Yuav ua li cas yog symmetry nyob rau hauv lej? Lus Txhais thiab piv txwv

To taub dab tsi symmetry nyob rau hauv kev kawm txog zauv, nws yog tsim nyog rau siab ntso kawm qhov yooj yim thiab advanced cov ntsiab lus ntawm algebra, geometry. Nws yog ib qho tseem ceeb rau qhov kev nkag ntawm daim duab, architecture, cov kev cai ntawm kev tsim kho drawings. Dua li ntawm qhov sib raug zoo nrog rau feem ntau pes tsawg science - kev kawm txog zauv, symmetry yog ib qho tseem ceeb rau lam, ntxias, creators, thiab rau cov neeg uas koom nyob rau hauv kev tshawb fawb kev ua ub no, thiab nyob rau hauv tej teb.

lus qhia dav dav

Tsis tsuas yog kev kawm txog zauv, tab sis kuj cov natural sciences yog lom zem ntau raws li lub tswvyim ntawm symmetry. Ntxiv mus, nws yog nyob rau hauv lub neej txhua hnub, nws yog ib tug ntawm cov yooj yim xwm ntawm ntug peb. Cais li cas yog symmetry nyob rau hauv kev kawm txog zauv, nws yog tsim nyog los hais tias muaj ntau ntau hom ntawm no phenomenon. Yuav kom tham txog cov kev xaiv:

• Ob sab sib dho, uas yog, xws li daim iav symmetry. Qhov no tshwm sim nyob rau hauv lub scientific ib puag ncig, feem ntau hu ua "ob sab sib dho".
• Al-rated hauv paus. Rau cov tswvyim no tseem ceeb tshwm sim - ib tug kev sib hloov lub xam division ntawm 360 degrees ntawm ib tug predetermined nqi. Nyob rau hauv tas li ntawd, pre-sau tseg axis txog uas kev sib hloov tshwm sim.
• Padialnaya thaum symmetry phenomenon cai yog kuas nyuas siv zug arbitrarily puv rau ib co random coob kaum sab xis. Axis kuj xaiv nyob rau hauv ib qho kev ywj yam. Yuav kom piav no tshwm sim thov li pab pawg neeg (2).
• Kheej kheej. Nyob rau hauv cov ntaub ntawv no peb yuav tham txog peb qhov ntev, nyob rau hauv uas tus kwv yog rotated, xaiv arbitrary cov ces kaum. Faib cov ntaub ntawv ntawm isotropic, thaum lub phenomenon ua ib tug hauv zos peculiar puag ncig los qhov chaw.
• Muab, combining ob yav tas los piav pawg.
• Lorentz invariativnaya thaum muaj arbitrary kev sib hloov. Rau no hom ntawm symmetry ntawm tus yuam sij tswvyim yuav "Minkowski space-time."
• Super, txhais tau hais tias cov kev hloov ntawm bosons, fermions.
• Dua qhia tau thaum lub sij hawm pab pawg neeg tsom xam.
• Lub cev qhuav dej, thaum muaj cov kev hloov ntawm qhov chaw, rau cov uas zaum qhia cov kev taw qhia, ze. Nyob rau lub hauv paus ntawm cov ntaub ntawv tau mus ua ib tug sib piv tsom xam hais tias qhia symmetry.
• Calibration cai nyob rau hauv cov ntaub ntawv ntawm ib tug gauge kev tshawb xav ntawm kev ywj pheej nyob rau hauv cov coj transformations. Ntawm no, tshwj xeeb mloog yog them rau cov kev tshawb xav ntawm liaj teb, nrog rau cov kub siab rau lub Yang-Mills tswv yim.
• Ka-ees, teej tug mus rau cov chav kawm ntawv ntawm electron configurations. Uas yog xws li ib tug symmetry, lej (Qib 6) twb tsis muaj lub tswv yim, vim hais tias nws yog qhov kev kawm ntawm lub siab tshaj plaws kev txiav txim. Cov tshwm sim yog tshwm sim los ntawm ob zaus. Nws twb nrhiav tau thaum lub sij hawm cov kev tshawb fawb E. Biron. Terminology C. Shchukarev tswvcuab.

