Fibonacci nhamba uye yendarama reshiyo: ukama

In zvakasikwa vachiri unsolved zvakavanzika zvizhinji, mamwe masayendisiti akakwanisa kuziva uye kurondedzera. Fibonacci nhamba uye yendarama reshiyo ndivo hwaro kutibatsira zvenyika, kuvaka chimiro chayo uye optimum dzevanhu kuona maonero, rwaakanga anogona kunzwa kunaka uye kuwirirana.

Golden Section

Nheyo yendarama chikamu hukuru ndiyo hwaro hwakakwana yose ayo mativi aro marongerwo uye basa, nokuratidzwa ayo anogona kuonekwa zvakasikwa, unyanzvi uye rwokugadzira. Dzidziso yendarama reshiyo kwave nevanopinda somugumisiro zvidzidzo dzidziso yekare hunhu nhamba.

Zvinonzi uchifungidzira kuti kukura uye ratios kuti urefu mumapoka kuti zvaitwa kusvika muzivi yekare uye yemasvomhu Achibvuma pfungwa yaPythagoras. Akaratidza kuti kuparadzana pakati chidimbu muzvikamu zviviri: kuti X (duku) uye Y (guru), nhamba yakakura kune duku akaenzana nhamba Verengai (Kureba):

X: Y = Y: X + Y.

Zvinoguma mukana wokuti vanhu vanga: x ² - X - 1 = 0, iro kugadziriswa sezvo x = (1 ± √5) / 2.

Kana tikatarisa nhamba 1 / X, zvino akaenzana 1,618 ...

Uchapupu kushandisa vekare nevafungi rwemabhera reshiyo anopiwa mubhuku Euclid kuti "Elements", zvakanyorwa kare 3. BC, izvo akashandisa mutemo uyu kuvaka zvakarurama 5-gon. The Pythagoreans, nhamba iyi anonzi matsvene nokuti zvose zvakafanana, ichibata uye asymmetrical. Pentagram rinomiririra upenyu uye utano.

Fibonacci nhamba

The akakurumbira bhuku Liber abaci yemasvomhu Leonardo Pizanskogo muna Italy, iyo akazozivikanwa sezvo Fibonacci, yakabudiswa muna 1202. Muna mairi musayendisiti wokutanga kutungamirira muenzaniso nhamba umo nhamba nomumwe ndicho kuwanda 2 yapfuura nhamba. Fibonacci urongwa huri sezvinotevera:

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

Uyewo, musayendisiti wakatungamirira nhamba remitemo:

• Chero uwandu mitsara yakakamurwa kwakazoitwa, achava akaenzana kukosha iyo uderedze 0.618. Uye wokutanga Fibonacci nhamba regai kupa nhamba yakadaro, asi sezvo iwe mberi kubva pakutanga kutevedzana, nhamba zvichava kunyatsoenderana.
• Kana isu vagovane uwandu mitsara iri yapfuura mumwe, ipapo mugumisiro acharirima kusvika 1,618.
• Imwe nhamba yakakamurwa unotevera, icharatidza kukosha kuti uderedze 0,382.

Kushandiswa pakukurukurirana uye mifananidzo yegoridhe chikamu, Fibonacci nhamba (0.618) anogona kuwanikwa kwete chete masvomhu asiwo zvakasikwa, nhoroondo, mapurani uye kuvaka, uye sayenzi nezvimwe zvakawanda.

Archimedean zononoka uye yendarama rectangle

Spirals kunowanzoitika chaizvo zvakasikwa, rakachengetedzwa kuongororwa ne Archimedes, izvo kunyange akatungamirira wake mukana wokuti vanhu vanga. Spiral chimiro inobva mitemo yendarama chikamu. In kwayo unwinding kureba inotengwa, izvo zvinogona kushandiswa, uye kukura Fibonacci nhamba, danho kuwedzera kunoitika noruvara.

