Amanani Fibonacci kwaye nomlinganiselo segolide: ubudlelwane

Xa iphela kusekho iimfihlelo ezininzi engekasonjululwa, ezinye izazinzulu baye bakwazi ukuchonga nokuchaza. amanani Fibonacci kwaye nomlinganiselo segolide asisiseko umkhondo zehlabathi, ulwakhiwo ukumila kwayo nendlela abayibona egqibeleleyo ezibonwayo abantu, athe nga va ubuhle nemvisiswano.

Section Golden

Umgaqo ubukhulu icandelo segolide sisiseko yogqibelelo yehlabathi lonke nezibilini zalo kubume bayo umsebenzi, ukubonakala kwayo kunokubonwa kwindalo, ubugcisa kunye nobugcisa. Imfundiso umlinganiselo wegolide iye yafakwa ngenxa izifundo yeemfundiso zamandulo amanani indalo.

Oku kusekelwe kwingcamango siswele zizalwa ubude yoqhekeko wayeyenze sobulumko yamandulo yezibalo kaPythagoras sele. Ungqinile ukuba ukwahlulwa abangakwaziyo ibe ngamaqela amabini: le X (ezincinane) kunye Y (elikhulu), umlinganiselo omkhulu amancinci ilingana lulwahlulo sum (total ubude):

X: Y = Y: X + Y.

Isiphumo inxaki: x ² - x - 1 = 0, nto leyo isonjululwe x = (1 ± √5) / 2.

Xa sijonga le umlinganiselo we-1 / x, ngoko ke ilingana 1.618 ...

Ubungqina bokusetyenziswa yawona yamandulo umlinganiselo wegolide zinikwe kwincwadi Euclid kaThixo "Elements", azibhalwanga kudala 3. BC, leyo isicelo lo mgaqo ukwakha echanekileyo-5-gon. I Pythagoreans, eli nani njengengcwele ngenxa yokuba zombini macala nezingafaniyo. Pentagram limela kunye nempilo.

amanani Fibonacci

Le edumileyo ethi Book abaci yezibalo Leonardo Pizanskogo e Italy, apho kamva owabizwa ngokuba Fibonacci, yapapashwa ngowe 1202. Kule leta, sisazinzulu yokuqala ipatheni esisisikhokelo amanani apho inani nganye umdibaniso inani amanani-2 edlulileyo. Sequence lumi ngolu hlobo lulandelayo:

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

Kwakhona, ISAZINZULU kuye kwakhokelela inani imithetho:

• Naliphi na inani lemiqolo lahlulwe ezilandelayo, iya kulingana kwixabiso okwakha 0.618. Kwaye amanani Fibonacci yokuqala ukunika inani ezinjalo, kodwa njengoko bepasa ukusuka ekuqaleni ukulandelelana, umlinganiselo iya kuba ngqo ngakumbi.
• Xa sisahlula inani lemiqolo kwi kowangaphambili, ngoko ke umphumo sukela 1.618.
• Elinye inani ulahlule yi lowo elilandelayo, uya kubonisa ukubaluleka ukuba uyabaleka 0,382.

Ukusetyenziswa konxibelelwano kunye neepateni kwicandelo yegolide, amanani Fibonacci (0.618) anokufunyanwa kuphela kwimathematika, kodwa kwindalo, imbali, ukwakha kunye nolwakhiwo, kunye nezinye izifundo zesayensi ezininzi.

siba Archimedean kunye uxande segolide

Ahamba aqhelekile kwindalo, iye uphando yi noArchimedes, apho kwade kwakhokelela equation yakhe. imilo Ukonakala isekelwe phezu imithetho kwicandelo yegolide. Ubude bayo imicu ifunyenwe, leyo ufakwe olinganise amanani Fibonacci, ukunyuka inyathelo kwenzeka ngokufanayo.

Umfuziselo phakathi amanani Fibonacci kunye icandelo yegolide, ungabona nokwakha "uxande yegolide", ogama macala ngokolungelelwano njengoko 1.618: 1. Ku yakhiwa, behamba ukuqala kuncinci ukuya uxande elikhulu ukuze ubude macala iya kulingana amanani manqaku. Ukwakhiwa enokwenziwa ukuze reverse, eqala kwisikwere "1". Xa uqhagamshela imigca, iimbombo uxande embindini wendlela ongenelayo ezifunyenwe Fibonacci okanye siba lwe logarithm olusezantsi.