daim iav

Thaum kawm nyob rau lub tsev kawm ntawv cov menyuam kawm ntawv yuav luag ib txwm hais kom ua txoj hauj lwm "Symmetry nyob ib ncig ntawm peb" (lej project). Raws li ib tug txoj cai, nws yog pom zoo kom mus nqa tawm nyob rau hauv lub thib rau lub qib tsev kawm ntawv nrog rau cov general kev pab cuam ntawm kev qhia kawm. Yuav kom tiv nrog peb tes num, koj yuav tsum xub ua me ntsis txog cov lub tswvyim ntawm symmetry, nyob rau hauv particular, kom paub tias dab tsi yog ib daim iav hom raws li ib tug ntawm cov yooj yim thiab feem ntau cov me nyuam-phooj ywg.

Yuav kom qhia tau tias tej yam kev mob ntawm symmetry xam tau tias yog ib qho geometric zoo, thiab lub dav hlau yog xaiv. Thaum tib neeg tham txog lub symmetry ntawm qhov khoom? Ua ntej, nws yog xaiv ib tug taw tes, thiab ces yog reflected rau nws. Nruab nrab ntawm ob ntawm lawv siv ya thiab xam lub kaum sab xis ntawm uas ib tug yav tas los xaiv dav hlau uas nws kis tau.

Cais li cas yog symmetry nyob rau hauv kev kawm txog zauv, nco ntsoov tias xaiv rau lub Nov ntawm no phenomenon yuav raug xa mus rau lub dav hlau yog cov symmetry dav hlau thiab tsis muaj dab tsi lwm tus. Tuav ya yuav tsum tshuam nws ntawm txoj cai ces kaum. Qhov kev ncua deb ntawm ib tug taw tes rau qhov no dav hlau thiab los ntawm tus taw tes rau lub thib ob ya yuav tsum sib npaug zos.

nuances

Yuav ua li cas lwm tus muaj peev xwm yuav nthuav kom paub, tshuaj ntsuam lub phenomenon ntawm symmetry? Mathematics (Qib 6) qhia rau peb hais tias ob nuj nqis no yog kuas, tsis tas zoo tib yam rau txhua tus lwm yam. Lub tswvyim ntawm koob pheej ntawm lawv tshwm sim nyob rau hauv lub nqaim thiab sab kev txiav txim zoo. Yog li ntawd, symmetrical khoom nyob rau hauv lub vos - tsis yog tib yam tshaj plaws.

Yuav ua li cas yog ib qho piv txwv ntawm lub neej yuav ua rau? Elemetarny! Yuav ua li cas koj xav hais tias hais txog peb cov hnab looj tes, hnab looj tes? Peb yog tag nrho cov siv los coj lawv, thiab peb paub tias koj yuav tsis poob, vim hais tias ib tug thib ob tug nyob rau hauv lub khub yog tsis khaws, thiab ces tau mus yuav ob leeg dua. Thiab yog vim li cas? Vim hais tias cov khub khoom, txawm hais tias symmetrical, tab sis tsim los rau sab laug thiab sab tes xis. Qhov no yog - ib tug raug piv txwv ntawm daim iav symmetry. Nrog kev xav txog koob pheej ntawm lawv, xws chaw paub txog lub "daim iav-sib npaug zos."

Thiab yog dab tsi txog qhov chaw?

Xam tias yog central symmetry pib los ntawm defining lub thaj chaw ntawm lub cev, nyob rau hauv kev sib raug zoo uas nws yog tsim nyog los soj ntsuam qhov tshwm sim. Nyob rau hauv thiaj li yuav hu nws ib tug symmetrical, ib tug taw tes thawj xaiv, centrally nyob. Tom ntej no xaiv point (peb hu nws A) thiab nrhiav tus khub (conventionally denoted E) rau nws.