Parallel pakati Fibonacci nhamba uye chendarama chikamu, unogona kuona uye kuvaka "yendarama rectangle", ane mativi vari Proportional sezvo 1,618: 1. It inovakwa, ichienda diki kusvika hombe rectangle kuitira kuti kureba mativi zvichava akaenzana kuwanda akatevedzana. The kuvakwa anogona kuitwa nekwekupedzesera, kutanga yaiungana "1". Kana unobatanidza mitsetse, makona rectangle iri nechepakati mharadzano akawana Fibonacci kana theorem zononoka.

Nhoroondo kushandiswa kukura zvendarama

Egypt mapurani Zvivako zhinji yekare dzakavakwa vachishandisa ndarama zvikuru: yakakurumbira Great Pyramid etc. Architects Ancient Greece ispolzoval navo zvikuru pakuvaka mapurani midziyo, dzakadai temberi, yemitambo, nhandare .. Somuenzaniso, kukura kwakadaro kushandiswa pakuvaka Parthenon yekare, yemitambo Dionysos (Athens), uye zvimwe zvinhu kuti ave Nounyanzvi akwegura mapurani, achiratidza kuwirirana, inobva kwemasvomhu kakawanda.

In emakore akazotevera, kufarira yendarama chikamu adzikira, uye mitemo vave kukanganwa, asi ndokutangazve zvakare muna Renaissance bhuku Franciscan mumongi L. Pacioli Di Borgo "zvinoenderana Divine" (1509). Zviri mifananidzo kubudikidza Leonardo da Vinci kunge vakauya, uye iyo vakanochengeta zita idzva "chikamu yendarama". Pane vave nesayenzi nekusimba 12 ehupfumi rwemabhera reshiyo, munyori akataura pamusoro sei chinoratidza pacharo zvakasikwa, zviri unyanzvi akaitumidza "nheyo kuvaka rugare uye hunhu."

Leonardo raMwari Vitruvian Man

Figure kuti Leonardo da Vinci muna 1492 akaenzanisira mubhuku Vitruvius, inotsanangura munhu kwevanhu mune 2-nzvimbo nemaoko vakarambana mu kumativi. Nhamba nokudhindwa denderedzwa uye sikweya. Nhamba iri kuonekwa dzakafuridzirwa kukura womunhu muviri (varume), yakarondedzerwa Leonardo nemhaka yokudzidza avo akadhindwa yeRoma akitekiti Vitruvius.

nomusimboti muviri sezvo pfungwa equidistant kubva pamugumo maoko nemakumbo vaiona dumbu, maoko urefu yakaenzana munhu urefu, mafudzi upamhi kunonyanyisa = 1/8 urefu, daro kubva pamusoro pechipfuva kusvikira bvudzi = 1/7, kubva chipfuva pamusoro musoro pamusoro = 1/6 etc.

Kubvira ipapo, mufananidzo unoshandiswa sechiratidzo, vachiratidza womukati symmetry womunhu muviri.

Shoko rokuti "Golden Section" Leonardo akashandisa kurondedzera Proportional ukama ari munhu nhamba. Somuenzaniso, daro kubva muchiuno kusvika tsoka makumbo anoenderana chete chinhambwe kubva guvhu kumusoro uyewo kukura rokutanga urefu (kubva muchiuno zvichidzika). Masvomhu izvi zvinoitwa chete nhamba zvikamu zvacho dzemaitirwe rwemabhera reshiyo uye uderedze 1,618.

rinopindirana kukura zvose izvi anowanzoshandiswa Artists rokusika mabasa akanaka uye anoyevedza.

yendarama chikamu zvidzidzo muna 16-19 emakore

Kushandisa yendarama reshiyo uye Fibonacci nhamba, ongororo kukura mberi kwemazana emakore. In zvinofambirana nezviri Leonardo da Vinci Artist German Albrecht Dürer aivawo kubatanidzwa kukura dzidziso yakarurama kukura dzemuviri. Nokuti ichi, ivo kunyange chinokosha kambasi akasikwa.

