Fibonacci tooj nrog peb

Fibonacci tooj yog tag nrho cov nyob ib ncig ntawm peb. Lawv yog cov tseem nyob rau hauv cov suab paj nruag, nyob rau hauv architecture, nyob rau hauv cov paj huam, kev kawm txog zauv, kev lagluam, cov ua lag luam Tshuag, nyob rau hauv cov qauv ntawm cov nroj tsuag nyob rau hauv lub cochlear kauv, nyob rau hauv lub proportions ntawm tib neeg lub cev thiab thiaj li nyob, ad infinitum ...

Naas ej medieval mathematician Leonardo Pizansky (c. 1170-c. 1250), zoo dua lub npe hu ua Fibonacci, yog ib tug ntawm cov feem ntau nto moo zaum ntawm nws lub sij hawm. Nws yog tus thawj nyob rau hauv cov teb chaws Europe pom tias cov kev siv ntawm Arabic numerals es tsis txhob ntawm Roman thiab qhib xaam ib theem zuj zus ntawm tus xov tooj, tom qab ntawd muaj npe tom qab nws, uas yog raws li nram no: 1,1,2,3,5,8,13,21, ... thiab thiaj li nyob ad infinitum. Cov kab sab ntawm cov zauv no hu ua "Fibonacci tooj."

Nws yog ib qho yooj yim mus pom tias nyob rau hauv no zoo kawg li ib theem zuj zus li nram qab no txhua tus xov tooj yog tsim los ntawm kev ntxiv lub ob yav dhau los sawv daws yuav. Thiab yog dab tsi yog nws zoo kawg li? Yog hais tias peb faib txhua tom ntej lub sij hawm ntawm no cim ib theem zuj zus ntawm yav tas los ib tug, peb yuav maj mam tuaj ze zog mus rau ib co amazing transcendental piv - tus xov tooj ntawm F (Fibonacci tooj) = 1.6180339887 ...

Qhov no xam, zoo li lub xov tooj Pi (3.1415 ...) muaj ib tug caij nyoog muaj nqis. Tus nab npawb ntawm tug lej tom qab tom qab tus zauv point yog infinite. Qhov no yog qhov pib thiab tsis tsuas zauv txuj ci tseem ceeb. Yog hais tias peb faib txhua lub sij hawm ntawm ib theem zuj zus mus raws li, peb yuav tau txais ib transcendental tooj 0 6180339887 ... Miracles tseem - tom qab tus zauv lej tom qab rov ua raws nraim ib theem zuj zus ntawm tug lej tom qab ntawm F, cia li ua ntej lub comma yog tsis 1, thiab 0.

Mus tom ntej. Yog hais tias peb square lub tej Fibonacci tooj, qhov tshwm sim yuav tsum tau sib npaug zos rau cov xov tooj ntawm sawv nyob rau hauv ib theem zuj zus nyob rau hauv pem hauv ntej ntawm nws, multiplied los ntawm tus xov tooj uas yog tom qab nws, ntxiv los yog rho tawm 1. Piv txwv li, tsib squared yog sib npaug zos rau 3x8 + 1; 8 squared sib npaug 5x13 rho tawm 1; 13 tsa mus rau lub square, raws li zoo 8x21 + 1 thiab thiaj li nyob. Tej yam tshwm sim "plus" thiab "rho tawm" hloov qho. Tej zauv txuj ci tseem ceeb ntau ntau yam ntawm no. Fibonacci tooj ua hauj lwm txuj ci tseem ceeb nyob ib ncig ntawm peb, tej zaum peb cia li tsis pom.

Fibonacci tooj nyob rau hauv lub ntuj

Fibonacci ratios, kev coj tus kheej npe txawv - Golden piv, Golden Section, Divine kev faib ua feem - yog pom nyob rau hauv lub feem ntau npaj txhij txog thiab mysterious qhov chaw. Piv txwv li, cov kev sib raug zoo muaj peev xwm yuav pom raws li qhov ceev faj saib xyuas ntawm lub geometrical proportions Hauv ntawm Giza, pyramids nyob rau hauv Mexico, Monument ancient architecture Parthenon.

Cov nroj tsuag muaj peev xwm kuj pom ib tug tej yam yees siv kev sib raug zoo. Peb yuav soj ntsuam cov Fibonacci tooj dua, yog hais tias peb ua tib zoo xav txog ib tug ntau yam ntawm kev tawg paj Asteraceae nroj: lub paj ntawm iris, peb nrhiav tau 3 tej nplaim, nyob rau hauv primrose - 5, los ntawm ragweed - 13, nyob rau hauv daisy -34, thaum asters - 55 thiab 89 tej nplaim .

Qhov zoo Goethe cai thiab kawm cov kev qhia ntawm helicity nyob rau hauv cov xwm. Qwj yuav pom nyob rau hauv txoj kev situated sunflower noob, ntoo thuv cones, nyob rau hauv cacti, pineapples thiab lwm tus neeg. Nyob rau hauv tag nrho cov mob tshwm Fibonacci tooj. Muab Kauv kab laug sab zaum hiab nws web. Kub yog cov spirally. Yog li ntawd cov thiab galaxies. "Lub nkhaus ntawm lub neej" - qhov thiaj li hu ua kauv Iogann Gote.

Yog manifested Fibonacci piv thiab biology ntawm txawv cov kab mob no. Piv txwv li, tus naj npawb ntawm rays ntses hnub qub sib haum mus rau Fibonacci tooj. Ib tug yooj yim yoov tshaj cum kuj nrhiav tau lawv: nws ob txhais ceg 3 officers, 8 feem muaj lub plab mog, thiab nyob rau nws lub taub hau muaj 5 antennae. Cov nab npawb ntawm cov pob txha caj qaum nyob rau hauv ib co tsiaj yog 55, thiab hais txog.

Nabqa tsiav piv qhov ntev ntawm nws tus ko tw mus rau tus so ntawm lub cev ntev ntawm 62 thiab 38, thiab kev sib raug zoo yog harmonious thiab pleasing mus rau peb lub qhov muag. Nyob rau hauv tus tsiaj thiab cog ntiaj teb no, qhov txhia chaw nws ua symmetry. Vajtswv, Xwm los yog lub Great kes duab vajtse ntawm lub pom tau hais faib mus rau hauv symmetrical theem, thiab cov golden ratio. Nyob rau hauv lub rov ib feem tau tag nrho cov qauv, uas yog ib tug manifestation ntawm fractal nyob rau hauv cov xwm.

Kub symmetry cai nyob rau hauv lub zaus txuam nrog lub zog tus nqi ntawm elementary hais, tus qauv ntawm ib tug neeg tshuaj tebchaw, nyob rau hauv qhov chaw nruab, kev tshuaj ntsuam genetic lug, tus qauv ntawm ib co tib neeg nruab nrog cev thiab lub cev, pom nyob rau hauv lub biorhythms, lub hlwb muaj nuj nqi thiab thaj chaw ntawm xaav.