Fibonacci helu a me ke gula hiʻohiʻona: ka pilina

Ma ka ke ao holoʻokoʻa i nō nui unsolved mea pohihihi, kekahi o ka aʻepekema i Ua hiki ke hōʻike a me ka wehewehe. Fibonacci helu a me ke gula hiʻohiʻona nō i ke kumu o clues o ko ke ao nei, i ke kūkulu o kona helehelena a me kaʻoi loa kanaka pilikia makapō pokole, a me i ka mea hiki ke haha aku i ka nani a me ka aloha.

Golden Section

I ka rula o ka gula pauku nui like 'ole o ke kumu o ka manao maikai, o ko ke ao nei a pau, a me kona wahi i loko o kona' ole a me ka hana, kona hoike ana hiki ke ike i ke ano maoli, oe a me ka 'ike loea. Ke ao ana o ke gula lākiō i, ua hoohui like me ka hopena o nā haʻawina o nā aʻo kahiko o ke ano helu.

Ua Ua nānā ma luna o ka pähola 'ana o huliāmahi a me ka lākiō. O ka lōʻihi o nā māhele mea i hanaʻia ai i ka poe akeakamai kahiko a me ka mathematician Pythagoras. He ho'āʻo ai i ka kaawale ana o ka Hoʻohana i loko o nā māhele: ka X (uuku) a me Y (nui), o ka lākiō o ka nui i ka poe liilii, o like me ka lākiō o ka huina (huina lōʻihi):

X: Y = Y: X + Y.

Ka hopena o ka helu kaulike. M ² - m - 1 = 0, i ua Wehewehe i nā hāʻina me m = (1 ± √5) / 2.

Inā mākou e nānā i ka lākiō o ka 1 / m, a laila ka mea, ua like pu ke 1.618 ...

Hoike ana i ka pono o na thinkers kahiko o ke gula lākiō i hāʻawiʻia i loko o ka buke o Euclid ka "oihana", kākau i kakahiaka nui me 3. BC, a noi aku la keia rula, e kūkulu i ka pololei 5-gon. Na Pythagoreans, keia huahelu ua kuhi laa no ka mea, o ka poe symmetrical a me ka asymmetrical. Pentagram nô kêia ke ola a me ka ola.

Fibonacci helu

Ke kaulana puke Liber abaci mathematician Leonardo Pizanskogo ma Italy, a ma hope, uaʻikeʻia me Fibonacci, i paʻiʻia ma ka 1202. Ma laila i ke nä känaka 'epekema mua kēpau kumu o ka nui loa i loko o i kēlā me kēia helu o ka huina o ka helu ana o 2 mua loa. Fibonacci ke kaʻina, Ua like penei:

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

Nō hoʻi, ke nä känaka 'epekema i alakai i ka helu o ke kānāwai:

• I kekahi helu o ka lalani i puunaueia e ka mea hope, e like me ka waiwai i mālama i ka 0.618. A me ka mea mua Fibonacci helu mai e haawi aku e like me ka helu, akā, e like me oe holomua, mai ka hoomaka ana mai o ke kaʻina, ke lākiō e e oi kūlike loa.
• Inā mākou e puunaue i ka helu o ka lalani ma ka mua kekahi, a laila, i ka hopena, e mai oukou, mailoko i 1.618.
• Kekahi helu i puunaueia e ka mea e hiki mai ana kekahi, e hōʻike i ka waiwai i mālama i ka 0,382.

Ka hoʻohana o ka 'ōlelo a me nā lauana o ka pauku gula, Fibonacci helu (0.618) hiki ke loaʻa ole wale ma ka makemakika, akā, i loko o ke ano maoli, mōʻaukala, kuhikuhipuʻuone, a kūkuluʻia, a me na mea he nui' ē aʻe sciences.

Archimedeanʻoni iho, a me ka gula rectangle

Spirals i nui loa, he pono ole ma ke ano maoli, ka mea, ua hoʻokolokoloʻia Archimedes, a i alakaʻi i kona helu kaulike. ʻoni iho shape ua muli ma luna o nā kānāwai o ka pauku gula. Ma kona unwinding lōʻihi ua loaa ia ia, a hiki ke pili a me na huliāmahi o Fibonacci helu, i ke anu u mea ulu ia lŘlŘ uniformly.

