I-Golden Ratio - a ... segolide kwesigaba imibhoshongo. Ifomula esigabeni segolide

Jiyomethri - isayensi eqondile futhi kuyinkimbinkimbi ukuthi uma konke lokhu uhlobo yobuciko. Line, indiza, olinganise - konke lokhu kusiza ukwakha izinto eziningi ezimangalisayo ngempela. Futhi Isimanga siwukuthi, lokhu kusekelwe geometry ngakho ezihlukahlukene izinhlobo. Kulesi sihloko sizohlola into eyodwa engavamile kakhulu, okuyinto ngqo exhumene naso. kwesigaba Gold - lena indlela weJiyomethri, okuzoxoxwa.

ukuma into kanye nombono yayo

Abasebenzisi ziqondiswa ikakhulukazi ukuma into ukuze sikubone phakathi nezigidi zabanye abenza okufanayo. Lokho ifomu sithole ukuthi iyini ukuthi into phambi kwethu noma imele kude. Siqale ukubazi abantu ukuma umzimba nobuso. Ngakho-ke, singasho kugcwale bagomela ngokuthi ifomu uqobo, usayizi waso kanye nohlobo - yezinto ezibaluleke kakhulu Umbono womuntu.

Kubantu yakha yini enye libaluleke ngenxa yezizathu ezimbili eziyinhloko: noma ke kuyimfuneko nje isuke ibangelwa ukuphila, noma enye okuthiwa injabulo yobuhle kusukela ubuhle. The best okuqonda sibonwa kanye umqondo ngokuvumelana nobuhle liza lapho omunye uyaphawula ifomu elisetshenziswa nokwakhiwa kwezindlu wesimethri kanye nobuhlobo obukhethekile, othiwa isilinganiso segolide.

Umqondo we esigabeni segolide

Ngakho, isigaba segolide - kusho segolide, okuyilona elisebenzayo futhi zihlukanise harmonic. Ukuze ukuchaza lokhu ngokucace kakhudlwana, cabanga ukuma abanye ethile. Okungukuthi, ukuma kuyinto sonke, kanye nokunye, yena, njalo inezingxenye eziningana. Lezi izingxenye kungenzeka babe nezici ezihlukahlukene, okungenani letingemasayizi lahlukene. Kodwa Ubukhulu enjalo zihlale endaweni isilinganiso esithile, kokubili bodwa futhi maqondana lonke.

Ngakho, ngamanye amagama, singasho ukuthi isilinganiso golden - isilinganiso nenani ezimbili, okuyinto has ifomula ayo. Ukusebenzisa le isilinganiso ukwakha amafomu kusiza ukwenza kube njengoba enhle nobunye ukuze ehlweni lomuntu.

Kusukela umlando esigabeni segolide lasendulo

Isilinganiso esigabeni segolide livame ukusetshenziswa ezindaweni eziningi ezahlukene zokuphila namuhla. Kodwa umlando ethemini iphindela endulo lapho esewusana ezifana wesayensi nesifundo sezibalo kanye nefilosofi. Njengoba umqondo yesayensi kwesigaba segolide eziphendulwa umoya zaqala ukusetshenziswa ngesikhathi Pythagoras, okungukuthi ku VI ekhulwini BC. Nokho ngisho nangaphambi kokuba ulwazi isilinganiso esinjalo, empeleni esetshenziswa eGibhithe lasendulo neBabiloni. A ubufakazi esiphawulekayo kule amaphiramidi, ayesetshenziselwa ukuze kwakhiwe nje golden angle ezinjalo.

inkathi entsha

I Renaissance kwaba umoya omusha division harmonic, ikakhulukazi sibonga uLeonardo da Vinci. Lobu buhlobo uya waqala ukusebenzisa sciences kanzima, ezifana geometry, kanye art. Ososayensi kanye abaculi babé ngaphezulu ukufunda kakhulu esigabeni segolide ukudala amabhuku ngale ndaba.

Omunye imisebenzi ezibaluleke kakhulu emlandweni ezihlobene isilinganiso segolide, - incwadi kaLuka Pancholi ngokuthi "ingxenye saphezulu." Izazi-mlando zicabanga ukuthi laba bameleli imifanekiso kule ncwadi zenziwa uLeonardo da Vinci.

Inkulumo zezibalo we isilinganiso segolide

Mathematics kunikeza incazelo ecacile kakhulu uma buqhathaniswa, othi kuba nokulingana okungu ezimbili. Izibalo, lokhu kungenziwa evezwe kule equation: a: b = a: d, lapho a, b, c, d - kuyinto inani elithile.