Nyob rau hauv kev txiav txim symmetry ntawm cov ntsiab lus A thiab E sib thooj, los ntawm ib tug ncaj kab, qhov exciting point ntawm lub hauv paus lub cev. Tom ntej no, ntsuas lub resulting kab. Yog hais tias ib tug kab ntawm taw tes A mus rau lub chaw ntawm cov kwv yog sib npaug zos rau lub luv nkauj nraug lub chaw los ntawm tus taw tes E, peb yuav hais tias qhov chaw ntawm symmetry yog pom. Lub hauv paus symmetry nyob rau hauv kev kawm txog zauv - ib qhov tseem ceeb cov ntsiab lus uas tso cai rau mus kawm tau cov kev tshawb xav ntawm geometry.

Thiab yog hais tias koj tig?

Cais li cas yog symmetry nyob rau hauv kev kawm txog zauv, ib tug yuav tsis nco cov xim ntawm lub tswvyim ntawm muab subtype ntawm no phenomenon. Nyob rau hauv thiaj li yuav to taub lub ntsiab lus, noj ib lub cev muaj ib tug central taw tes, thiab txhais tau integer.

Thaum lub sij hawm xyaum ua tej yam, lub cev yog rotated los ntawm ib tug predetermined lub sib npaug zos rau cov kev tshwm sim ntawm faib 360 degrees ntawm ib tug xaiv tus nqi. Ua li no, koj yuav tsum paub dab tsi yog qhov axis ntawm symmetry (2 chav kawm ntawv, kev ua lej, lub tsev kawm ntawv qhov kev pab cuam). Qhov no axis - lub kab txuas rau ob tug xaiv cov ntsiab lus. Nyob rau kev sib hloov symmetry yuav hais tias, yog hais tias nyob rau hauv lub xaiv lub kaum sab xis ntawm kev sib hloov ntawm lub cev yuav tsum tau nyob rau hauv tib txoj hauj lwm raws li ua ntej lub manipulations.

Nyob rau hauv lub rooj plaub uas lub ntuj tooj 2 yog xaiv, thiab sab rau tshwm sim ntawm symmetry hais tias axial symmetry yog txhais nyob rau hauv kev kawm lej. Qhov no yog cov yam ntxwv ntawm ib tug xov tooj ntawm cov nuj nqis. Ib tug raug txwv li: ib tug daim duab peb sab.

Hais txog qhov kev piv txwv ntau

Cov kev xyaum ntawm ntau xyoo ntawm kev qhia lej thiab geometry nyob rau hauv high school qhia tau hais tias qhov uas yooj yim txoj kev uas yuav to taub lub phenomenon ntawm symmetry, piav qhia txog nws nrog tej piv txwv.

Ua ntej, xav txog qhov uas duav txhua yam. Rau xws li ib lub cev nyob rau tib lub sij hawm yus muaj los ntawm lub phenomenon ntawm symmetry:

• center;
• daim iav;
• muab.

Raws li lub ntsiab taw tes yuav tsum tau xaiv, nyob raws nraim nyob rau hauv lub center daim duab. Yuav kom tuaj tos ib tug dav hlau txhais los ntawm lub voj voog loj thiab seemed yuav "txiav" nws mus rau hauv khaubncaws sab nraud povtseg. Li cas rau cov kev ua lej? Tig thiab central symmetry nyob rau hauv cov ntaub ntawv ntawm ib lub pob - tswv yim hais txog nrog lub cheeb ntawm cov nuj nqis yuav pab raws li lub axis rau lub phenomenon.

Lwm cuab piv txwv - ib tug yeej lub khob hliav qab. Rau no zoo xam qhovkev axial symmetry. Nyob rau hauv kev kawm txog zauv thiab architecture ntawm no phenomenon yog ntau theoretical thiab ua daim ntawv thov. Nco ntsoov: raws li cov axis rau lub phenomenon ntawm kev ua ntawm lub khob hliav qab axis.