Muzana remakore rechi16. pamusoro ukama Fibonacci nhamba uye yendarama chikamu chakatsaurwa kuti basa zvomuchadenga Kepler, uyo akatanga kushanda mitemo idzi bhotani.

New "Zvakawanikwa" kutarisirwa ari yendarama chikamu 19. pamwe Bhuku "Aesthetic Studies" musayendisiti wokuGermany Professor Tseyziga. Akamutsa maererano Mhedziso uye akazivisa kuti ivo yezvisikwa zvose zvakasikwa. Vakanga adzidza guru nhamba yevanhu, kana panzvimbo dzavo muviri zvikuru (zvuru 2.), On izvo ndezvipi zviri migumisiro Statistical regularities nekusimbiswa kukura dzakasiyana dzomuviri: maoko urefu, maoko, maoko, minwe, etc.

uyewo iwe zvinhu (vases, mapurani zvivako), navarongo pasi vakanga amutsvaka, kukura mune yokunyorwa nhetembo - zvose Tseyzig akaratidza kuburikidza kureba pemitsara nenhamba, naiyewo rokuti "kwemasvomhu aesthetics." Pashure pokugamuchira zvabuda kwakaratidza kuti Fibonacci akatevedzana inotengwa.

Fibonacci nhamba uye yendarama chikamu zvakasikwa

Munguva romuriwo uye mhuka nyika, pane zviri kuitika kune kuumba muchimiro symmetry, iro kuchengetwa nenzira kukura uye sangano. Weboka kupinda zvakafanana, ichibata mitezo, izvo zvaidiwa yendarama zvinoenderana - ndiwo muenzaniso zvinozivikanwa Zvirimwa zvakawanda nemhuka.

Nature yakatipoteredza anogona ratombonzi Fibonacci nhamba, somuenzaniso:

• nzvimbo chero matavi kana mashizha zvinomera, uyewo madaro anoenderana vanoverengeka vakapiwa kuwanda 1, 1, 2, 3, 5, 8, 13 uye zvakare;
• sunflower mbeu (pamwero pasikweya, chihenge sero), avete misara miviri yakakoswa spirals kwakasiyana-siyana;
• nhamba kureba muswe uye muviri nedzvinyu;
• zai chimiro, kana mutsetse yakaturikwa achiyambuka navanopinda chikamu;
• zvakaita nhamba minwe ruoko rwomunhu.

Uye, chokwadi, mashoko anofadza zvikuru siyana vari spirals nedhambakura goko mapatani padandemutande, kufamba mhepo ine dutu, miviri akamonyoroka DNA mamiriro, uye mapoka enyeredzi - vose zvinosanganisira Fibonacci kutevedzana.

Kushandisa chikamu yendarama iri mifananidzo

Vatsvakurudzi munyaya unyanzvi kuwana mienzaniso kushandiswa yendarama chikamu, akadzama kuongorora akasiyana mapurani zvinhu uye mabasa ounyanzvi. Inozivikanwa yakakurumbira zvivezwa, ivo creators iyo vanoomerera endarama kukura, - the pechifananidzo yeOlympia Zeus, Apollona Belvederskogo uye Athena Parthenos.

Mumwe mabasa Leonardo da Vinci - "Portrait of Mona Lisa" - vagara pasi kutsvakurudza masayendisiti. Vakawana kuti murwiyo basa ine zvachose kuti "Golden Triangle", akabatana pamwe chete nePentagon dzose nyeredzi. basa All da Vinci ndiyo testamendi sei zvakadzama aiva ruzivo yake marongerwo kukura muviri, saka kuti aigona kubata kusimba enigmatic kunyemwerera vanhu Mona Lisa.

Golden Section akitekicha

Somuenzaniso, masayendisiti akadzidza ounyanzvi ose mapurani, vakasikwa mitemo "chikamu yendarama"; muEgipita mapiramidhi, ari Pantheon, ivo Parthenon, Notre-Dame de Paris, St. Vasiliya Blazhennogo nevamwe.