Ia laua ma waena o ka Fibonacci helu, a me ka pauku gula, e hiki ke ike, a kūkulu i ke "gula rectangle", nona na aoao elua, ua hapaʻauhau like 1.618: 1. Ua Ua kūkulu, e hele ana, mai ka poe liilii, a hiki i nui rectangle no laila, i ka lōʻihi o na aoao e e like me ka helu o ka moʻo. Ke kukulu hiki ke hana i loko aʻe o ka papa, e hoʻomaka ana me ka huinahalike "1". I ka ai pili aku laina, kihi o ka rectangle ma ka waena konu o ke kuʻina loaa Fibonacci a pālākiōʻoni iho.

I ka moolelo o ka pono o ke gula huliāmahi

Ua kūkulu He nui kahikoʻAigupita kuhikuhipuʻuone kia hoʻomanaʻo i hoʻohana gula huliāmahi: kaulana Great Pyramid etc. nā kānaka kuhikuhipuʻuone Kahiko Greece ispolzoval ia kaiāulu i loko o ka hana o kuhikuhipuʻuone mea, e like me ka maha, o ka amphitheater, ainoeieoa .. No ka laʻana, ua huliāmahi i ua hoʻohana ma o ka hana o ka mea kahiko Parthenon, keaka Dionysos (Athens), a me nā mea i lilo masterpiece kahiko kuhikuhipuʻuone, hōʻike lokahi, ma muli o ka makemakika regularity.

Ma hope kenekulia, hoihoi i loko o ka pauku gula emi, a ua ua hoʻopoina kānāwai, akā, laila, hou i loko o ka pakebona me ka puke Franciscan mōneka L. Pacioli Di Borgo "Akua me Lākiō Like" (1509). Ua ki io ma Leonardo ka Vinci i ua lawe mai, a i loaa i ka inoa hou o ke "gula pauku". Aia i kekahi ua scientifically ai 12 waiwai o ke gula lākiō, ka mea kākau kamailio e pili ana pehea e hoike mai ai ia ia iho ma ke ano maoli, ma ka ke akamai, a kapa ia "ka loina o ka hana ana i ka maluhia a me ka ano."

Leonardo ka Vitruvian Man

Ke Kii i Leonardo ka Vinci i ka 1492 ia manaʻo o ka buke o Vitruvius, ia depicts he kanaka huahelu i loko o ka 2-kulana me ka lima wahine hemo la, ma na aoao elua. Me ke kiʻi kākauʻia i loko o ka poai nei, a me ka ahalike. Kēia huahelu ua manaoia e ia i ka canonical huliāmahi o ke kanaka kino (kane), i ho'ākāka 'ia ma Leonardo ma ka muli o ko lākou mau kuka nei i loko o ka hoonoho o ke Roma kanaka kuhikuhi puʻuʻone Vitruvius.

Hub ke kino e like me ka wahi equidistant, mai ka pau ana mai o na lima a me nā wāwae noonoo opu, i na mea kaua lōʻihi like i kekahi kanaka ka kiekie,'ūhā mua laula i kā mākou = 1/8 kiʻekiʻe, ka mamao mai ka luna o ka pahu i ka lauoho = 1/7, mai ka pahu a hiki i ka luna o ke poʻo luna = 1/6 etc.

Mai laila, ke kiʻi ua hoʻohana 'ia e like me ka hōʻailona, e hoike ana i ke kipi symmetry o ke kanaka kino.

Kaʻia "Golden Section" Leonardo hoʻohana i ka hōʻike hapaʻauhau pili i loko o ke kanaka huahelu. No ka laʻana, i ka mamao mai ka pūhaka a hiki i na wawae o ka wāwae hoʻopili like i ka mamao mai ka piko a hiki i ka luna, a me ka ulu ana o ka lōʻihi mua (mai ka puhaka mai). Mau helu i hana ai i loko o ka hookahi lākiō o na Hoʻohana i loko o ka i ka ho omaulia ana o ka mea gula hiʻohiʻona a me ka mālama i ka 1,618.

A pau kēia mau harmonious huliāmahi kēia mea pinepine hoʻohana Artists e hana nani, a kilakila hana.

gula pauku haʻawina i loko o 16-19 kenekulia

E ho ohana i ke gula hiʻohiʻona a me Fibonacci nui, ka noiʻi hana ma luna o nā huliāmahi hoʻomau no kenekulia. Ma ia laua me ka Leonardo ka Vinci Kelemānia artist Albrecht Dürer ka mea, ua i ke komo pū o loko o ka ulu ana o ka pähola 'o ka pololei huliāmahi o ke kanaka kino. No keia, mea, a hiki i hana kūikawā panana.

Ma ka 16th kenekulia. ma ka pilina o Fibonacci loa, a me ka pauku gula i hoolilo ai i ka hana ana i ka astronomer Kepler, ka mea mua pili i kēia mau rula e botany.