Imbali ukusetyenziswa siswele zegolide

Abaninzi Egypt zesikhumbuzo zokwakha yamandulo kwakhiwa kusetyenziswa enkulu zegolide: edumileyo nePiramidi Enkulu njl Architects Ancient Greece ispolzoval kubo ngokubanzi ukwakhiwa izinto zokwakha, ezifana kwiitempile, yemidlalo yeqonga, amabala .. Umzekelo, yobuninzi ziye zasetyenziswa xa kusakhiwa kuyo itempile iParthenon yamandulo, yeqonga Dionysos (eAthene), kunye nezinye izinto eziyifaneleyo wobugcisa bokwakha ubudala, ebonisa ngokuvumelana, ngokusekelwe ukufika zemathematika.

Kwiinkulungwane ezalandelayo, umdla kwicandelo segolide ingasekho, kunye nemithetho sele ulibele, kodwa waphinda waqala Renaissance le ncwadi Franciscan indela L. Pacioli Di Borgo "Umlinganiselo KaThixo" (1509). It Imifanekiso uLeonardo da Vinci baye bezisa, kwaye balinqabisa igama elitsha "kwicandelo yegolide". Kukho nazo angqiniweyo ngokwezenzululwazi 12 iimpawu ratio segolide, umbhali wathetha ngayo kuziveza ngayo ngokwayo kwindalo, kwizinto zobugcisa, waza wayibiza ngokuba 'umgaqo yokwakha uxolo kunye nendalo. "

Leonardo kaThixo Vitruvian Man

Figure ukuba uLeonardo da Vinci ngo-1492 wazekelisa incwadi Vitruvius, oko ubonisa inani labantu kwi-sikhundla 2 ngezandla umtshato kwi emacaleni. Inani abhaliwe kwisangqa kunye isikwere. Eli nani ithathwa ukuba olinganise eziphefumlelweyo komzimba womntu (oyindoda), ezichazwe yi Leonardo ngenxa isifundo kwabo azibhala womzobi waseRoma Vitruvius.

umzimba hub njengenqaku equidistant ukususela ekupheleni iingalo kunye nesisu ingqalelo, iingalo ubude ngokulinganayo nobude bomntu, igxalaba iphezulu ububanzi = 1/8 ukuphakama, umgama ukusuka phezulu esifubeni ukuya iinwele = 1/7, ukususela esifubeni ukuya phezulu phezulu intloko = 1/6 imilenze njl

Ukususela ngoko, lo mfanekiso isetyenziswa njengomfuziselo, ebonisa wolingano lwangaphakathi emzimbeni womntu.

Igama elithi "Icandelo Golden" Leonardo lisetyenziswa ukuchaza ubudlelwane bulingane kulo mzobo yabantu. Umzekelo, umgama ukusuka esinqeni ukuya iinyawo imilenze ekwafanekisa kumgama elifanayo ukusuka inkaba ukuya phezulu kwakunye nokukhula ubude lokuqala (ukusuka esinqeni phantsi). Ezi zibalo zenziwa kwi umlinganiselo elinye zentetho ekubaleni ratio legolide kuyaphela 1,618.

Zonke ezi enkulu manyano adla ngokusetyenziswa amagcisa ukuba ukudala imisebenzi ezintle emikhulu.

izifundo kwicandelo yegolide kwiinkulungwane 16-19

Ukusebenzisa i ratio legolide amanani Fibonacci, umsebenzi uphando olinganise kuqhubeka kangangeenkulungwane. Ngokunxuseneyo ne uLeonardo da Vinci artist German Albrecht Dürer nayo inxaxheba kuphuhliso kwengcamango olinganise elichanekileyo omzimba womntu. Ngenxa yoko ke, kwakuhlwa zadalwa ikhampasi okhethekileyo.

Ngenkulungwane ye-16. ulwalamano lwamanani Fibonacci kunye icandelo segolide enikelwe ukuba umsebenzi ngeenkwenkwezi Kepler, ngubani okokuqala le migaqo ukuze Botany.

