Fibonacci lambobin da zinariya rabo: dangantakar

A cikin sararin samaniya har yanzu suna da yawa ta kasa warwaruwa asirai, wasu daga wanda masana kimiyya sun iya gano da kuma bayyana. Fibonacci lambobin da zinariya rabo su ne tushen alamu na duniya, da gina da siffar da ganiya adam gani ji, da wanda ya iya ji da kyakkyawa da jituwa.

Golden Sashen

Ka'idar da zinariya sashen masu girma dabam ne tushen na kammala na dukan duniya da kuma sassa a cikin sifa da aiki, ta bayyana za a iya gani a cikin yanayi, al'adu da fasaha. Rukunan zinariya rabo da aka kafa a sakamakon nazarin da tsoho koyarwar yanayi lambobi.

Yana dogara ne a kan ka'idar rabbai da rabo daga tsawo na rarrabuwa da aka yi wa tsoho Falsafa da lissafi Pythagoras. Ya tabbatar da cewa rabuwar kan kashi kashi biyu: X (karami) da kuma Y (babba), da rabo daga manyan zuwa kananan shi ne daidaita da rabo daga cikin Naira Miliyan Xari (total tsawon):

X: Y = Y: X + Y.

A sakamakon haka ne da lissafi: x ² - x - 1 = 0, wanda aka warware kamar yadda x = (1 ± √5) / 2.

Idan muka dubi rabo daga 1 / x, to, shi ne daidai to 1.618 ...

Evidence na yin amfani da zamanin d Thinkers na zinariya rabo da aka bã a cikin littafin na Euclid ta "Abubuwa", rubuta a farkon 3. BC, wanda amfani da wannan mulkin gina daidai 5-gon. A Pythagoreans, wannan adadi yana dauke tsarki saboda yana da biyu tsakaitã da asymmetrical. Pentagram alama ce ta rayuwa da kuma kiwon lafiya.

Fibonacci lambobin

Shahararren littafin Liber abaci lissafi Leonardo Pizanskogo a Italiya, wanda daga baya ya zama sananne a matsayin Fibonacci, aka buga a 1202. A da shi da masanin kimiyyar farko gubar juna na lambobin a cikin abin da kowane lambar shi ne Naira Miliyan Xari da yawan 2 gabata lambobi. Fibonacci jerin ne kamar haka:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, da dai sauransu

Har ila yau, masana kimiyya ya jagoranci wani yawan dokokin:

• Wani yawan layuka raba da m, zai zama daidai da darajar wanda o ƙarin 0.618. Kuma na farko Fibonacci lambobin ba ba da irin wannan lamba, amma kamar yadda ka ci gaba daga farkon da jerin, rabo zai zama mafi daidai.
• Idan muka raba yawan layuka a baya daya, sa'an nan sakamakon hanzarta zuwa 1.618.
• Daya yawan raba da gaba daya, zai nuna darajar da cewa o ƙarin tabbatar da 0,382.

A amfani da sadarwa da kuma alamu na zinariya sashe, Fibonacci lambobi (0.618) za a iya samu ba kawai a cikin lissafi, amma kuma a cikin yanayi, tarihi, gine da kuma yi, kuma da yawa wasu kimiyyar.

Archimedean karkace da zinariya murabba'i mai dari

Spirals ne sosai na kowa a cikin yanayi, an bincika da Archimedes, wanda ko da ya jagoranci ta lissafi. Karkace siffar dogara ne a kan dokokin da zinariya sashe. A ta unwinding tsawon aka samu, wanda za a iya amfani da rabbai na Fibonacci lambobi, da mataki karuwa auku gaba ɗaya.

A layi daya tsakanin Fibonacci lambobin da zinariya sashe, za ka iya gani da kuma gina wani "zinariya murabba'i mai dari", wanda tarnaƙi ne na gwargwado kamar yadda 1.618: 1. Yana da aka gina, za daga kananan zuwa fi girma murabba'i mai dari haka da cewa tsawon na bangarorin za su zama daidai ga lambobin daga cikin jerin. A yi za a iya yi a baya domin, suka fara da square "1". Lokacin da za a haɗa Lines, sasanninta na murabba'i mai dari a tsakiyar mahada samu Fibonacci ko logarithmic karkace.

A tarihin na yin amfani da zinariya rabbai

Mutane da yawa zamanin d Misira gine-gine Monuments aka gina ta amfani da zinariya rabbai: shahara Great Dala da dai sauransu masu zanen gine-gine Ancient Girka ispolzoval su yadu a cikin shiri na gine-gine da abubuwa, kamar haikali, da amphitheater, filayen wasa .. Alal misali, irin rabbai an yi amfani da shiri na zamanin d Parthenon, wasan kwaikwayo Dionysos (Athens), da kuma sauran abubuwa da zama fitacciyar tsohon gine-gine, da nuna ma jituwa, dangane da ilmin lissafi tsari.