New "Kaka" i manaoia ma ka pauku gula 19. me ka lehulehu ākea o ka "Aesthetic Haʻawina" German nä känaka 'epekema Kumu Tseyziga. He hoala mai i ka like ana i ka loa a me ka hai mai i ka mea, ua paʻa no nā mea a pau maoliʻike manaʻo. Ka mea, ua aʻo nui helu ana o kanaka, a he oiaio, i ko lakou mau kino huliāmahi (ma kahi o 2 tausani.), Ma i ka hopena o ka hopena o ke ana helu regularities hoʻopaʻa i loko o ka huliāmahi o kekahi kino wahi: i na mea kaua lōʻihi, i na mea kaua, na lima, manamanalima, etc.

pū nō mea (vases, kuhikuhipuʻuone hale), bila nanahe i hookolokolo aku la ia, i nā Ana i loko o ka palapala o ka poem - a pau Tseyzig i hōʻike 'ia ma ka lōʻihi o ka laina a me na kii, dala la no hoi oia i ka manawa "makemakika aesthetics." Ma hope o ka loaa ana i nā hualoaʻa hoikeia mai i ka Fibonacci moʻo ua loaa.

Fibonacci helu a me ka pauku gula ma ke ano maoli

Ma kaʻai a me ka holoholona ke ao nei, he mea kekahi au i shaping i loko o ka palapala o ka symmetry, a ua ike ia ma ke ala e hiki aku ana i ka ulu a me ka neʻeʻana. Ka mahele i loko o symmetrical loa, a hoʻokō me ka gula e like me - mea he kumu, he pono ole i na mea kanu a me nā holoholona.

Nature a puni mākou i e ho'ākāka 'ia ma ka Fibonacci nui, no kekahi laʻana:

• wahi ana i kekahi lālā a me ka lau o nā mea kanu, e like me ka mamao hoʻopili like me ka helu ana i haawi mai ai helu 1, 1, 2, 3, 5, 8, 13 a me no hoi;
• pua nānālā na anoano (ma ka pālākiō cone, Pineapple aeea), e moe ana ma ka lalani elua o hilo spirals ma kekahiʻaoʻao;
• ka lākiō o ka lōʻihi o ka huelo a me ke kino moo;
• hua manu kinona, ina ka laina kaulia ana ma ka laulā hapa o ka ia;
• ka lākiō hiʻohiʻona o na manamana ma ka lima kanaka.

A, o ka papa, i ka loa hoihoi 'pepa i spirals hometa iwi kumu hoohalike ma luna o ka pūnaewele puni honua, i ka holo ana o ka makani i loko o ka makani pāhili, ka waʻa helix DNA' ole, a me ka galaxies - a pau o ia nā ka Fibonacci kaʻina.

E ho ohana i ka pauku gula i loko o ke akamai

Noiʻi 'ole i loko o ke akamai o ka loaa examples o ka pono o ka pauku gula, au mamuli makaikai i kekahi mau kuhikuhipuʻuone mea a me na hana o ke akamai. Kinohi mai ua ikeia no ka mea kaulana sculptures, na kanaka haku o ka i hoopili aku ai i ke gula huliāmahi, - i ke kiʻi o Olympian Dia, Apollona Belvederskogo a me Athena Parthenos.

Kekahi o na hana o Leonardo ka Vinci - "Makuahine o Mona Lisa" - Ua lōʻihi Ua he kumuhana o ka noiʻiʻepekema. A loaa ia lakou i ka haku mele 'ana o ka hana ninoieo loa o ka "Golden triangle", hui pu iho i loko o ka papa pentagon hoku. All hana nā Vinci mea he kauoha hooilina, e pehea hohonu i kona ike ana i ka 'ole a me ka huliāmahi o ke kino o ke kanaka, no laila, e hiki ia ia ke hopu i ka incredibly enigmatic minoʻaka o ka Mona Lisa.

Golden Section kuhikuhipuʻuone

Me lakou i mea hoike, i? Anoeeʻepekema na masterpieces o kuhikuhipuʻuone, ho okumu ia ma na rula o ka "gula pauku": i ke kanaka o Aigupita pyramids, ka Pantheon, ka Parthenon, Notre Dame-de Ka Paris, St. Vasiliya Blazhennogo a me na mea e ae.

Parthenon - kekahi o ka loa maikai na hale ma Makamua Greece (5 kenekulia BC.) - ua 8 kolamu a me 17 ma ke alo o aoao, ka lākiō o kona kiekie i ka loa o na aoao elua, ua like me 0,618. ʻO nā wānana waiwai ma luna o kona mea helehelena i ke "gula pauku" (Hawaii photo ma lalo nei).

