Piv txwv ntawm Golden Ratio tuaj yeem pom nyob txhua qhov chaw hauv classic architecture, artwork, xwm, thiab txawm suab paj nruag. Qhov kev qhia ntawm kev faib ua feem, tseem hu ua Divine Ratio, muaj kev sib haum xeeb los ntawm kev siv tus lej irrational (1.618) hauv kev tsim, ob qho tib si ntuj thiab tib neeg tsim. Feem ntau, koj tsis paub txog kev ua lej tom qab qhov kev zoo nkauj ntawm Golden Ratio vim nws tsim cov khoom thiab suab paj nruag uas koj yuav pom kev txaus siab yam tsis xav tau kev piav qhia.
Golden Ratio hauv Architecture
Golden Ratio tsim yuav luag zoo nkauj zoo nkauj nyob rau hauv cov xwm thiab kos duab. Thaum koj pib nrhiav Golden Ratio piv txwv hauv lub neej niaj hnub, koj yuav xav tsis thoob los ntawm ntau qhov xwm txheej uas nws tau siv los tsim ntau lub tsev thiab cov vaj tse. Thaum Golden Ratio yog siv nyob rau hauv architecture, lub tsev hais tias tsim los ntawm kev siv "dawb huv architecture." Los ntawm kev siv kev suav ntawm Golden Ratio rau ib lub xwmfab, architects thiab designers muaj peev xwm tsim Golden Rectangle, uas ntseeg tau tias muaj qhov zoo nkauj zoo nkauj tshaj plaws rau tib neeg lub qhov muag.
Golden Rectangle Piv txwv: Lub Parthenon
Phidias, tus sculptor Greek, siv Golden Ratio hauv nws txoj haujlwm, tshwj xeeb tshaj yog thaum nws pib ua haujlwm nrog cov qhab uas nws sculpted saum cov kab Parthenon. Nws tseem ceeb heev uas yuav tsum nco ntsoov tias tus lej tus nqi tau muab rau Golden Ratio, Phi, tau raug hu ua nws lub meej mom.
Yog tias koj ntsuas qhov ntev ntawm Parthenon sab nrauv, koj yuav pom tias nws tsis yog tsuas yog ua Golden Rectangle xwb, tab sis kuj tseem muaj ntau Golden Rectangles ntawm txhua kab. Cov qauv dawb ceev no yog ib qho piv txwv zoo nkauj ntawm Golden Ratio hauv architecture.
Golden Daim duab peb sab Piv txwv: Great Pyramid ntawm Giza
Lub Golden Ratio, Golden Rectangle, thiab Golden Daim duab peb sab tuaj yeem pom nyob rau hauv qhov zoo tshaj plaws ntawm ib qho ntawm Xya Lub Ntiaj Teb, Lub Pyramid ntawm Giza. Txhawm rau nrhiav Golden Ratio, koj yuav tsum tau txiav ib nrab ntawm lub hauv paus ntawm lub pyramid thiab kos ib txoj kab ntsug ntawm qhov nruab nrab ntawm lub pyramid. Thaum qhov no txuas nrog lub kaum sab xis ntawm lub pyramid, koj tuaj yeem pom tau yooj yim yuav ua li cas nws tsim Golden Daim duab peb sab nrog 1.618 piv, Golden Ratio.
Lwm Cov Piv Txwv Architectural
Koj tuaj yeem pom ntau yam piv txwv ntawm ancient mus rau niaj hnub dawb huv architecture thiab Golden Ratio vaj tse.
- Chartre Cathedral - Centre, Fabkis
- Notre Dame - Paris, Fabkis
- Porch of Maidens - Acropolis, Athens
- Taj Mahal - Agra, India
- United Nations Lub Tsev - New York City, New York
Golden Ratio in Art Piv txwv
Koj tuaj yeem pom ntau yam piv txwv los ntawm cov kws kos duab zoo nkauj uas siv Golden Ratio. Cov hauj lwm ntawm kev ua tiav no tau tsim los ntawm kev siv qhov piv ntawm Golden Rectangles thiab Golden Daim duab peb sab. Daim duab tsim raws li Golden Rectangle ua pov thawj kom txaus siab rau tib neeg lub qhov muag. Nws yog ib qho kev paub tsis meej uas nyob ib puag ncig lub duab plaub zoo meej thiab Golden Ratio.