"Ukufunyanwa" New kulindeleke kwicandelo segolide 19. kunye kokupapashwa "zobuhle Studies" Inzululwazi waseJamani UNjingalwazi Tseyziga. Wavusa ngokomlinganiselo ukuya ngokugqibeleleyo isaziso ukuba jikelele kuzo zonke iziganeko zendalo. Kokuba befunde inani elikhulu labantu, okanye mandithi isilinganiso zabo ngokomzimba (2 amawaka.), Apho izigqibo ngeziphumo regularities manani kuqinisekiswa olinganise amalungu ahlukeneyo omzimba: iingalo ubude, iingalo, izandla, iminwe, njl

izinto ungowabo (zitsha, izakhiwo izakhiwo), iithowuni zomculo zaxilongwa, imilinganiselo ekubhalweni yemibongo - zonke Tseyzig sele ibonakala ubude kwimigca manani, naye elitsha elithi "nobuhle zemathematika." Emva kokufumana iziphumo lwabonisa ukuba series Fibonacci ifunyenwe.

amanani Fibonacci kunye icandelo segolide yendalo

Xa imifuno kunye nezilwanyana kwihlabathi, kukho isiqhelo ekubumbeni ngohlobo macala, nto leyo iqatshelwe kwicala ukukhula kunye nentshukumo. Icandelo lezabelo macala, othobela golden - ngumzekelo eqhelekileyo ukuba izityalo ezininzi kunye nezilwanyana.

Uhlobo esiphila ukuba Zichazwe ngumyalelo iinombolo Fibonacci, umzekelo:

• indawo naziphi amasebe okanye namagqabi izityalo, kwakunye imigama naleyo inani amanani anikiweyo 1, 1, 2, 3, 5, 8, 13 no ngakumbi;
• imbewu kajongilanga (kwi izixhobo isikali, iseli nepayina), lulele imikrozo emibini ahamba ezijijekileyo kumacala ahlukeneyo;
• umlinganiselo ubude umsila nomzimba necikilishe;
• egg imilo, ukuba umgca anqunyanyiswe enqumla yinxalenye ebanzi yalo;
• ulwalamano lomba iminwe kwi isandla.

Kakade ke, iintlobo ezininzi ezinomdla kakhulu ahamba indlovu iipateni iqokobhe kwi web, ukuhamba umoya inkanyamba, isakhiwo DNA kweleli kabini, ziwe - bonke bephela ziquka sequence.

Ukusebenzisa icandelo segolide zobuciko

Abaphandi ababandakanyekayo ubugcisa lokufumana imizekelo kusetyenziswe icandelo yegolide, iinkcukacha baphonononge izinto ezahlukeneyo zokwakha kunye nemisebenzi yobugcisa. Eyaziwa ngokuba imifanekiso eziziingangamsha, yiko athe ngqo olinganise zegolide, - nomfanekiso Olympian kaZeyus, Apollona Belvederskogo kunye Athena Parthenos.

Enye imisebenzi uLeonardo da Vinci - "Umfanekiso Mona Lisa" - elide iye isifundo oososayensi zophando. Bafumanisa ukuba ukwakhiwa umsebenzi iqulathe ngokupheleleyo le "Golden Triangle", wajoyina kunye yinkwenkwezi pentagon rhoqo. Wonke umsebenzi da Vinci yi womyoleli anzongonzongo kangakanani ulwazi lwakhe ngesakhiwo olinganise umzimba womntu, ukuze akwazi ukubamba uncumo emangalisayo qembu lwe Mona Lisa.

Icandelo bokwakha Golden

Ngokomzekelo, izazinzulu ezifunde yobuciko izakhiwo, okudalwe imithetho "kwicandelo yegolide": iiphiramidi umYiputa, oothixo, iParthenon, yaseNotre-Dame de Paris, eSt Vasiliya Blazhennogo kunye nabanye.

IParthenon - enye zakhiwo ezona zintle Greece Intshabalalo yaMandulo (5 BC.) - uye imiqolo-8 no-17 kumacala esahlukileyo, umlinganiselo ukuphakama kwayo ubude macala ilingana 0,618. Le projections on kwemi yawo yenziwe "kwicandelo yegolide" (ifoto ngezantsi).