Nws qha kawm phenomenon plaub. Qhov no xam yog cov yam ntxwv daim iav symmetry. Dav hlau xaiv "txiav", thaum uas tig mus rau lub hauv paus daim duab, tej thaj chaw deb ntawm lawv tu ncua. Tsim duab, piav txog, architectural tsim (lej symmetry yog ib qho tseem ceeb, tsis tsawg tshaj leej thiab piav txog sciences), kom nyob rau hauv lub siab lub tswv yim applicability thiab usefulness nyob rau hauv qhov kev npaj load-tau cov kabmob ntsiab ntawm specular los.

Thiab yog hais tias nthuav ntau daim?

Yuav ua li cas peb yuav qhia Mathematics (Qib 6)? Central symmetry tsis yog tsuas yog nyob rau hauv ib tug yooj yim thiab to taub tus kwv, zoo li ib tug zais pa. Nws yog peculiar, thiab nthuav ntau thiab complex nrhiav. Piv txwv li, qhov no yog qhov parallelogram. Rau xws li ib tug kwv yuav lub hauv paus ntawm ib tug nyob rau hauv uas hla kab pheeb ces kaum.

Tab sis yog hais tias peb xav txog lub ceskaum Trapezoid, nws yuav yog ib daim duab nrog axial symmetry. Qhia nws yuav ua tau nyob rau hauv cov ntaub ntawv uas, yog tias koj xaiv txoj cai axis. Lub cev yog symmetrical nrog rau ib tug kab perpendicular mus rau hauv av thiab dhau los ntawm nws raws nraim nyob rau hauv nruab nrab.

Symmetry nyob rau hauv kev kawm txog zauv thiab architecture yuav tsum coj mus rau hauv tus account lub pob zeb diamond. Qhov no xam yog zoo tshaj plaws uas ib txhij combines ob hom ntawm symmetry:

• centerline;
• central.

Raws li cov axis ntawm lub kab pheeb ces kaum yuav tsum xaiv tus kwv. Thaum lub point qhov twg lub diagonals ntawm ib tug rhombus tshuam, nws yog ib qhov chaw zoo ib yam.

Hais txog kev zoo nkauj thiab symmetry

Txoj kev ua ib lej project, lub symmetry uas yuav ua tau ib tug tseem ceeb lub npe, feem ntau yog nyob rau hauv thawj qhov chaw nco ntsoov cov neeg txawj ntse lus ntawm tus poj tus paub txog Weil: "Symmetry - ib lub tswv yim uas rau centuries ua kom to taub cov txiv neej, vim hais tias nws yog nws leej twg tsim tau ib tug zoo meej kev zoo nkauj los ntawm ib tug tshwj xeeb kev txiav txim."

Raws li koj paub, lwm yam zoo li yuav zoo nkauj tshaj plaws, thaum lwm tus neeg thawb deb, txawm yog hais tias lawv tsis muaj cuab flaws. Yog vim li cas yog no mas? Lo lus teb rau lo lus nug no qhia tau hais tias cov kev sib raug zoo ntawm architecture thiab lej nyob rau hauv symmetry, vim hais tias nws yog ib qhov tshwm sim thiab ua lub hauv paus rau kev soj ntsuam ntawm cov kev kawm raws li aesthetically txaus nyiam.

Ib qho ntawm feem poj niam zoo nkauj nyob rau hauv lub ntiaj chaw - nws yog ib qhov supermodel txhuam Tarlikton. Nws yog tseeb tias kev vam meej tau tuaj nyob rau hauv thawj qhov chaw ua tsaug rau ib tug tshwj xeeb tshwm sim: nws daim di ncauj yog symmetrical.

Raws li yog lub npe hu, qhov xwm thiab nyhav symmetry, thiab muaj peev xwm tsis cuag nws. Nws tsis yog cov general txoj cai, tab sis saib cov neeg nyob ib ncig ntawm lawv: nyob rau hauv tib neeg cov ntsej muag yuav luag nrhiav tsis tau lub meej symmetry, txawm hais tias nws yog ib qhov tseeb lub siab xav rau nws. Qhov ntau symmetrical lub ntsej muag ntawm lub interlocutor, li ntawd, nws zoo zoo.

