Manambala Fibonacci ndi golide chiŵerengero: ubale

M'chilengedwe chonse adakali ambiri sanathetsedwe zinsinsi, ena amene asayansi akwanitsa ndi kufotokoza. Fibonacci manambala ndi chiŵerengero golide ndi maziko a maumboni osiyanasiyana a dziko, kumanga mawonekedwe ake ndi akadakwanitsira anthu zithunzi kuzindikira, ndi amene amamva kukongola ndi mogwirizana.

Golden Gawo

Mfundo kukula kwake golide gawo ndi maziko a ungwiro wa dziko lonse ndi ziwalo mwa matabwa ake ndi ntchito, mawonetseredwe ake Tingaone mu chikhalidwe, luso ndi luso. Chiphunzitso cha chiŵerengero golide wakhala kuwonjezekeredwa chifukwa cha maphunziro a ziphunzitso zakale za manambala chikhalidwe.

Bukuli lili ndi chiphunzitso cha kufanana ndi magawanidwe a zotalika m'magulu kuti chidachitika kuti nzeru zapamwamba akale ndi masamu Pythagoras. Iye anatsimikizira kuti kulekana kwa gawo mu mbali ziwiri: X (zing'onozing'ono) ndipo Y (lalikulu), chiŵerengero lalikulu ang'ono ndi wofanana chiŵerengero Uwerenge (okwana kutalika):

X: Y = Y: X + Y.

Chifukwa ndi anthu aone kuti pali: × ² - × - 1 = 0, amene zosatheka × = (1 ± √5) / 2.

Ngati tiyang'ana pa chiŵerengero cha 1 / ×, ndiye wofanana 1.618 ...

Umboni wa ntchito za aphunzitsi wakale wa chiŵerengero golide apatsidwa m'buku la Euclid a "Zochitika", olembedwa mwamsanga 3. BC, amene ntchito lamulo limeneli kumanga zolondola 5-gon. The Pythagoreans, chithunzi ichi yopatulika chifukwa onse symmetrical ndi asymmetrical. Pentagram kufanizira ndi moyo.

manambala Fibonacci

Wotchuka buku Liber abaci masamu Leonardo Pizanskogo ku Italy, amene anadzatchedwa Fibonacci, linasindikizidwa mu 1202. Bukuli wasayansi woyamba kutsogolera chitsanzo cha manambala mu angapo wina ndi Uwerenge chiwerengero cha 2 manambala m'mbuyomu. Fibonacci ndondomeko ili:

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

Komanso, wasayansi kwachititsa angapo malamulo:

• Pali mizere akufufuta wotsatira, adzakhala wofanana ndi mtengo umene amamuchititsa 0.618. Ndipo woyamba manambala Fibonacci musataye chiwerengero oterowo, koma pamene inu patsogolo pa chiyambi cha ndondomeko ya, chiŵerengero adzakhala bwino.
• Ngati ife gawani nambala mizere pa wina m'mbuyomu, ndiye zotsatira adzangozindikira kuti 1.618.
• nambala wani akufufuta yotsatira, ndidzakuwonetsa mtengo zimene zimakupangitsani kuti 0,382.

The ntchito kulankhulana ndi dongosolo la chigawo golide, manambala Fibonacci (0.618) angapezeke osati masamu komanso chikhalidwe, mbiri, zomangamanga ndi kumanga ndi sayansi zina zambiri.

Archimedean mwauzimu ndi rectangle golide

Mizere yozungulira sizachilendo kwambiri mwachibadwa, chinafufuzidwa ndi Archimedes, amene ngakhale anatsogolera aone kuti pali ake. mawonekedwe mwauzimu zachokera malamulo a chigawo golide. Mu m'litali unwinding analandira, yomwe ingagwiritsidwe ntchito ndi anapangira manambala Fibonacci, kuwonjezeka sitepe amapezeka uniformly.