Omnye (njalo-ebizwa ngokuba "Modulor") zobunzululwazi ceba kwaye ngempumelelo isicelo ukuphuculwa kwenkqubo seemodyuli ngenxa olinganise izinto zokwakha - yaba wezakhiwo French Le Korbyuze. Isiseko se Modulor wabeka inkqubo yokulinganisa ezinxulumene kunye ukwahlulwa olunemiqathango zibe ngamalungu omzimba womntu.

umyili Russian uMikhail Kazakov, owakha izakhiwo zokuhlala eziliqela e Moscow, kwakunye isakhiwo yeeNgwevu incwadi yesicelo, kunye Hospital Golitsyn (ngoku Clinical Pirogov 1.) - wayengomnye labazobi abasebenzisa uyilo kunye nolwakhiwo imithetho icandelo yegolide.

ibonwe Isicelo kuyilo

Uyilo zonke abathungi iingubo kwenza imifanekiso ezintsha kunye neemodeli kuthathelwa ingqalelo olinganise umzimba oluntu kunye nemithetho icandelo yegolide, nangona ngemvelo, asingabo bonke abantu babe olinganise efanelekileyo.

Xa becwangcisa isifundo uyilo landscape kunye nokudalwa ezaqanjwa womthamo ipaka usebenzisa izityalo (imithi namatyholo), imithombo kunye nezinto ezincinci zokwakha kunye neendlela ezinokusetyenziswa "enkulu kaThixo". Ngapha koko, ukwakhiwa epakini kufuneka zijoliswe ekudaleni zayichukumisa le ndwendwe, ngubani na ukuhamba ngokukhululekileyo kwaye ufumane iziko zizonke.

Zonke izinto ezibandakanyekilyo nepaki kwi yobuninzi esebenzisa isakhiwo zejometri, indawo efanelekileyo, ukukhanyisa, ukukhanya, bavelise umntu umbono ngokuvumelana kunye nemfezeko.

Ukusetyenziswa kwe candelo legolide cybernetics kunye nobuchwepheshe

Laws of the amanani Section Golden kunye Fibonacci zivele kwi utshintsho yamandla kwiinkqubo eziqhubeka kunye amasuntswana eziziziqalelo ezenza compound kwemichiza, kwiinkqubo indawo kwezakhi zofuzo ye DNA.

iinkqubo ezifanayo kwenzeka emzimbeni womntu, esizibonakalisa kwi biorhythms yobomi yayo, kwizigqeba senzo, ezifana ubuchopho okanye umbono.

Ubuchule kunye neepatheni enkulu zegolide ezisetyenziswa kakhulu cybernetics mihla kunye yokwazisa. Omnye wemisebenzi elula, ezikunika badwelisi benkqubo mafikizolo ukusombulula - uze ubhale indlela yokubekwa isixa kwamanani Fibonacci kwinani elithile, esebenzisa iilwimi kweenkqubo.

Uphando lwakutshanje kwingcamango umlinganiselo wegolide

Ukususela phakathi kwinkulungwane yama-20, umdla iingxaki kunye nefuthe kwemithetho ngumlinganiselo yegolide ukunyuka ubomi bomntu ngendlela emangalisayo, yaye zizazinzulu ezininzi imisebenzi eyahlukeneyo: zezibalo, uhlanga babaphandi, zebhayoloji, iingcali zefilosofi, iingcali zonyango, abezoqoqosho, iimvumi kunye nabanye.

Kwi-US ukusukela ngo-1970-hgodov iqalisa ukuba apapashe iphephandaba The Fibonacci Quarterly, ephethe amaphepha ngalo mbandela. Zipapashwa kumaphepha-ndaba kukho imisebenzi apho ulawulo ngokubanzi kwicandelo segolide kunye Fibonacci series zisetyenziswa kwiinkalo ezahlukeneyo zolwazi. Umzekelo, ukuba encoder ulwazi, imichiza zophando, begazi, njl

Konke oku kuqinisekisa ukuba iziphumo abaphengululi bamandulo mihla ukuba golden ngokubanzi ezinxulumene imibuzo ebalulekileyo kwinzululwazi macala kubonakala imisebenzi emininzi, kunye izenzakalo olujongwayo lubonwe.