Dab tsi yog qhov axis ntawm symmetry? Qhov no yog ib txheej ntawm cov ntsiab lus uas tsim ib txoj kab ncaj nraim, uas yog lub hauv paus ntawm symmetry, uas yog, yog tias ib qho kev ncua deb tau muab tso tseg los ntawm txoj kab ncaj nraim ntawm ib sab, ces nws yuav cuam tshuam rau lwm qhov kev taw qhia hauv tib qhov loj.. Txhua yam tuaj yeem ua raws li axis - taw tes, kab, dav hlau, thiab lwm yam. Tab sis nws yog qhov zoo dua los tham txog qhov no nrog cov piv txwv.
Symmetry
Yuav kom nkag siab tias lub axis ntawm symmetry yog dab tsi, koj yuav tsum delve rau hauv lub ntsiab txhais ntawm symmetry. Qhov no yog qhov kev sib txuas lus ntawm qee qhov tawg ntawm lub cev nrog kev hwm rau txhua qhov axis, thaum nws cov qauv tsis hloov pauv, thiab cov khoom thiab cov duab ntawm cov khoom no tseem zoo ib yam nrog kev hwm rau nws cov kev hloov pauv. Peb tuaj yeem hais tias symmetry yog cov cuab yeej ntawm lub cev los tso saib. Thaum ib qho tsis tuaj yeem muaj qhov sib tw, nws hu ua asymmetry lossis arrhythmia.
Qee cov duab tsis muaj symmetry, yog vim li cas lawv thiaj li hu ua irregular lossis asymmetric. Cov no suav nrog ntau yam trapezoids (tshwj tsis yog isosceles), daim duab peb sab (tshwj tsis yog isosceles thiab sib npaug) thiab lwm yam.
Nyob ntawm symmetry
Peb kuj tseem yuav tham txog qee yam kev sib raug zoo txhawm rau txhawm rau tshawb xyuas lub ntsiab lus no. Lawv muab faib li no:
- Axial. Lub axis ntawm symmetry yog ib txoj kab ncaj nraim los ntawm qhov nruab nrab ntawm lub cev. Zoo li no? Yog hais tias koj impose qhov chaw nyob ib ncig ntawm lub axis ntawm symmetry, ces lawv yuav sib npaug. Qhov no tuaj yeem pom hauv qhov piv txwv ntawm tus kheej.
- Daim iav. Lub axis ntawm symmetry ntawm no yog ib txoj kab ncaj nraim, tus txheeb ze uas lub cev tuaj yeem cuam tshuam thiab nthuav tawm. Piv txwv li, npauj npaim tis yog daim iav-symmetrical.
- Central. Lub axis ntawm symmetry yog lub ntsiab lus nyob rau hauv nruab nrab ntawm lub cev, piv txwv li, nyob rau hauv tag nrho cov transformations, qhov chaw ntawm lub cev yog sib npaug zos thaum superimposed.
History of symmetry
Lub tswvyim ntawm symmetry feem ntau yog qhov pib ntawm qhov kev xav thiab kev xav ntawm cov kws tshawb fawb thaum ub uas tau ntseeg hauv kev ua lej sib haum xeeb ntawm lub qab ntuj khwb, nrog rau kev tshwm sim ntawm Vajtswv txoj ntsiab cai. Cov Greeks thaum ub tau ntseeg ruaj khov tias lub qab ntuj khwb yog symmetrical, vim hais tias symmetry yog qhov zoo kawg li. Tus txiv neej tau ntev siv lub tswv yim ntawm kev sib haum xeeb hauv nws txoj kev paub txog daim duab ntawm lub ntiaj teb.
Nyob rau xyoo pua 5 BC, Pythagoras suav hais tias tus kheej kheej yog daim ntawv zoo tshaj plaws thiab xav tias lub ntiaj teb muaj cov duab puab thiab txav mus rau tib txoj kev. Nws kuj ntseeg tias lub ntiaj teb txav mus rau hauv daim ntawv ntawm qee yam "qhov hluav taws kub nruab nrab", uas nyob ib ncig ntawm 6 lub ntiaj teb (paub thaum lub sijhawm ntawd), Lub hli, Lub Hnub thiab tag nrho lwm cov hnub qub yuav tsum tau tig mus.