Kufanana chiwerengero Fibonacci ndi gawo golide, mukhoza kuona ndi kumanga "golide rectangle" amene adzamenyane ndi njila monga 1.618: 1. Iwo anamanga, kupita kuyambira wamng'ono mpaka rectangle zazikulu kuti kutalika kwa mbali adzakhala wofanana ndi chiwerengero cha mndandanda. pomanga zikhoza kutheka kuti n'zosiyana, kuyambira ndi lalikulu "1". Pamene polumikiza mizere, ngodya ya rectangle pakati pa mphambano analandira Fibonacci kapena logarithmic mwauzimu.

Mbiri ya ntchito za tinthu golide

Ambiri akale Egypt zipilala mapulani zinamangidwa ntchito kufanana golide: wotchuka Great Piramidi etc. mapulani Ancient Greece ispolzoval iwo ankagwiritsa ntchito yomanga zinthu kamangidwe, monga akachisi, ndi Bwalo la maseŵera, mabwalo .. Mwachitsanzo, kutalika ngati akhala akugwiritsidwa ntchito yomanga Parthenon akale, zisudzo Dionysos (Athens), ndi zinthu zina kuti akhale mwaluso zomangamanga akale, kusonyeza chiyanjano, zochokera zonse masamu.

Patapita zaka zambiri, chidwi mu gawo golide zinaleka, ndipo malamulo wawaiwala, koma anayambiranso kachiwiri mu Kubadwa Kwatsopano ndi buku Francis mmonke L. Pacioli Di Borgo "Divine molingana" (1509). Ndi mafanizo ndi Leonardo da Vinci mwakulira, ndi amene pamalo dzina latsopano "golide gawo". Pali akhala chatsimikiziridwirapo mwasayansi 12 katundu wa chiŵerengero golide, wolemba analankhula za mmene kumaonekera m'chilengedwe, luso ndi kuti "mfundo ya kumanga mtendere ndi chikhalidwe."

Leonardo a Vitruvian Man

Chithunzi kuti Leonardo da Vinci mu 1492 ikusonyezera buku la Vitruvius, izo akunena chithunzi anthu mu 2-udindo ndi manja linatha mu mbali. Chithunzi alembedwa bwalo ndi lalikulu. chiwerengerochi imatengedwa kuti ndi kufanana ovomerezeka a thupi (amuna), anafotokozedwa ndi Leonardo pa pophunzira awo Mfundo za mmisiri Roma Vitruvius.

likulu thupi monga mfundo equidistant ku mapeto a manja ndi miyendo ankaona m'mimba, mikono kutalika wofanana ndi kutalika munthu, phewa m'lifupi pazipita = 1/8 kutalika, kutalika kuchoka pamwamba pa chifuwa kwa tsitsi = 1/7, ku chifuwa pamwamba pa mutu pamwamba = 1/6 etc.

Kuyambira pamenepo, chithunzi ntchito chizindikiro chabe, kusonyeza chosokonekera mkati mwa thupi la munthu.

Mawu akuti "Golden Gawo" Leonardo ntchito pofotokoza ubale njila mu chithunzi anthu. Mwachitsanzo, mtunda kuchokera mchiuno mpaka mapazi a miyendo limafanana ndi mtunda wofanana ku Mchombo pamwamba komanso kukula kwa kutalika choyamba (miyendo). kuwerengetsera izi zimachitika mu chiŵerengero chomwecho cha zigawo mu mawerengedwe a chiŵerengero golide ndi amamuchititsa 1,618.

kufanana onsewa zogwirizana Mankhwalawa amagwiritsidwa ntchito amisiri kulenga ntchito zokongola ndi zochititsa chidwi.

golide gawo maphunziro zaka 16-19

Ntchito golide chiŵerengero ndi manambala Fibonacci, kufufuza ntchito kufanana ndi kupitiriza kwa zaka zambiri. Mu kufanana ndi Leonardo da Vinci German wojambula Albrecht Dürer iyenso anali nawo chitukuko cha chiphunzitso cha anapangira olondola a thupi. Chifukwa cha zimenezi, ngakhale kampasi wapadera analengedwa.

