isikwele. Lesi sibalo ubhekwa olinganise ezakha umzimba womuntu (owesilisa), esichazwa Leonardo ngesisekelo yokutadisha kwazo kule azibhala wezakhiwo Roman Vitruvius.

Ihabhu umzimba njengendlela iphuzu equidistant kusukela ekupheleni izingalo nemilenze esiswini kubhekwe, izingalo obuphelele ilingana ukuphakama womuntu, ehlombe esiphezulu width = 1/8 ukuphakama, ibanga kusuka phezulu esifubeni kuya izinwele = 1/7, kusukela esifubeni kuya phezulu phezulu ikhanda = 1/6 njll

Kusukela ngaleso sikhathi, lesi sithombe isetshenziswa njengophawu olumelela, okubonisa wesimethri yangaphakathi zomzimba womuntu.

Igama elithi "Golden Isigaba" ULeonardo elisetshenziselwa ukuchaza ubudlelwano obuhambisanayo figure womuntu. Ngokwesibonelo, ibanga kusuka okhalweni kuya ezinyaweni imilenze sifana elifanayo ukusuka inkaba kuya phezulu kanye ukukhula ubude lokuqala (kusuka okhalweni kwehle). Lezi izibalo kwenziwa okufanayo zingxenye kulesi sibalo isilinganiso segolide futhi avame 1,618.

Zonke lezi ngezabelo obunobunye avame ukusetshenziswa abaculi ukudala imisebenzi amahle umxhwele.

segolide izifundo isigaba 16-19 eminyaka

Ukusebenzisa isilinganiso segolide Fibonacci izinombolo, umsebenzi ucwaningo ku olinganise siqhubeke amakhulu eminyaka. Ngo parallel uLeonardo da Vinci umculi German Albrecht Dürer wayebuye esibandakanyeka ekwakhiweni inkolelo-mbono yokuziphendukela olinganise lesifanele zomzimba womuntu. Ngenxa yalokhu, ngisho Ikhampasi ekhethekile yadalwa.

Ekhulwini le-16. ku ubuhlobo Fibonacci izinombolo kanye esigabeni segolide yayizimisele umsebenzi isazi sezinkanyezi Kepler, ngubani asebenza okokuqala kulezi zimiso ukuba wezitshalo.

"Ukutholakala" okusha kulindeleke esigabeni segolide 19. lapho kunyatheliswa "Tebuciko Studies" Usosayensi German UProfesa Tseyziga. Evusa ngokulingana okuphelele futhi imemezele ukuthi kukhona jikelele kubo bonke zemvelo. Wawutadishe inani elikhulu labantu, noma kunalokho ngezabelo kakhulu kujabulisa umtimba wabo (mayelana 2 eyinkulungwane.), On okuyinto iziphetho imiphumela regularities kwezibalo ukuqinisekisile olinganise ezahlukene zomzimba: izingalo ubude, izingalo, izandla, iminwe, njll

futhi art izinto (isitsha sezimbali, izakhiwo yezakhiwo), amathoni zomculo Kwahlolisiswa, izinhlangothi ekulotshweni izinkondlo - konke Tseyzig uye wabonisa ngokusebenzisa ubude imigqa izibalo, wabuye owaqamba igama elithi "sobuhle bayo zezibalo." Emva kokuthola imiphumela yembula ukuthi Fibonacci uchungechunge is eyatholakala.

Fibonacci izinombolo kanye esigabeni segolide ngokwemvelo

Ezweni yemifino kanye isilwane, kukhona mkhuba maqondana ekubumbeni efomini wesimethri, okuyinto okubonakale isiqondiso ukukhula kanye nokunyakaza. I division zibe izingxenye ziyalingana, okuyinto ngokuvumelana golden angle - yiphethini ezivamile kuya Izitshalo nezilwane eziningi.

Nature abasizungezile bangase lingachazwa ngumuntu izinombolo Fibonacci, isibonelo:

• indawo yanoma yimuphi amagatsha noma amaqabunga izitshalo, kanye amabanga zivumelana eziningi yezinombolo ezinikeziwe 1, 1, 2, 3, 5, 8, 13 futhi eminye;
• imbewu sunflower (kwi Izigaxa esikalini, uphayinaphu cell), elele ezimbili zezitokisi ezingu-lemiklamo ezisontekile bacondze etindzaweni letehlukene;
• isilinganiso ubude umsila nomzimba isibankwa;
• Iqanda umumo, uma umugqa okwesikhashana yonkana ingxenye ebanzi ke;
• aspect ratio iminwe esandleni somuntu.

Futhi-ke, amafomu ezithakazelisayo kakhulu kukhona lemiklamo umnenkhe amaphethini igobolondo kuwebhu, ukuhamba umoya isiphepho, kabili isakhiwo Helix DNA nemithala - bonke zihlanganisa ukulandelana Fibonacci.

Ukusebenzisa kwesigaba yegolide art

Abacwaningi ehilelekile ubuciko ekutholeni izibonelo ukusetshenziswa kwesigaba segolide, imininingwane ukuhlola izinto yezakhiwo ezahlukene nemisebenzi yobuciko. Babaziwa Ngokungenisa kwezithombe abadumile, abadali okuyinto abanamathela olinganise segolide, - statue Olympian uZeyusi, Apollona Belvederskogo futhi Athena Parthenos.