A baya ƙarni, sha'awa a cikin zinariya sashe ya kwanta, da kuma dokokin da aka manta, amma koma sake a cikin Renaissance da littafin Franciscan m L. Pacioli Di Borgo "Divine anya" (1509). Yana da misalai da Leonardo Vinci aka kawo, da kuma wanda kulla sabon sunan "zinariya sashe". Akwai sun kuma an tabbatar ta hanyar kimiya 12 Properties na zinariya rabo, marubucin ya yi magana game da yadda za ta bayyana kanta a cikin yanayi, a art kuma ya kira shi da "manufa na gina zaman lafiya da kuma yanayi."

Leonardo ta Vitruvian Man

Figure cewa Leonardo Vinci a 1492 kwatanta littafin Vitruvius, shi ya siffanta wani mutum adadi a 2-matsayin da hannuwa saki a cikin bangarorin. A adadi rubũtacce a da'irar da kuma wani square. Wannan adadi da aka dauke su canonical rabbai na jikin mutum (namiji), aka bayyana ta Leonardo a kan tushen da su binciken a cikin treatises na Roman m Vitruvius.

cibiya jiki a matsayin batu equidistant daga ƙarshen hannuwansu da ƙafãfunsu dauke ciki, makamai tsawon daidaita mutum tsawo, kafada nisa iyakar = 1/8 tsawo, da nisa daga saman da kirji da gashi = 1/7, daga cikin kirji zuwa saman shugaban saman = 1/6 da dai sauransu.

Tun daga nan, hoton da aka yi amfani a matsayin wata alama ce, da nuna ciki fasali na jikin mutum.

Kalmar "Golden Sashen" Leonardo amfani da su bayyana gwargwado dangantaka a cikin mutum adadi. Alal misali, da nisa daga kunkumin sa zuwa ƙafa na kafafu yayi dace da wannan nesa daga cibiya zuwa saman kazalika da ci gaban da farko tsawon (daga kwankwasonsa zuwa ƙasa). Wadannan lissafin da ake yi a cikin wannan rabo na segments a cikin lissafi na zinariya rabo da o ƙarin tabbatar da 1,618.

Duk wadannan jitu rabbai sukan yi amfani da artists don ƙirƙirar kyau da kuma ban sha'awa ayyukansu.

zinariya sashen binciken a 16-19 ƙarni

Amfani da zinariya rabo da Fibonacci lambobi, da bincike aikin a kan rabbai ci gaba da ƙarni. A layi daya tare da Leonardo Vinci Jamus artist Albrecht Dürer ya kasance kuma da hannu a cikin ci gaban da ka'idar da daidai rabbai na jikin mutum. Domin wannan, su ma musamman kamfas an halitta.

A 16th karni. a kan dangantakar Fibonacci lambobin da zinariya sashe da aka kishin aikin falakin Kepler, wanda da farko yi amfani da wadannan dokoki, domin o.

New "samu" sa ran a cikin zinariya sashe 19. da littafin na "ado Nazarin" Bajamushe masanin kimiyya Farfesa Tseyziga. Ya ɗaukaka ta gwargwado ga cikakkar da kuma sanar da cewa suna duniya domin dukan halitta mamaki. Da suka yi karatu manyan yawan mutane, ko wajen su jiki rabbai (game da 2 da dubu.), A wanda da karshe na sakamakon da ilimin kididdiga regularities tabbatar a cikin rabbai na daban-daban sassan jiki: makamai tsawon, makamai, hannuwa, yatsunsu, da dai sauransu

ma art abubuwa (vases, gine-gine ginen), m sautunan aka yi nazari, da girma a cikin rubuce-rubuce na waqe - duk Tseyzig ya nuna ta hanyar da tsawon layin da kuma Figures, ya kuma buga da Kalmar "ilmin lissafi ilmi." Bayan samun sakamakon bayyana cewa Fibonacci jerin aka samu.

Fibonacci lambobin da zinariya sashe a cikin yanayi

A cikin kayan lambu da dabbobi duniya, akwai wani Trend zuwa siffata a cikin nau'i na fasali, wanda aka lura a cikin shugabanci na ci gaba da motsi. A rabo a cikin tsakaitã sassa, wanda complied tare da zinariya rabo - shi ne mai juna kowa da yawa shuke-shuke da dabbobi.

Nature kewaye da mu iya bayyana ta a Fibonacci lambobi, misali:

• wuri na wani rassan ko ganyen shuke-shuke, kazalika da nisa dace da dama ba lambobin 1, 1, 2, 3, 5, 8, 13 da kuma kara.
• sunflower tsaba (a kan sikelin Cones, abarba cell), kwance a jeri biyu na Twisted spirals a daban-daban kwatance.
• da rabo daga tsawon wutsiya da jiki lizard.
• kwai siffar, idan wani layin dakatar da fadin mai fadi da na shi.
• da al'amari rabo daga cikin yatsunsu a cikin hannun mutum.

Kuma, ba shakka, mafi ban sha'awa siffofin ne spirals katantanwa harsashi alamu a kan yanar gizo, da motsi na da iska a guguwa, da biyu Helix DNA tsarin, da kuma taurari - dukkan su sun hada da Fibonacci jerin.