M'zaka za m'ma 16. pa ubale wa manambala Fibonacci ndi gawo golide zoyenera ntchito ya zakuthambo Kepler, amene poyamba ntchito malamulowa kwa zomera.

Latsopano "anapeza" amafunika golide gawo 19. ndi bukhu la "zokongoletsa Studies" German wasayansi Professor Tseyziga. Anaukitsa yolingana ndi mtheradi ndipo analengeza kuti aliyense ali pa zochitika zonse za chilengedwe. Anaphunzirapo ambiri anthu, kapena m'malo kwake thupi (2 zikwi.), Limene mfundo za zotsatira za regularities ndi zowerengera anatsimikizira mu anapangira thupi m'madera osiyanasiyana: kutalika manja, mikono, manja, zala, etc.

komanso luso zinthu (Miphika, nyumba mapulani), malankhulidwe nyimbo ankafunsidwa, miyeso mu kulemba ndakatulo - onse Tseyzig wasonyeza kudzera kutalika kwa mizere ndi kanjedza, iye anayambitsa mawu akuti "aesthetics masamu." Atalandira zotsatira anasonyeza kuti mndandanda Fibonacci analandira.

manambala Fibonacci ndi gawo golide m'chilengedwe

Mu masamba ndi nyama dziko, pali azimuth kwa ulili mu mawonekedwe a chosokonekera, amene asunga motsogozedwa kukula ndi kayendetsedwe ka thupi. Kudulidwa m'magulu symmetrical, amene anamvera chiwerengero golide - chitsanzo wamba kwa zomera ndi nyama zambiri.

Nature otizungulira akhoza kutchulidwa ndi manambala ndi Fibonacci Mwachitsanzo:

• malo a nthambi kapena masamba a zomera, komanso kutalika zizigwirizana ndi nambala ya manambala anapatsidwa 1, 1, 2, 3, 5, 8, 13 ndi zina;
• mbewu ya mpendadzuwa (pa cones lonse, chinanazi khungu), atagona mizere iwiri ya mizere yozungulira zopotoka mu madera osiyana;
• chiŵerengero cha kutalika kwa mchira ndi thupi buluzi;
• dzira mawonekedwe, ngati mzere inaimitsidwa kudutsa gawo lonse la izo;
• ndi makulidwe a zala pa dzanja.

Ndipo, ndithudi, mitundu chidwi kwambiri ndi mizere yozungulira Nkhono dongosolo chipolopolo pa intaneti, kayendedwe ka mphepo mvula yamphamvu, pawiri dongosolo helix DNA, ndi nyenyezi - onse a iwo zikuphatikizapo Fibonacci zinayendera.

Ntchito gawo golide zaluso

Akatswiri nawo luso kupeza zitsanzo za ntchito ya chigawo golide, mwatsatanetsatane kufufuza zinthu zosiyana mapulani ndiponso zosemasema. Amadziwika ziboliboli wotchuka, ndiAmene amene amatsatira kufanana golide, - fano la Olimpiki Zeus, Apollona Belvederskogo ndi Athena Parthenos.

Imodzi mwa ntchito za Leonardo da Vinci - "Chithunzi cha Mona Lisa" - kalekale nkhani asayansi kafukufuku. Iwo anapeza kuti zikuchokera ntchito tichipeza kwathunthu cha "Golden Triangle", pamodzi mu zonse Pentagon nyenyezi. ntchito zonse da Vinci ndi pangano kwa kuya anali kudziŵa zokhudza kapangidwe ndi kufanana kwa thupi, kotero kuti athe kugwira amazipanga enigmatic kumwetulira wa Mona Lisa.

Golden Gawo zomangamanga

Mwachitsanzo, asayansi aphunzira katswiri wa zomangamanga, analengedwa ndi malamulo a "golide gawo": mapiramidi Igupto, Pantheon, Parthenon Notre-Dame de A Paris, St. Vasiliya Blazhennogo ndi ena.

