Fibonacci lambobi tare da mu

Fibonacci lambobin suna kewaye da mu. Su ma a music, a gine-gine, a shayari, lissafi, da tattalin arziki, da kasuwar jari, a cikin tsarin da shuke-shuke a cikin cochlear karkace, a cikin rabbai na jikin mutum da sauransu, ad infinitum ...

Famous na da lissafi Leonardo Pizansky (c. 1170-c. 1250), wanda aka fi sani a matsayin Fibonacci, ya kasance daya daga cikin shahararrun masana kimiyya a lokacinsa. Ya kasance na farko a Turai da shawarar yin amfani da Larabci numerals maimakon Roman kuma ya bude wani ilmin lissafi jerin lambobi, daga baya suna biye da shi, wanda aka kamar haka: 1,1,2,3,5,8,13,21, ... da sauransu ad infinitum. A jerin wadannan lambobin wani lokaci ana kiransu "Fibonacci lambobi."

Abu ne mai sauki, a lura cewa a wannan gagarumin jerin wadannan kowane lambar da aka kafa ta ƙara biyu baya wadanda. Kuma abin da yake da shi na ƙwarai? Idan muka raba kowace m lokaci na wannan musamman jerin baya daya, za mu sannu a hankali zo kusa da wasu ban mamaki transcendental rabo - yawan F (Fibonacci yawan) = 1.6180339887 ...

Wannan adadi, kamar yawan PI (3.1415 ...) yana da wani daidai darajar. Yawan lambobi bayan da gidan goma batu ne iyaka. Wannan shi ne farkon da kuma ba kawai shifran riyadiyah. Idan muka raba kowane lokaci na da jerin to bi, za mu iya samun wani transcendental yawan 0 6180339887 ... Ayyukan al'ajibai ci gaba - bayan da gidan goma lambobi maimaita daidai da jerin lambobi na F, kafin wakafi ne ba 1, da kuma 0.

Ku ci gaba. Idan muka Square da wani Fibonacci lambar, sakamakon zai zama daidai da yawan tsaye a cikin jerin a gaban shi, ta tara da lambar da yake a baya shi, da ko debe 1. Alal misali, biyar Squared ne daidai 3x8 + 1. 8 Squared daidai 5x13 debe 1; 13 tashi zuwa square, kazalika 8x21 + 1 da sauransu. Ãyõyi "da" da "debe" canje-canje a tarnaƙi. Irin wannan shifran riyadiyah girma iri-iri a nan. Fibonacci lambobin yin mu'ujizai a kewaye da mu, wani lokacin mu kawai ba su lura.

Fibonacci lambobi a cikin yanayi

Fibonacci rabo, qazanta sunaye daban-daban - Golden rabo, Golden Sashin, Divine anya - aka samu a cikin mafi m da m wurare. Alal misali, wadannan dangantakar za a iya gani a kan m shawara na geometrical rabbai Dala na Giza, pyramids a Mexico, Monument tsoho gine Parthenon.

The shuke-shuke iya ganin wani sihiri dangantaka. Mun iya tsayar da Fibonacci lambobin sake, idan muka hankali la'akari da dama blossoms Asteraceae shuka: flower na Iris, mu sami 3 petals, a Primrose - 5, daga ragweed - 13, a Daisy -34, yayin da asters - 55 da kuma 89 petals .

Babban Goethe ya lura da karatu da magana daga helicity a yanayi. Spirals za a iya gani a cikin hanyar ayi sunflower tsaba, Pine Cones, a cacti, pineapples da sauransu. A duk wadannan lokuta bayyana Fibonacci lambar. Karkace gizo-gizo weaves ta yanar gizo. Mahaukaciyar guguwa da ake juya spirally. Saboda haka juya da kuma taurari. "A kwana na rayuwa" - abin da ake kira karkace Iogann Gote.

Aka bayyana Fibonacci rabo da ilmin halitta na daban-daban kwayoyin. Alal misali, yawan haskoki tarwada dace Fibonacci lambobi. A sauki sauro kuma iya samun su: ya kafafu 3 nau'i-nau'i, 8 segments yana da ciki, da kuma a kan kansa yana da 5 antennae. Yawan vertebrae a wasu dabbobi ne 55, da sauransu.

Lizard rabo na da tsawon da wutsiya to sauran na jiki tsawon na 62 da kuma 38, da kuma wannan dangantaka shi ne jitu da kuma faranta wa idanunmu. A dabba da shuka duniya, a ko'ina bayyana fasali. Allah, Nature ko Great Architect na gane rabo a cikin tsakaitã segments, sassa da zinariya rabo. A maimaita kashi iya duka tsarin, wanda yake shi ne bayyanuwar fractal a yanayi.

Gold fasali lura a cikin mi} a hade tare da makamashi kudin na firamare barbashi, tsarin da mutum sinadaran mahadi, a sarari tsarin, tsarin jinsin, tsarin wasu mutum gabobin da kuma jiki, gani a biorhythms, kwakwalwa aiki da kaddarorin ji.