Golden Ratio in Art
Golden ratio art piv txwv suav nrog:
- Leonardo Di Vinci - Mona Lisa, Vitruvian txiv neej
- Botticelli - Yug ntawm Venus
- Michelangelo - Tsev Neeg Dawb Huv, 'David'
- Raphael - Crucifixion
- Rembrandt - Self-Portrait
- Salvador Dali - Lub Cim Nco Txog Hnub Nyoog Kawg, Kev Cia Siab Ntawm Kev Nco
Siv Golden Ratio in Art Composition
Nyob rau hauv lub Golden Rectangle yog qee qhov chaw uas pom tias muaj kev pom zoo dua li lwm qhov chaw. Cov ntsiab lus no tau pom los ntawm kev kos ib kab los ntawm lub kaum sab xis hauv qab ntawm lub duab plaub mus rau lub ces kaum sab nraud thiab rov ua dua nrog lwm lub ces kaum hauv qab. Cov kab no yuav sib tshuam ntawm qhov chaw nruab nrab ntawm Golden Rectangle. Tom ntej no, ntsuas qhov nruab nrab ntawm txhua kab pib los ntawm qhov chaw nruab nrab. Plaub lub ntsiab lus no yog hu ua lub qhov muag ntawm daim duab plaub (Golden Ratio). Lub ntsiab focal point ntawm painting yog kos los yog pleev xim rau hauv cov ntsiab lus ntawm kev txaus siab (piv txwv).
Golden Ratio in Music
Suab paj nruag yog tsim los ntawm cov lej thiab thaum Golden Ratio siv los tsim ib lub suab paj nruag, nws dhau los ua piv txwv ntawm lej. Fibonacci Sequence kuj tseem muaj nyob hauv suab paj nruag:
- Muaj yim sau hauv ib teev.
- Qhov thib peb thiab thib tsib yog lub hauv paus ntawm chords.
- Qhov ntev, lossis octave, ntawm ib daim ntawv yog 13 sau ntawv.
Qhov kev sib txuas txuas ntxiv mus thoob plaws ib daim nkauj thiab ua nyuaj dua thaum nws mus txog Golden Ratio.
Kwv Txhiaj Siv Yis Ntuj Neeb
Ib txhia ntawm cov classical composers uas paub zoo tshaj plaws siv Golden Ratio thiab Fibonacci Sequencing hauv lawv cov suab paj nruag, xws li Bach, Beethoven, Chopin, thiab Mozart. Qee cov kws sau nkauj niaj hnub zoo li Casey Mongoven tau tshawb txog Golden Ratio hauv lawv cov suab paj nruag.
Golden Ratio Piv txwv hauv Xwm
Golden Ratio nyob qhov twg? Nws nyob hauv Golden lossis Fibonacci Kauv, uas tuaj yeem tsim los ntawm kev siv Golden Ratio. Qhov no yog ib qho tshwm sim uas tau pom dav dav hauv lub ntiaj teb ntuj. Ib tsob nroj nplooj tuaj yeem loj hlob kom ntau li ntau tau tuaj yeem muab kauv rau ntawm qia. Daim nplooj tshiab tsuas yog tsim tom qab qhov kev hais plaub uas nws tau tsim.
- kab laug sab cacti
- kab laug sab galaxies
- Sunflowers
Paj Nrog Fibonacci Sequence
Qee paj muaj paj paj uas ua raws li Fibonacci Sequence:
- 3 petals:Iris, lily, orchids, trillium
- tsib petals: Buttercups, geraniums, hibiscus, thaum sawv ntxov glory, nasturtium
- Eight petals: Delphiniums
- 13 petals: Qee yam ntawm daisies, ragwort, marigold
Fibonacci Kauv hauv Pinecones
Nyob ntawm tsob ntoo, koj tuaj yeem pom Golden Ratio ntawm kev ua haujlwm hauv Fibonacci tooj series hauv pinecones. Koj tuaj yeem nrhiav tau yim spirals ntawm ib sab ntawm pinecone, nrog 13 spirals ntawm lwm qhov. Lwm tus qauv pinecone muaj tsib kauv ntawm ib sab nrog yim rau lwm qhov.
Golden Ratio in Humans
qhov piv txwv no kuj tseem ceeb heev uas tsis yog tib neeg saib ib leeg nkaus xwb tab sis kuj yog lawv lub cev ua haujlwm, thiab hauv lawv cov DNA.