Parthenon - mumwe zvivako zvikuru yakaisvonaka Ancient Greece (5 remakore BC.) - ane 8 mbiru uye 17 kumativi akasiyana, nhamba kukwirira kwayo kusvikira kureba mativi akaenzana 0,618. The Maberere yacho France rakagadzirwa "chikamu yendarama" (mufananidzo pazasi).

Mumwe masayendisiti tega uye vakabudirira vakashandisa kuvandudzika ari modular marongedzero kukura mapurani zvinhu (vanonzi "Modulor") - raiva murongedzeri French Le Korbyuze. Hwaro Modulor akaisa tambo ezvinhu chokuita CONDITIONAL kupesana migove dzemuviri.

Russian mapurani Mikhail Kazakov, uyo akavaka zvivako zvinoverengeka dzinogarwa muMoscow, uyewo weSeneti chivakwa muna Kremlin, uye Golitsyn Hospital (zvino wa1 Clinical Pirogov.) - aiva mumwe ezvivako uyo akashandisa magadzirirwo uye kuvaka mitemo chikamu yendarama.

Application zvikuru muna patani

Magadzirirwo yose nenguvo vagadziri kuti mifananidzo itsva uye mhando kufungisisa kukura nomuviri womunhu uye mitemo yendarama chikamu, kunyange pachisikirwo, kwete vanhu vose vane yakanaka kukura.

Kana kuronga serakavakwa magadzirirwo uye pakusika volumetric paka nziyo vachishandisa miti (pamiti), tsime uye duku mapurani zvinhu uye mapatani zvinogona kushandiswa "zvikuru waMwari". Uyewo, Kuronga paki zvinofanira zvainanga kusika mupfungwa muenzi, ndiani anogona takasununguka kufamba nayo uye kuwana chine muzinda.

zvinhu zvose zviri Park zviri zvikuru zvakadai kuti achishandisa geometrical mamiriro, hama chinzvimbo, chiedza, chiedza, kubereka munhu pfungwa kuwirirana uye zvakakwana.

Kushandiswa yegoridhe chikamu cybernetics rwokugadzira

Mitemo Yechinwiwa Section uye Fibonacci nhamba vo ari simba kuchinja mu kwemasayendisiti kuitika pamwe zvokutanga nezvimedu vanoumba makemikari remubatanidzwa muchadenga enyika dziri Gene maumbirwo DNA.

pezvakaitwa Similar kuitika mumuviri womunhu, iyo kunooneka pacharo ari biorhythms zvoupenyu hwayo, muzviito nhengo, zvakadai uropi kana chiono.

Algorithms uye mapatani yendarama kukura vari zvinowanzoshandiswa cybernetics ano uye informatics. Rimwe basa nyore kuti anopiwa kugadzirisa ruzivo programmers - nyora nzira uye kuziva uwandu Fibonacci nhamba imwe nhamba vachishandisa ekombiyuta mitauro.

Modern tsvakurudzo pamusoro dzidziso yendarama reshiyo

Sezvo pezana remakore rechi20, kufarira dambudziko uye matambudziko mitemo yendarama kukura munhu upenyu inowedzera zvinoshamisa, uye nemasayendisiti akawanda akasiyana-siyana: mathematicians, dzinza Vatsvakurudzi, zvipenyu, vazivi, nyanzvi dzezvokurapa, nezvoupfumi, vaimbi nevamwe.

Muna US kubva 1970-hgodov anotanga kubudisa magazini The Fibonacci Quarterly, izvo rinobudisa mapepa panyaya. Pachaunga mabasa apo generalized kutonga yegoridhe chikamu uye Fibonacci akatevedzana anoshandiswa muminda zivo siyana. Somuenzaniso, kuti encode ruzivo, tsvakurudzo makemikari, utachiona, etc.

izvi zvose anosimbisa zvakawanwa nenyanzvi dzekare uye ano kuti yendarama zvinoenderana comprehensively kwakabatana zvikuru mibvunzo sayenzi symmetry pachena mabasa mazhinji, uye zviitiko zvenyika yakatipoteredza.