Amfani da zinariya sashe a cikin art

Masu bincike da hannu a cikin art na gano misalai na yin amfani da zinariya sashe, daki-daki, bincika daban-daban gine-gine da abubuwa da kuma ayyukan art. Aka sani ga sanannen sculptures, da halitta na da bi da zinariya rabbai, - da mutum-mutumi na wasannin Zeus, Apollona Belvederskogo da Athena Parthenos.

Daya daga cikin ayyukan Leonardo Vinci - "Vertical na Mona Lisa" - ya dade wani batu na bincike da masana kimiyya. Sun gano cewa, da abun da ke ciki na aikin kunshi gaba ɗaya na "Golden Bamuda", shiga tare a yau da kullum Pentagon star. All aikin Vinci ne wasiya ga yadda zurfin ya ya sanin tsarin da kuma rabbai na jikin mutum, don haka ba ya iya kama da wuce yarda enigmatic murmushi na Mona Lisa.

Golden Sashen gine

A matsayin misali, masana kimiyya sun yi karatu da Masterpieces na gine-gine, a halitta da dokoki na "zinariya sashe": Masar pyramids, da pantheon, da Parthenon, Notre Dame-de Paris, St. Vasiliya Blazhennogo da sauransu.

Parthenon - daya daga cikin mafi kyau gine-gine a Ancient Girka (5 karni BC.) - yana 8 ginshikan da 17 a tarnaƙi, da rabo daga rufinta zuwa tsawon na bangarorin ne daidai da 0,618. A tsinkaya a kan ta facade sanya na "zinariya sashe" (photo kasa).

Daya daga cikin masana kimiyya suka ƙirƙirarru, kuma nasarar amfani da kyautata na daidaitaccen sassa tsarin for rabbai na gine-gine da abubuwa (da ake kira "Modulor") - ya kasance Faransa m Le Korbyuze. Dalili na Modulor sa ƙaddarãwar tsarin hade da wani matukar rabo a cikin sassa na jikin mutum.

Rasha m Mikhail Kazakov, wanda ya gina da dama zama gine-gine a birnin Moscow, kazalika da majalisar dattijai gini a Kremlin, da kuma Golitsyn Hospital (yanzu 1st Clinical Pirogov.) - ya kasance daya daga cikin gine-ginen da suka yi amfani da zane da kuma yi dokokin zinariya sashe.

Aikace-aikace rabbai a zane

The zane na duk tufafi designers yi sabon images da kuma model shan la'akari da rabbai na jikin mutum da kuma dokoki na zinariya sashe, ko da yake da yanayi, ba dukkan mutane suna da manufa rabbai.

A lokacin da shirin wani wuri mai faɗi da kuma zane halittar volumetric shakatawa qagaggun ta amfani da shuke-shuke (itãce, kuma shrubs), marẽmari da kananan gine-gine da abubuwa da alamu za a iya amfani da "allahntaka rabbai". Hakika, da abun da ke ciki na shakatawa ya kamata a da nufin samar da ra'ayi a kan baƙo, wanda zai iya da yardar kaina kewaya shi kuma sami wani kumshin cibiyar.

Duk abubuwa na shakatawa ne a cikin wannan rabbai cewa ta hanyar lissafi tsarin, dangi matsayi, lighting, haske, samar da wani mutum da alama na jituwa da kammala.

Da yin amfani da zinariya sashe a cybernetics da fasaha

Dokokin na Golden Sashen da Fibonacci lambobin ma bayyana a cikin makamashi a mi} a tafiyar matakai faruwa tare da na farko barbashi da ke cikin sinadaran fili, a sarari tsarin a gene tsarin DNA.

Similar matakai faruwa a jikin mutum, wanda bayyana kanta a cikin biorhythms na ta rayuwa, a mataki gabobin, kamar kwakwalwa ko hangen nesa.

Algorithms da alamu zinariya rabbai an yadu a yi amfani da zamani cybernetics kuma informatics. Daya daga cikin sauki ayyuka, wanda ba novice shirye-shirye don warware - da kuma rubuta wani dabara domin sanin Naira Miliyan Xari Fibonacci lambobin da wani adadi, ta amfani da shirye-shirye da harsuna.

Modern bincike kan ka'idar da zinariya rabo

Tun tsakiyar karni na 20th, sha'awa a cikin matsaloli da kuma tasirin da dokoki na zinariya rabbai na rayuwar mutum ƙaruwa da cika fuska, kuma ta masana kimiyya da dama daga daban-daban fasahohin: lissafi, kabila na masu bincike, masana kimiyyar, falsafa, likita kwararru, tattalin arziki, kida da sauransu.

A Amurka tun shekarar 1970-hgodov fara buga mujallar The Fibonacci kwata, wanda wallafa takardun a kan batun. A latsa akwai ayyuka a cikin abin da jimlace mulkin na zinariya sashe da Fibonacci jerin suna amfani a fannoni daban daban na ilimi. Alal misali, zuwa encode bayanai, bincike sinadaran, nazarin halittu, da dai sauransu

Duk wannan ya tabbatar da binciken na dā da na zamani malamai cewa zinariya rabo fahimce nasaba da muhimman hakkokin tambayoyi na kimiyya da fasali bayyanannu a da yawa ayyuka, da kuma mamaki na duniya kewaye da mu.