Parthenon - imodzi mwa nyumba zokongola kwambiri Ancient Greece (5 m'ma BC.) - 8 mizati ndi 17 pa zomenyanazo, chiŵerengero cha kutalika kwake ndi kutalika kwa mbali ndi wofanana 0,618. The zolosera pa wapakamwa ake kuti "golide gawo" (chithunzi m'munsimu).

Mmodzi wa sayansi amene anapanga ndi bwino ntchito kusintha kwa dongosolo yodziyimira payokha chifukwa anapangira zinthu mapulani (otchedwa "Modulor") - anali French wamanga Le Korbyuze. Maziko a Modulor kuyika dongosolo chingwe kugwirizana ndi kugawikana pa makonzedwe mu ziwalo za thupi la munthu.

Russian wamanga Mikhail Kazakov, amene anamanga nyumba zingapo zogona mu Moscow, komanso nyumba Senate mu boma la Russia, ndi Hospital Golitsyn (tsopano 1st chipatala Pirogov.) - anali mmodzi wa mapulani amene ntchito kapangidwe ndi kumanga malamulo lagolide gawo.

kufanana ntchito ya kapangidwe

Kamangidwe ka okonza onse chobvala kupanga zifanizo latsopano ndi zitsanzo kutenga nkhani anapangira thupi ndi malamulo a chigawo golide, ngakhale mwa chirengedwe, si anthu onse ndi kufanana abwino.

Pamene akukonzekera kapangidwe malo ndi chilengedwe cha nyimbo volumetric paki ntchito zomera (mitengo ndi zitsamba), akasupe ndi zazing'ono zinthu mapulani ndi dongosolo angagwiritsidwe ntchito "kufanana Mulungu". Ndipotu, zikuchokera paki ayenera umalimbana kulenga kuganiza pa mlendo amene momasuka kuyenda ndi kupeza malo limapereka.

mbali zonse za paki ali mu magawo oterowo kuti mwa dongosolo zojambula, malo ake, kuunikira, kuwala, zimatulutsa munthu kuganiza za mogwirizana ndi ungwiro.

Kugwiritsa ntchito gawo agolidi cybernetics ndi luso

Malamulo a Golden Gawo ndipo Fibonacci manambala tione mu kusintha mphamvu mu njira chikuchitika ndi particles pulayimale amapanga mankhwala pawiri, mu kachitidwe danga dongosolo jini ya DNA.

njira wofanana mu thupi la munthu, amene kumaonekera mu biorhythms a moyo wake, ziwalo kanthu, monga ubongo kapena masomphenya.

Ma aligorivimu ndi dongosolo kufanana golide ankagwiritsa ntchito cybernetics zamakono informatics. Mmodzi wa zing'onozing'ono omwe akutipatsa mapulogalamu novice kuthetsa - ndi kulemba dongosolo kuti mutenge ndalama za manambala Fibonacci ku nambala inayake, ntchito zinenero mapulogalamu.

Akatswiri ofufuza pa chiphunzitso cha chiŵerengero golide

Kuyambira pakati pa zaka za m'ma 20, chidwi mavuto ndi mmene malamulo a kufanana golide wa ukuwonjezeka moyo wa munthu kumasinthiratu kwakukuru ndi asayansi ambiri a kudzinenera zosiyanasiyana: masamu, fuko gulu la ofufuza a sayansi, akatswiri a nzeru za, madokotala, chuma, oimba ndi ena.

Mu US kuyambira 1970-hgodov ayamba kufalitsa magazini ya Fibonacci Quarterly, amene limafalitsa mapepala pa nkhaniyi. Womkanikizawo pali ntchito imene ulamuliro zowombetsa mkota wa chigawo zagolide ndi mndandanda Fibonacci ntchito zosiyanasiyana chidziwitso. Mwachitsanzo, encode zambiri, kufufuza mankhwala, kwachilengedwenso, etc.

Zonsezi chitsimikizira zomwe anapeza akatswiri zakale ndi zamakono kuti chiwerengero golide comprehensively kumayambitsa mafunso ofunika a sayansi ndi chosokonekera zimaoneka m'ntchito zambiri, ndiponso zochitika za m'dzikoli.