Yuav ua li cas yog lub tswv yim ntawm symmetry ntawm qhov zoo nkauj

Nws yog li ntawd nyob rau hauv lub teeb ntawm tus tib neeg xaav ntawm kev zoo nkauj raws li nws ncig thiab cov khoom nyob rau hauv nws. Rau ntau centuries, cov neeg yuav to taub li cas rau nkawd zoo meej, thiab hais tias pushes impartially.

Lub symmetry, proportions - tias yog dab tsi yuav pab tau visually perceive ib tug kwv thiab ntsuam xyuas nws zoo. Tag nrho cov ntsiab, qhov yuav tsum tau balanced thiab nyob rau hauv lub tsim nyog proportions nrog txhua lwm yam. Nws tau ntev tau pom hais tias asymmetric khoom zoo li cov neeg tsawg npaum li cas. Tag nrho cov no yog txuas nrog rau lub tswvyim ntawm "kev sib raug zoo". Hais txog yog vim li cas nws yog li ntawd ib qho tseem ceeb rau ib tug neeg uas ancient ntev puzzled sages, ntxias.

Nws yuav tsum saib cov duab cov nuj nqis, thiab tus phenomenon ntawm symmetry yuav cuab kev thiab yooj yim rau to taub. Qhov tseem raug symmetrical phenomena nyob rau hauv cov cheeb tsam surrounding:

• pob zeb;
• paj thiab nplooj ntawm cov nroj tsuag;
• paired txheej nruab nrog cev xam qhovkev nyob rau hauv uas muaj sia nyob.

Lub piav phenomena yog qhov uas qhov. Thiab ntawm no yog dab tsi koj yuav saib tau yam, nrhiav los ze zog mus rau lub khoom ntawm tib neeg txhais tes? Nws yog hnov hais tias cov neeg gravitate mus rau lub creation ntawm ib tug yog sim ua kom ib yam dab tsi zoo nkauj los yog tej qhov (los yog ob qho tib si, thiab yog nyob rau tib lub sij hawm):

• cov qauv thiab ornaments, nrov txij ancient sij hawm;
• tsev hais;
• siv cov ntsiab yog;
• needlework.

Hais txog terminology

"Symmetry" - lo lus tuaj mus rau hauv peb cov lus los ntawm cov ancient Greeks uas thawj ntaub ntawv rau qhov no phenomenon xim thiab sim mus tshawb nws. Lub sij hawm qhia lub xub ntiag ntawm ib tug system thiab harmonious ua ke ntawm qhov chaw ntawm tus kwv. Neeg txhais lus ntawm cov lo lus "symmetry", koj yuav tau khaws txhais:

• proportionality;
• sameness;
• proportionality.

Txij ancient sij hawm lub symmetry yog ib qho tseem ceeb tswvyim rau txoj kev loj hlob ntawm noob neej nyob rau hauv ntau yam teb thiab industries. Haiv neeg los ntawm antiquity rau muaj ib qho kev nkag siab ntawm no tshwm sim, mas xav tias yuav nws broadly. Symmetry sawv rau kev sib raug zoo thiab tshuav nyiaj li cas. Nyob rau hauv peb lub sij hawm, lub terminology yog qhia nyob rau hauv zoo tib yam tsev kawm ntawv. Piv txwv li, dab tsi yog qhov axis ntawm symmetry (2 chav kawm ntawv kev kawm txog zauv) me nyuam tus kws qhia ntawv hais lus rau cov pa hauv chav kawm ntawv.

Raws li lub tswv yim ntawm no phenomenon yog feem ntau pib lo lus cog tseg ntawm kev hypotheses thiab theories. Tshwj xeeb tshaj yog nrov nyob rau hauv lub yav dhau los xyoo pua, thaum tag nrho cov thoob lub ntiaj teb yeej lub tswv yim ntawm kev kawm txog lej sib raug zoo xam qhovkev nyob rau hauv lub heev system ntawm lub ntug. Connoisseurs ntawm cov sij hawm tau convinced tias symmetry yog ib tug manifestation ntawm Vajtswv txoj kev sib raug zoo. Tab sis nyob rau hauv ancient Greece, philosophers tau thov hais tias lub ntug tag nrho symmetrical, thiab nws tag nrho raws li nyob rau hauv lub postulate: "Lub symmetry yog zoo meej."