Uma sicabangela ingxenye ingxenye, ihlukaniswe yaba izingxenye ezimbili, kungaba ukuhlangabezana izimo ezimbalwa kuphela:

• Ingxenye ihlukaniswe yaba izingxenye ezimbili ngokuphelele alinganayo, futhi ngenxa yalokho AB: AC = AB: BC, uma AB - lena ekuqaleni ngqo futhi ekupheleni ingxenye, futhi C - iphuzu, okuyinto uhlukanisa ingxenye yaba izingxenye ezimbili alinganayo.
• Ingxenye ihlukaniswe yaba izingxenye ezimbili ukungalingani, okungaba olinganise ezahlukene nomunye, okusho ukuthi kukhona ngokuphelele buqhathaniswa.
• Ingxenye ihlukaniswe ukuze AB: AC = AC: Sun.

Ngokuqondene kwesigaba segolide, kuba wakhona ubude division zibe izingxenye ukungalingani bodwa, lapho yonke ingxenye libhekisela engxenyeni kakhulu, njengoba ingxenye enkulu kakhulu libhekisela esincane. Kunenye ekwakhiweni: ingxenye ezincane libhekisela enkulu kangaka njengoba emikhulu yonke ingxenye. Ngamagama zezibalo kunjengoba kulandela: a: b = b: c noma c: b = b: a. Kuyinto lolu hlobo ifomula esigabeni segolide.

I-Golden Ratio Emvelweni

kwesigaba Golden, izibonelo zazo manje sicabangela iphathelene lomkhuba Amazing nemvelo. Lesi yisibonelo esihle kakhulu ngalokho izibalo - akusiwona izinombolo nje amafomula, nesayense, okuyinto njalo seliphindeke izikhathi ezingaphezu reflection wangempela imvelo kanye ezimpilweni zethu ngokuvamile.

Ukuze izinto eziphilayo ingenye imisebenzi esemqoka zokuphila - kuba ukukhula. Leso sifiso ukuthi athathe indawo yakhe emkhathini, eqinisweni, kwenziwe izinhlobo eziningana - i ukwanda cishe ovundlile esakaza kanye phansi noma cockling kwamanye ukwesekwa. Futhi kungakhathaliseki ukuthi kwenzeke kanjani ukuba Amazing, izitshalo eziningi zikhula zibe ngokuhambisana isilinganiso segolide.

Elinye iqiniso cishe Amazing - kuyinto isilinganiso izibankwa umzimba. umzimba wabo ubukeka ngempela uyabukeka emehlweni womuntu, futhi lokhu Sibonga kungenzeka ukuba isilinganiso segolide. Ukuze yini ukunemba kakhudlwana, umsila yabo obuphelele busho ubude bomzimba wonke njengendlela 62: 38.

Amaqiniso ethakazelisayo imithetho esigabeni segolide

kwesigaba Gold - lena ngempela umqondo Amazing, okusho ukuthi kuwo wonke umlando singakwazi ukubhekana ngokuphumelelayo eziningi amaqiniso athakazelisayo ngempela ingxenye efanayo. Sethula wena ezinye zazo:

• I isilinganiso golden ngenkuthalo lisetshenziswe ekwakhiweni kwemibhoshongo yaseGibhithe. Ngokwesibonelo, elidume umhlaba wonke Tutankhamun futhi Cheops esakhiwe usebenzisa maqondana ezinjalo. Futhi engxenyeni segolide mbhoshongo namanje akwaziwa ukuthi waphelelaphi, ngoba kuze kube yilolu suku akazi ezihambela noma akhethe Ubukhulu enjalo lezisekelo zazo, nokuphakama.
• Ukubusa kwesigaba segolide iyabonakala ngokusobala olungaphambili lwesonto Parthenon - sezakhiwo ezinhle kakhulu izakhiwo eGrisi lasendulo.
• Kuyefana nasendleleni kwakhiwe Cathedral of Notre Dame (Notre-Dame de Paris), akusiyo mbumbulu nje, kodwa futhi nezinye izingxenye isakhiwo esakhiwe ngesisekelo lesi Ingxenye Amazing.
• Umklamo Russian zingatholakala izibonelo eziningi izakhiwo Amazing, nekuhambisana esigabeni segolide.
• division Evumelanayo futhi umuntu azalwa nalo lokuhlaziya umzimba womuntu, futhi ngenxa yalokho ebaziwe, ikakhulukazi emifanekisweni zabantu. Ezinjalo njengoba Apollon Belvedersky - esifanekisweni, lapho ukuphakama umugqa enkabeni lihlukaniswe esigabeni segolide.
• Painting - indaba ahlukahlukene, ikakhulukazi uma ucabangela indima uLeonardo da Vinci emlandweni isilinganiso segolide. abadumile yakhe Mona Lisa Yiqiniso, ingaphansi kwalo mthetho.

Isigaba Golden emzimbeni womuntu

Kule ngxenye, kumelwe ukusho umuntu obaluleke kakhulu - okungukuthi, S. Zeising. Umcwaningi-German owenze umsebenzi omkhulu kule mkhakha wocwaningo we isilinganiso segolide. Wanyathelisa umsebenzi enesihloko esithi "Izifundo Tebuciko". Encwadini yakhe ethi waletha kwesigaba segolide njengenhlangano umqondo ngokuphelele okungukuthi jikelele zonke izenzakalo kokubili semvelo art. Lapha singakhumbula golden kwesigaba imibhoshongo kanye Ingxenye obunobunye zomzimba womuntu nokunye.

