Lub Golden piv - ib tug ... golden seem pyramids. Cov mis ntawm lub golden seem

Geometry - leej thiab tham science hais tias thaum tag nrho cov no yog ib yam ntawm cov kos duab. Kab, lub dav hlau, cov proportions - tag nrho cov no yuav pab tau tsim ib tug ntau ntawm yeej zoo kawg nkaus yam. Thiab oddly txaus, qhov no yog raws li nyob rau hauv lub geometry ntawm nws nyob rau hauv ib tug ntau yam ntawm nws cov ntaub ntawv. Nyob rau hauv no tsab xov xwm peb yuav saib ib yam txawv heev tshaj plaws, uas yog ncaj qha kev cob cog rua nrog nws. Kub seem - qhov no yog qhov geometric mus kom ze, uas yuav tsum tau los sib tham.

zoo ntawm tus kwv thiab nws cov xaav

Cov neeg siv yog coj feem ntau nyob rau hauv qhov zoo ntawm cov khoom nyob hauv thiaj li yuav paub txog nws cov lub tsheej lab ntawm lwm tus neeg. Uas daim ntawv peb seb zoo li cas ntawd tshaj plaws yog nyob rau hauv pem hauv ntej ntawm peb los yog sawv tam sim ntawd. Peb thawj tau paub cov neeg nyob rau hauv lub cev zoo thiab lub ntsej muag. Yog li ntawd, peb yuav confidently vajhuam uas daim ntawv nws tus kheej, nws loj thiab hom - ib qho ntawm feem tseem ceeb uas nyob rau hauv ib tug neeg xaav.

Rau cov neeg uas tsim dab tsi ntxiv yog ntawm kev txaus siab rau ob lub ntsiab yog vim li cas: yog nws yog ib tug yuav tsum dictated los ntawm lub neej, los yog lwm tus hu ua aesthetic Library los ntawm txoj kev zoo nkauj. Qhov zoo tshaj plaws pom tau qhov sib xaav thiab cov kev txiav txim zoo ntawm kev sib raug zoo thiab kev zoo nkauj feem ntau los thaum muaj ib tug observes rau hauv daim ntawv siv nyob rau hauv kev tsim kho ntawm ib tug symmetry thiab ib tug tshwj xeeb kev sib raug zoo, uas yog hu ua tus golden ratio.

Lub tswvyim ntawm cov golden seem

Yog li ntawd, cov golden seem - ib tug Golden txhais li cas, uas kuj yog ib harmonic division. Nyob rau hauv thiaj li yuav piav no ntau kom meej meej, xav txog ib co kev zoo. Namely, tus duab yog ib yam dab tsi tag nrho, zoo thiab tag nrho cov, nyob rau hauv lem, yeej ib txwm muaj ob peb qhov chaw. Cov feem yuav muaj ntau yam ntxwv, yam tsawg kawg sib txawv ntau thiab tsawg. Tab sis xws li qhov ntev yog ib txwm nyob rau hauv ib tug tej yam ratio, ob qho tib si ntawm lawv tus kheej thiab nyob rau hauv kev sib raug zoo rau tag nrho cov.

Yog li ntawd, nyob rau hauv lwm yam lus, peb yuav hais tias cov golden piv - tus piv ntawm ob qhov ntau, uas nws muaj nws tus kheej mis. Siv no piv rau tsim ntaub ntawv yuav pab kom nws zoo nkauj thiab harmonious mus rau tib neeg lub qhov muag.

Los ntawm cov ancient keeb kwm ntawm lub golden seem

Qhov ratio ntawm cov golden seem yog feem ntau siv nyob rau hauv ntau ntau cov cheeb tsam ntawm lub neej niaj hnub no. Tab sis cov keeb kwm ntawm lub sij hawm mus rov qab mus rau lub sij hawm ancient thaum tseem me me xws sciences li lej thiab philosophy. Raws li ib tug scientific tswvyim ntawm tus Golden seem tuaj rau hauv kev siv nyob rau hauv lub sij hawm ntawm Pythagoras, namely nyob rau hauv lub xyoo pua VI BC. Tab sis txawm ua ntej qhov kev paub ntawm xws li ib tug ratio, nyob rau hauv kev xyaum, siv nyob rau hauv ancient Egypt thiab Babylon. Ib tug striking pov thawj ntawm no yog cov pyramids, uas tau siv rau qhov kev siv ntawm xwb xws li ib tug Golden kev faib ua feem.

ib tug tshiab lub sij hawm

Lub Renaissance yog ib tug tshiab ua tsis taus pa rau hauv lub harmonic division, tshwj xeeb tshaj yog ua tsaug rau Leonardo da Vinci. Qhov no kev sib raug zoo yog nce pib siv nyob rau hauv lub zog sciences, xws li geometry, raws li tau zoo raws li nyob rau hauv kos duab. Zaum thiab ntxias tau ua tsaug ntau kawm golden seem thiab tsim phau ntawv uas nyob rau qhov no qhov teeb meem.