Great Greeks thiab symmetry

Symmetry raug rho tawm haujlwm hauv lub hlwb ntawm lub nto moo tshaj plaws kws tshawb fawb ntawm ancient Greece. Yuav kom dim yog cov pov thawj uas Plato hu ua cais admired kev polyhedra. Nyob rau hauv nws lub tswv yim, xws nuj nqis - ib tug personification ntawm lub ntsiab ntawm peb lub ntiaj teb no. Muaj cov nram qab no kev faib:

caij	daim duab
hluav taws kub	Tetrahedron, raws li cov pinnacle ntawm nws aims Skyward.
dej	Icosahedron. Xaiv yog vim "katuchestyu" daim duab.
huab cua	Octahedron.
lub ntiaj teb	Qhov tseem ruaj khov kwv, uas yog lub thawv muaj rau sab.
ntug	Dodecahedron.

Lom zem ntau vim hais tias ntawm no ziag no yog feem ntau hu ua kev polyhedra Platonic cov khib nyiab.

Tab sis lub terminology nkag ua ntej lawm, thiab tsis muaj ib lub xeem lub luag hauj lwm ua si los ntawm lub sculptor Polycleitus.

Pythagoras thiab symmetry

Thaum lub sij hawm lub neej ntawm Pythagoras thiab tom qab ntawd, thaum nws qhia tau muaj nws heyday, lub phenomenon ntawm symmetry ua tsis tau tejyam rau qhov teeb meem tseeb. Nws twb ces raug kev tsom xam ntawm lub teeb, uas tau muab tseem ceeb mus rau lub tswv yim daim ntawv thov ntawm cov kev tshwm sim.

Raws li cov lus xaus:

• Symmetry yog raws li nyob rau hauv lub tswv yim ntawm kev faib ua feem, uniformity thiab koob pheej ntawm lawv. Nyob rau hauv cov ntaub ntawv ntawm kev ua txhaum cai ntawm ib lub tswvyim yuav tsawg symmetrical daim duab, maj mam tsiv mus rau lub siab asymmetric.
• Muaj 10 officers ntawm tawm tsam. Raws li cov lus qhuab qhia, lub symmetry yog ib tug tshwm sim uas thiaj li nyob rau hauv lub rov qab niaj hnub thiab yog li txoj kev ua ntug raws li ib tug tag nrho. Qhov no postulate rau centuries tau ib tug muaj zog cawv rau ib tug xov tooj ntawm cov caij nyoog sciences raws li philosophy, raws li zoo li tej yam ntuj tso.

Pythagoras thiab nws cov thwjtim tau cais "kiag li symmetrical lub cev," uas ranked li txaus siab qhov tej yam kev mob:

• txhua lub ntsej muag - polygon;
• seb pom nyob rau hauv lub ces kaum;
• daim duab yuav tsum tau muaj sib npaug zos sab thiab cov ces kaum.

Nws yog Pythagoras thawj hais tias cov neeg lub cev muaj tsuas yog tsib. Qhov no yog ib tug zoo kawg foundations cim pib ntawm geometry thiab yog qhov tseem ceeb rau niaj hnub architecture.

Thiab koj xav mus ua tim khawv rau hauv lub zoo nkauj tshaj plaws tshwm sim ntawm symmetry? Catch ib Paj daus caij ntuj no. Coj txawv txawv, tiam sis yeej muaj tseeb - nws yog ib tug me me daim ntawm cov dej khov ntog saum ntuj yog tsis tsuas tsis tshua muaj neeg complex siv lead ua qauv, tab sis kuj zoo kawg nkaus symmetrical. Xav txog nws kom zoo zoo: Paj daus yog tiag tiag zoo nkauj, thiab nws cov sophisticated kab fascinate.