It Zeising ukufakazela ukuthi isilinganiso segolide, eqinisweni, yiba umthetho kwezibalo isilinganiso nomzimba womuntu. Lokhu kuboniswa umkhuba, ngoba ngesikhathi umsebenzi wakhe ayenakho ukukala eziningi imizimba yabantu. Izazi-mlando zilinganisela ukuthi abantu abangaphezu kwezigidi ezimbili ayizinkulungwane wathatha ingxenye kule experiment. Ngokwe Zeising cwaningo, inkomba eyinhloko isilinganiso segolide - a division of iphuzu komzimba inkaba. Ngakho, umzimba besilisa nge ireshiyo 13: 8 kancane eduze esigabeni segolide kuka insikazi, lapho inani esigabeni golden 8: 5. Futhi, kuvela isilinganiso segolide kungabonakala nasemkhakheni nezinye izingxenye zomzimba, ezifana, isibonelo, isandla.

On ukwakhiwa esigabeni segolide

Eqinisweni, ukwakhiwa esigabeni segolide - ilula ngokwanele. Njengoba singabona, abantu basendulo ababhekana ngayo kuba lula. Yini ukukhuluma yolwazi nobuchwepheshe lesintu. Kulesi sihloko, ngeke wakubonisa kanjani lokhu kungenziwa nje kwi ephepheni bese umsizi esandleni, kodwa kuphephile ukusho ukuthi lokhu, eqinisweni, kungenzeka. Ngaphezu kwalokho, kungenziwa kude ngezindlela ezingaphezu kweyodwa.

Njengoba lena geometry kahle elula, isilinganiso golden oluphakeme elula ukwakha, ngisho esikoleni. Ngakho-ke, ulwazi ingatholakala kalula ezincwadini ezikhethekile. Ukutadisha segolide kwesigaba 6 ekilasini uyakwazi ngokugcwele ukuqonda izimiso yokwakhiwa kwayo, okusho ukuthi ngisho izingane smart ngokwanele ukuze balukhulume msebenzi.

Ingxenye Golden mathematics

Ukwazana kuqala ngesigaba yegolide umkhuba iqala elula kuhlukane line ingxenye zonke olinganise ofanayo. Ngokuvamile lokhu kwenziwa ubuso bombusi, ikhampasi kanye, yebo, ipensela.

I izingxenye isilinganiso golden wezwakalisa njengoba elingapheli ingxenyenamba engenangqondo AE = 0.618 ..., uma AB sithathwa iyunithi, BE = 0,382 ... Ukuze wenze lezi izibalo zama-practical, ngokuvamile zisebenzisa akusilo eliqondile, kodwa amanani eseduze, okungukuthi - 0 62 futhi 0.38. Uma ingxenye AB sithathwa izingxenye 100, iningi kuyoba ulingana 62, kahle, ezincane - izingxenye 38, ngokulandelana.

Impahla eyinhloko isilinganiso segolide ngokushaya ezothando: x ² -X 1 = 0. Ekuxazululeni sithola izimpande ezilandelayo: x = _1.2. Nakuba izibalo kuba nesayensi enembile futhi akanhlanhlatsi, kanye nesigaba yayo - izibalo zama-engela, kodwa ukuthi izakhiwo ezifana segolide isilinganiso amaphethini, ukuphakamisa imfihlakalo ngakho.

Harmony ubuciko ngokusebenzisa kwesigaba segolide

Ngamafuphi, ake sihlole kafushane ukuthi yini kakade.

Empeleni, ngaphansi kokubusa isilinganiso segolide kukhonjelwe izibonelo eziningi zobuciko, lapho waphawula isilinganiso eduze 3/8 futhi 5/8. Lena indlela olunzima esigabeni segolide. Isihloko sekushiwo eziningi izibonelo ukusetshenziswa cross-section, kodwa waphinda sibheka-ke ngokusebenzisa iphrizimu art zasendulo nezanamuhla. Ngakho, izibonelo yesiteleka kakhulu bezikhathi zasendulo,

• Golden Isigaba ecijile Cheops futhi Tutankhamun sivezwe yonke indawo: amathempeli, bas-imifanekiso, izinto zasekhaya, yebo, umhlobiso kakhulu emathuneni.
• Nethempeli Seti mina e Abydos imifanekiso abadumile ngemifanekiso ezahlukene, konke okuyizinto zivumelana zonke umthetho ofanayo.

Njengoba ukusetshenziswa cishe bayazi kakade uma buqhathaniswa ke, kusukela esikhathini uLeonardo da Vinci, ke ongene ukusetshenziswa cishe yonke imikhakha yokuphila - kusuka isayensi ubuciko. Ngisho biology imithi okuye kwenziwa kuye kwabonisa ukuthi isilinganiso golden usebenza ngisho zezinto eziphilayo nezinto eziphilayo.