Ib tug ntawm cov tseem ceeb tshaj plaws keeb kwm ua hauj lwm muaj feem xyuam rau cov golden ratio, - ib phau ntawv ntawm Lukas Pancholi hu ua "divine kev faib ua feem". Historians xav tias cov duab nyob rau hauv phau ntawv no twb tau los ntawm Leonardo da Vinci.

Cov zauv qhia ntawm lub golden piv

Lej muab ib tug heev ntshiab ntsiab txhais ntawm kev faib ua feem, uas hais tias nws yog ib lub koob pheej ntawm lawv ntawm ob ratios. Lej, qhov no yuav qhia nyob rau hauv no kab zauv: yog ib tug: b = ib: d, qhov twg ib tug, b, c, d - yog ib tug tej yam muaj nuj nqis.

Yog hais tias peb xav txog cov kev faib ua feem ntawm lub ya, muab faib ua ob qhov chaw, nws ua tau raws li ob peb zaus:

• Lub ya yog muab faib ua ob kiag li sib npaug zos qhov chaw, thiab yog li ntawd AB: AC = AB: BC, Yog hais tias AB - qhov no yog lub caij nyoog pib thiab thaum xaus ntawm lub ya, thiab C - point, uas cais lub ya mus rau hauv ob sib npaug zos qhov chaw.
• Lub ya yog muab faib ua ob teej qhov chaw, uas yuav ua tau nyob rau hauv qhov sib txawv proportions rau txhua lwm yam, uas txhais tau tias lawv yog cov tag tawm ntawm kev faib ua feem.
• Lub ya yog muab faib li ntawd AB: AC = AC: tiv tshav ntuj kub

Raws li rau lub golden seem, nws yog proportional rau qhov ntev ntawm lub division rau hauv zoo tib qhov chaw ntawm lawv tus kheej, thaum tag nrho cov ya hais txog cov feem ntau yog ib feem, raws li cov heev loj ib feem yog hais txog mus rau lub me ib. Yog lwm formulation: me ya hais txog qhov thiaj li loj li tus loj dua cov tag nrho ya. Nyob rau hauv lej ntsiab lus uas nws yog raws li nram no: ib tug: b = b: c los yog c: b = b: a. Nws yog ib qhov zoo ntawm ib tug formula ntawm cov golden seem.

Lub Golden piv nyob rau hauv Xwm

Golden seem, piv txwv uas peb tam sim no xav txog koom zoo kawg tshwm sim ntawm qhov. Qhov no yog ib tug zoo nkauj heev piv txwv ntawm dab lej - nws tsis yog tus xov tooj thiab tus qauv, thiab science, uas muaj ntau tshaj li ib tug tiag tiag thiaj yuav ntawm qhov thiab peb lub neej nyob rau hauv feem ntau.

Rau muaj sia nyob yog ib tug ntawm lub ntsiab kev pab raws qib ntawm lub neej - nws yog txoj kev loj hlob. Xws li ib tug lub siab xav mus coj lawv qhov chaw nyob rau hauv qhov chaw, nyob rau hauv qhov tseeb, nqa tawm nyob rau hauv ob peb ntaub ntawv - ib qho kev nce mus yuav luag kab rov tav kis raws hauv av los yog cockling rau ib co kev pab txhawb nqa. Thiab tsis muaj teeb meem yuav ua li cas nws yog ib qho zoo kawg, muaj ntau yam nroj tsuag loj hlob nyob rau hauv raws li cov golden ratio.

Lwm luag zoo kawg qhov tseeb - yog tus piv ntawm lub cev lizards. Lawv lub cev zoo heev pleasing mus rau lub qhov muag tib neeg, thiab qhov no yog tau ua tsaug rau lub golden ratio. Yuav kom ua tau ntau leej, lawv tus Tsov tus tw ntev hais txog qhov ntev ntawm lub tag nrho lub cev raws li ib tug 62: 38.