DNA nthuav tawm qhov sib piv Golden
Ib qho piv txwv zoo tshaj plaws ntawm Golden Ratio muaj nyob hauv tib neeg DNA qauv. Qhov no tuaj yeem pom hauv ib qho DNA hla ntu uas qhia txog DNA ob lub helix tsim cov duab decagon. Qhov no yog kev sib txuas ntawm ob lub pentagons, tig 36 degrees los ntawm ib leeg, ua rau DNA ob lub helix. Ob chav helix kauv nws tus kheej tsim ib lub pentagon. Txawm tias ib qho DNA molecule qhia txog lub hauv paus ntawm Golden Tshooj lossis Divine Proportion.
lej tom qab tus lej Golden
Nrhiav qhov sib piv Golden hauv lub neej tiag tiag yog qhov yooj yim, raws li nws tshwm nyob ib puag ncig koj. Nws yog kev ua lej truism uas tau siv los txheeb xyuas qhov uas feem ntau hu ua tus lej zoo meej pom nyob rau hauv qhov xwm txheej uas tau muab luam tawm thiab coj los ntawm tib neeg rau ntau pua xyoo. Lub simplistic kev zoo nkauj ntawm tus xov tooj no disguises nws complexity nyob rau hauv kev tua. Yuav kom nkag siab txog txoj kev xav tom qab qhov sib piv Golden, koj yuav tsum xub tshawb xyuas Fibonacci Sequencing ntawm qhov piv.
Fibonacci Sequence thiab Golden Ratio
Fibonacci Sequence lossis Series muaj kev sib raug zoo rau Golden Ratio. Fibonacci Series qhia txog cov nplooj ntawm cov nroj tsuag thiab cov paj ntawm cov paj. Lub Fibonacci Kauv, uas pom nyob rau hauv qhov, yog ib txwm ib feem ntawm lub Golden Rectangle nrog ib tug Golden ratio.
Fibonacci Series lej yog qhov yooj yim:
- Cov kab ke pib nrog 0 thiab 1.
- Tsuas ntxiv ob tug lej kawg ua ke kom tau tus lej tom ntej hauv koob.
- 0+1=1, 1+1=2, 1+2=3, 2+3=5, 3+5=8, thiab lwm yam.
- Fibonacci Series piv txwv no dhau los ua: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, thiab lwm yam.
Fibonacci txoj kev sib raug zoo rau Golden Ratio tau paub thaum nws ntxiv rau pem hauv ntej, ntxiv, thiab ntxiv. Qhov ntau koj ntxiv cov koob, qhov ze koj mus rau Golden Ratio.
Creating Golden Rectangle and Triangle
Los tsim lub Golden Rectangle nrog Fibonacci Sequence, koj pib nrog ib lub xwmfab. Koj yuav pib tsim ib lub duab plaub los ntawm kev ntxiv lwm square rau lub qub square. Nco ntsoov siv tus qauv: 0 + 1=1 yog thawj square, 1 + 1=2 - koj yuav ntxiv lwm square.1 + 2=3 koj yuav ntxiv peb squares thiab tom ntej, 2 + 3=5, koj yuav ntxiv tsib squares. Koj tseem yuav ntxiv cov squares thiab thaum kawg tsim Golden Rectangle.
Ib daim duab peb sab Golden tuaj yeem tsim los ntawm bisecting Golden Rectangle los ntawm ib lub ces kaum mus rau sab nraud. Qhov no tsim ib daim duab peb sab uas nws peb sab los yog lub kaum sab xis muaj 2: 2: 1 piv, txhais tau hais tias ob sab ntev yog sib npaug ntawm qhov ntev thiab lub kaum sab xis yog raws nraim ib nrab ntawm qhov ntev ntawm ob qhov ntev.
Golden Ratio in the Real World
Golden Ratio feem ntau hu ua Divine Ratio vim nws qhov tseem ceeb hauv qhov xwm txheej, thiab hauv tib neeg lub cev. Qhov kev tshawb pom tias Golden Ratio yog tam sim no nyob rau hauv ntau yam muaj sia nyob ua rau muaj kev hwm rau qhov kev faib ua tej yam yees siv no, thiab nws tseem ua rau muaj kev tshoov siab rau cov neeg ua yeeb yam thiab cov neeg tsim niaj hnub no.