Kekahi o nā kānakaʻepekema i invented a ana pili i ka hana o ka māhele'ōnaehana no na huliāmahi o kuhikuhipuʻuone mea (ai-kapaia "Modulor") - ua ka Palani kanaka kuhikuhi puʻuʻone Le Korbyuze. Ke kumu o ka Modulor i ke ana'ōnaehana pili me ka conditional mahele i māhele o ka kanaka kino.

Russian kanaka kuhikuhi puʻuʻone Mikhail Kazakov, nana i kukulu ia kekahi mau hale noho hale ma Moscow, e like me ka Senate hale i loko o ka Kremlin, a me ka Halemai Moiwahine Golitsyn (e ka 1st lapaʻau Pirogov.) - i kekahi o na nā kānaka kuhikuhipuʻuone i hoʻohana i ka manao a me ka? Ieoaeunoai kanawai ke gula pauku.

Noi huliāmahi ma ka manao

I ka manao o ka mea a pau lole akamai e hou i nā kiʻi a me nā ana hoʻohālike e lawe i ka mooolelo o ka huliāmahi o ke kanaka kino a me na rula o ka pauku gula, no nae ma ke ano maoli,ʻaʻole kanaka a pau i ka maikaʻi huliāmahi.

I ka hoʻolala i kekahi panorama manao a me ka hanaia'na o volumetric aieai mele ka hoʻohana mea kanu (laau a me ka laau uuku), na punawai a me na mea uuku kuhikuhipuʻuone mea a me nā lauana hiki ke hoʻohana ' "kilokilo huliāmahi". Ma hope o nā mea a pau, o ka haku mele 'ana o ka paka e e nona e pili ana i ka manaʻo ma luna o ka malihini, ka mea hiki ke alalai ole ho okele ia, a loaʻa i ka lua-oaio? A.

A pau oihana mua o ka paka i loko o ia mau huliāmahi i ka lilo ana o ka geometric 'ole, pili kulana, kau iho, malamalama, paka i kekahi kanaka i ka manaʻo o ke aloha a me ka oo.

I ka hoʻohana 'ana i ka pauku gula ma cybernetics a me ka' ike loea hou

Na kanawai o ka Golden Pauku a me Fibonacci nui hou no hoi ma o ka ikehu nā mahele ma ka keʻano o ka hanaʻana e lawe me ka haʻahaʻa (particles) aha i ka Nine Inch hui, ma ka makahiki nenoai ma ka'ōewe 'ole o ka DNA wahi.

Similar keʻano o ka hanaʻana ana i loko o ke kino o ke kanaka, i hoike mai ai ia ia iho i loko o ka biorhythms o kona ola, ma ka hana nā loko, e like me lolo a me ka hihio.

Algorithms a me nā lauana gula huliāmahi e hoʻomano hoʻohana i ke kālā no cybernetics a me informatics. Kekahi o ka poe noonoo ole hana, a haawi novice programmers e hoʻoponopono i - a kākau i ka haʻilula e hooholo i ka huina o Fibonacci nui a hiki i ka kekahi helu, hoʻohana 'iaaiey' ōlelo.

Hoikehonua, noiʻi ma o ka pähola 'ana o ke gula lākiō

Mai ka waena o ka 20th kenekulia, hoihoi i loko o ka pilikia a me ka hopena o nā kānāwai o ke gula, huliāmahi o ke kanaka ka ola, piʻi pū dramatically, a ma na mea he nuiʻepekema o nāʻoihana kahuna, ai: mathematicians, ka lāhui i pae o ka noiʻi, biologists, poe akeakamai, 'inikua' Oihana, economists, hoʻokani pila a me na mea e ae.

Ma ka US mai 1970-hgodov hoʻomaka e hoolaha i ka puke pai ka Fibonacci hapahā, i publishes na pepa ma ke kumuhana. Ma ke kaomi, he hana ma i ka generalized rula o ka pauku gula, a me ka Fibonacci moʻo e hoʻohana i loko o kekahi mau kihapai o ka ike. No ka laʻana, e encode ike, noiʻi Nine Inch, liluwelo, etc.

A pau keia keʻae i nā haʻina o ka wa kahiko a me kaʻiʻo nō o kēia haumana i ke gula e like me comprehensively ua hoʻopili i kumu ninau o ka 'epekema a me ka symmetry akaka no ma na hana, a me kaʻike manaʻo o ko ke ao nei a puni mākou.