Nthuav lus tseeb hais txog cov kev cai ntawm lub golden seem

Kub seem - qhov no yog tiag tiag ib qho zoo kawg tswvyim, uas txhais tau tias thoob plaws keeb kwm peb ua tau raws li ib tug ntau ntawm nthuav tiag tiag tseeb txog tib yam kev faib ua feem. Peb qhia rau koj ib co ntawm lawv:

• Tus Golden piv koom siv nyob rau hauv kev tsim kho ntawm lub pyramids. Piv txwv li, lub ntiaj teb no-nrov Tutankhamun thiab Cheops tsa siv xws li ib tug kev sib raug zoo. Thiab cov golden seem ntawm lub pyramid tseem tseem yog ib tug paub tsis meej, vim hais tias mus hnub no tsis paub casually los yog lawv xaiv xws ntev mus rau lawv bases thiab heights.
• Cov cai ntawm cov golden seem yog kom meej meej pom nyob rau hauv lub facade ntawm lub Parthenon - ib qho ntawm feem zoo nkauj vaj tse nyob rau hauv lub architecture ntawm ancient Greece.
• Tib yam siv rau lub tsev ntawm cov Cathedral ntawm Notre Dame (Notre-Dame de Paris), nws tsis yog cia li facades, tab sis tseem muaj lwm qhov chaw ntawm cov qauv tsa rau lub hauv paus ntawm no zoo kawg kev faib ua feem.
• Lavxias teb sab architecture yuav pom ntau yam piv txwv zoo kawg vaj tse, nyob rau hauv tag nrho raws li cov kev golden seem.
• Harmonious division kuj xam qhovkev rau cov tib neeg lub cev, thiab yog li ntawd cov duab puab, tshwj xeeb yog rau saum cov neeg. Xws li Apollon Belvedersky - pej thuam, nyob qhov twg qhov siab ntawm txoj hlab kab yog muab faib nyob rau hauv lub Golden seem.
• Painting - ib tug zaj dabneeg sib txawv, tshwj xeeb tshaj yog thaum koj xav txog lub luag hauj lwm ntawm Leonardo da Vinci nyob rau hauv lub keeb kwm ntawm lub golden ratio. Nws nto moo Mona Lisa, ntawm chav kawm, yog raug rau txoj kev cai no.

Golden Section nyob rau hauv tib neeg lub cev

Nyob rau hauv seem no, peb yuav tsum hais ib tug tseem ceeb heev neeg - namely, S. Zeising. Ib tug German soj ntsuam uas tau ua ib txoj hauj lwm nyob rau hauv lub tshav pob ntawm kev kawm txog cov golden ratio. Nws luam tawm ib tug ua hauj lwm hu ua "nkauj Studies". Nyob rau hauv nws cov hauj lwm nws qhia golden seem li ib tug meej ntsiab hais tias yog universal rau tag nrho cov tshwm sim ob leeg nyob rau qhov thiab nyob rau hauv kos duab. Ntawm no yog peb muaj peev xwm nco qab lub golden seem pyramids nrog harmonious kev faib ua feem ntawm tib neeg lub cev thiab thiaj li nyob.

Nws Zeising tau los ua pov thawj hais tias cov golden ratio, nyob rau hauv qhov tseeb, muaj ib tug nruab nrab statistical txoj cai rau tib neeg lub cev. Qhov no tau raug qhia nyob rau hauv kev xyaum, vim hais tias thaum lub sij hawm nws ua hauj lwm nws yuav tsum tau ntsuas ib tug ntau ntawm tib neeg lub cev. Historians kwv yees tias ntau tshaj li ob txhiab neeg coj ib feem nyob rau hauv no xyaum ua tej yam. Raws li cov kev tshawb Zeising, lub ntsiab qhia ntawm lub golden piv - ib tug faib ntawm lub cev taw tes ntawm lub puj ntaws. Yog li, tus txiv neej lub cev nrog ib tug nruab nrab piv ntawm 13: 8 me ntsis los ze zog mus rau lub golden seem tshaj tus poj niam, nyob rau hauv lub xov tooj ntawm cov golden seem yog 8: 5. Tsis tas li ntawd, cov kev faib ua feem ntawm kub yuav tsum muaj cai nyob rau hauv lwm qhov chaw ntawm lub cev, xws li, piv txwv li, rau tes.