Omunye imisebenzi uLeonardo da Vinci - "Portrait of Mona Lisa" - Sekuyisikhathi eside isihloko ososayensi ucwaningo. Zathola ukuthi i-Ukwakheka komsebenzi siqukethe ngokuphelele "yeGolden Triangle", wajoyina ndawonye njalo pentagon inkanyezi. Zonke umsebenzi da Vinci kuyinto yeTestamente kuya ezijulile kanjani ulwazi lwakhe isakhiwo kanye olinganise zomzimba womuntu, kangangokuthi wayengakwazi ukubamba ukumamatheka emangalisayo Ayindida we Mona Lisa.

Golden Isigaba izakhiwo

Njengoba isibonelo, ososayensi behlola yobuciko bokwakha, adalwe imithetho "kwesigaba osemqoka": imibhoshongo baseGibhithe, onkulunkulu, le Parthenon, Notre-Dame de Paris, St Vasiliya Blazhennogo nabanye.

Parthenon - sezakhiwo ezinhle kunazo in Ancient Greece (5 Ekhulwini BC.) - has 8 amakholomu kanye 17 ezinhlangothini ezihlukene, isilinganiso ukuphakama kwalo kuya ubude emaceleni ilingana 0,618. Tilinganiso ku olungaphambili lwesonto yayo eyenziwe "kwesigaba osemqoka" (isithombe ngezansi).

Omunye ososayensi owasungula futhi ngempumelelo isicelo ngcono uhlelo Modular for olinganise lezinto yezakhiwo (okubizwa ngokuthi "Modulor") - kwaba umakhi French Le Korbyuze. Ngesisekelo Modulor ukubeka uhlelo wokulinganisa ephathelene ne-division okunemibandela ibe izingxenye zomzimba womuntu.

Uhlelo Lokufaka Lwe-Russian Mikhail Kazakov, eyakha eziningana izakhiwo zokuhlala e Moscow, kanye isakhiwo iSigele ku ezibiyele, kanye Golitsyn Isibhedlela (manje 1st Pirogov Clinical.) - wayengomunye walaba abaklami ababesebenzisa ukuklanywa nokwakhiwa kwemithetho esigabeni segolide.

ngezabelo Isicelo design

Umklamo zonke Abaklami isembatho ukwenza izithombe ezintsha futhi onobuhle ikhumbula olinganise ngomzimba womuntu nangendawo imithetho esigabeni segolide, nakuba ngokwemvelo, akubona bonke abantu babe olinganise ekahle.

Uma uhlela design landscape nokudalwa volumetric epaki izingoma usebenzisa izitshalo (kwemithi nezihlahla), nemithombo, izinto yezakhiwo amancane amaphethini ingasetshenziswa "ngezabelo saphezulu." Phela, indlela yokwakheka kwepaki kufanele okuhloswe ngawo ukudala umbono phezu isivakashi, abangakwazi ngokukhululekile uzulazule futhi ukuthola isikhungo oluyinhlanganisela.

Zonke izici yaleli paki kukhona ngezabelo yokuthi esebenzisa isakhiwo weJiyomethri, isikhundla isihlobo, ukukhanyisa, ukukhanya, ukukhiqiza umuntu umbono ongahambisani nokuphelela.

Ukusetshenziswa kwesigaba yegolide cybernetics nobuchwepheshe

Imithetho ye-Golden Sesigaba Fibonacci izinombolo futhi avele ukuhwebelana amandla e izinqubo ezenzeka izinhlayiya aphansi akha enkompolo zamakhemikhali, emkhathini izinhlelo ukukhubazeka kwezakhi ezithile zofuzo isakhiwo DNA.

izinqubo ezifanayo zenzeke emzimbeni womuntu, okuyinto kubonakala biorhythms sokuphila kwayo, esenzweni izitho, ezifana ingqondo noma umbono.

Algorithms kanye amaphetheni ngezabelo segolide kabanzi cybernetics yesimanje kanye Informatics. Omunye imisebenzi elula, anikeza program imfundamakhwela ukuxazulula - nokubhala ifomula ukunquma isamba Fibonacci izinombolo inombolo ethile, usebenzisa izilimi izinhlelo.

Ucwaningo lwamuva ngemfundiso yokuziphendukela isilinganiso segolide

Kusukela maphakathi nekhulu lama-20, kwavuselelwa isithakazelo izinkinga futhi umthelela imithetho olinganise yegolide umuntu aphila inyuka kakhulu, futhi ososayensi abaningi ukuzibonakalisa ahlukahlukene: zezibalo, uhlanga labacwaningi, izazi zezinto eziphilayo, izazi zefilosofi, ochwepheshe bezokwelapha, osomnotho, abaculi kanye nabanye.

E-US kusukela 1970-hgodov iqala ukushicilela umagazini Fibonacci Quarterly, okuyinto ishicilela amaphepha mayelana nale ndaba. In the press kukhona imisebenzi lapho umthetho generalized esigabeni segolide kanye Fibonacci uchungechunge asetshenziswa emikhakheni ehlukahlukene. Ngokwesibonelo, ukuze encode ulwazi, wokucwaninga ngamakhemikhali, yemvelo, njll

Konke lokhu kuqinisekisa okutholakele izazi zasendulo nezanamuhla ukuthi golden angle icubungulisise exhumene emibuzweni eyisisekelo isayensi wesimethri kubonakala emisebenzini eminingi, futhi izenzakalo of kwezwe elisizungezile.