Nyob rau hauv kev tsim kho ntawm lub golden seem

Nyob rau hauv qhov tseeb, qhov kev siv ntawm cov golden seem - yog yooj yim txaus. Raws li peb tau pom, lub ancient cov neeg coped nrog nws yooj yim heev. Yuav ua li cas mus hais lus ntawm kev txawj ntse thiab technology ntawm noob neej. Nyob rau hauv no tsab xov xwm, peb yuav tsis qhia yuav ua li cas no yuav ua tau tsuas yog nyob rau hauv ib daim ntawm daim ntawv thiab xaum rau hauv tes, tab sis nws muaj kev ruaj ntseg hais tias qhov no yog, nyob rau hauv qhov tseeb, tej zaum. Ntxiv mus, nws yuav ua tau ntau tshaj li ib txoj kev.

Vim qhov no yog ib tug yooj yim haum geometry, Golden piv haum yooj yim rau tsim, txawm nyob rau hauv lub tsev kawm ntawv. Yog li ntawd, cov ntaub ntawv yuav muab tau yooj yim nyob rau hauv tshwj xeeb cov phau ntawv. Kawm golden seem 6 chav kawm ntawv yeej muaj to taub tej ntsiab cai ntawm nws siv, uas txhais tau tias txawm cov me nyuam yog ntse txaus lug tau sai dlua xws li ib tug neeg ua hauj lwm.

Golden kev faib ua feem nyob rau hauv kev kawm txog zauv

Tus thawj acquaintance nrog cov golden seem nyob rau hauv txoj kev xyaum pib nrog tej yam yooj yim Paub Faib kab ya tag nrho cov nyob rau hauv tib proportions. Feem ntau cov feem ntau qhov no yog ua li cas nrog ib tug kav, ib tug compass thiab, ntawm chav kawm, ib tug cwj mem.

Cov theem ntawm cov golden piv qhia raws li infinite irrational feem AE = 0.618 ..., Yog hais tias AB yog coj li ib chav tsev, YUAV = 0,382 ... Nyob rau hauv thiaj li yuav ua rau cov suav ntau tswv yim, feem ntau siv tsis yog caij nyoog, tab sis approximate qhov tseem ceeb, namely - 0 62 thiab 0,38. Yog hais tias lub ya AB yog coj li 100 qhov chaw, feem ntau ntawm nws yuav ua ncaj rau 62, zoo, me - 38 qhov chaw, ntsig txog.

Lub ntsiab cuab yeej ntawm tus Golden piv tej zaum yuav qhia los ntawm cov kab zauv: x ² -hluav 1 = 0. Nyob rau hauv kev daws uas peb tau txais hauv qab no cov hauv paus hniav: x = _1.2. Txawm hais tias kev ua lej yog muaj tseeb thiab kev kawm science, raws li zoo raws li nws cov nqe lus - lub geometry, tab sis hais tias cov khoom xws li cov golden piv cov qauv, hais tsis txog nws.

Sib raug zoo nyob rau hauv lub kos duab los ntawm golden seem

Mus sum txog, cia peb xav txog luv luv li cas yog twb hais tias.

Yeej, nyob rau hauv cov cai ntawm cov golden piv yuav muaj ntau piv txwv ntawm cov kos duab, qhov twg lub cai piv ze rau 3/8 thiab 5/8. Qhov no yog ib tug ntxhib mis ntawm lub golden seem. Cov tsab xov xwm twb hais ib tug ntau ntawm cov piv txwv ntawm qhov kev siv ntawm tus ntoo khaub lig-section, tab sis ib zaug dua peb saib nws los ntawm cov plaub ntawm ancient thiab niaj hnub kos duab. Yog li, lub feem ntau cov tawm cov piv txwv ntawm ancient sij hawm:

• Golden Section Pyramids ntawm Cheops thiab Tutankhamun yog qhia qhov txhia chaw: lub tuam tsev, bas-reliefs, tsev neeg cov khoom thiab, ntawm chav kawm, cov kho kom zoo nkauj heev tombs.
• Tuam tsev ntawm Seti kuv nyob rau hauv Abydos nto moo reliefs nrog txawv cov dluab, tag nrho cov uas sib haum mus rau tag nrho cov tib txoj cai.

Raws li rau tej zaum twb meej pem ntawm kev faib ua feem, ces, pib los ntawm lub sij hawm ntawm Leonardo da Vinci, nws tau nkag mus rau hauv kev siv nyob rau hauv txhua lub sectors ntawm lub neej - los ntawm science thiab cov kos duab. Txawm ib thiab tshuaj tau tseeb hais tias golden piv tej hauj lwm txawm nyob rau hauv nyob systems thiab kab mob.