Thiab tus kws tshawb fawb Plato suav tias yog polyhedrons ua tus neeg ntawm plaub lub ntsiab lus:
- tetrahedron yog hluav taws, raws li nws sab saum tojtaw tes;
- cube - ntiaj teb, raws li nws yog lub cev ruaj khov tshaj;
- octahedron - huab cua, tsis muaj lus piav qhia;
- icosahedron - dej, vim lub cev tsis muaj cov duab geometric ntxhib, lub kaum sab xis, thiab lwm yam;
- daim duab ntawm tag nrho lub qab ntuj khwb yog lub dodecahedron.
Vim tag nrho cov kev xav no, cov polyhedra tsis tu ncua hu ua Platonic solids.
Symmetry tau siv los ntawm cov kws tsim vaj tsev ntawm Ancient Greece. Tag nrho lawv lub tsev tau sib luag, raws li pom los ntawm cov duab ntawm lub tuam tsev qub ntawm Zeus ntawm Olympia.
Tus kws kos duab Dutch MC Escher kuj tau siv symmetry hauv nws cov duab. Tshwj xeeb, mosaic ntawm ob tug noog ya mus los ua lub hauv paus ntawm daim duab "Hnub thiab Hmo Ntuj".
Tsis tas li ntawd, peb cov neeg thuam kev kos duab tsis tau tso tseg txoj cai ntawm kev sib haum xeeb, raws li tuaj yeem pom hauv cov piv txwv ntawm cov duab los ntawm Vasnetsov V. M. "Heroes".
Kuv tuaj yeem hais li cas, symmetry yog lub ntsiab lus tseem ceeb rau txhua tus neeg ua yeeb yam rau ntau pua xyoo, tab sis nyob rau xyoo pua 20th nws lub ntsiab lus kuj tau txais txiaj ntsig los ntawm tag nrho cov duab ntawm cov kev tshawb fawb tseeb. Cov pov thawj tseeb yog lub cev thiab cosmological theories, piv txwv li, txoj kev xav ntawm kev sib raug zoo, txoj hlua txoj hlua, txhua yam ntawm quantum mechanics. Los ntawm lub sijhawm ntawm Ancient Babylon thiab xaus nrog kev tshawb pom ntawm cov kev tshawb fawb niaj hnub no, txoj hauv kev ntawm kev kawm symmetry thiab nrhiav pom nws cov cai yooj yim tuaj yeem taug qab.
Symmetry ntawm cov duab geometric thiab lub cev
Cia peb saib ze dua ntawm lub cev geometric. Piv txwv li, lub axis ntawm symmetry ntawm ib tug parabola yog ib txoj kab ncaj nraim hla nws vertex thiab txiav los ntawm lub cev muab.hauv ib nrab. Daim duab no muaj ib axis.
Tab sis nrog cov duab geometric, qhov xwm txheej txawv. Lub axis ntawm symmetry ntawm lub duab plaub kuj ncaj, tab sis muaj ob peb ntawm lawv. Koj tuaj yeem kos ib qho axis mus rau qhov dav ntu, lossis koj tuaj yeem kos qhov ntev. Tab sis tsis yog txhua yam yooj yim heev. Ntawm no cov kab tsis muaj axes ntawm symmetry, vim nws qhov kawg tsis tau txhais. Tsuas yog lub hauv paus symmetry tuaj yeem tshwm sim, tab sis, raws li, yuav tsis muaj ib qho.
Koj yuav tsum paub tias qee lub cev muaj ntau lub axes ntawm symmetry. Qhov no yog qhov yooj yim los twv. Koj tsis tas yuav tham txog ntau npaum li cas axes ntawm symmetry ib lub voj voog muaj. Ib txoj kab dhau los ntawm qhov nruab nrab ntawm lub voj voog yog qhov zoo li no, thiab muaj ntau tus lej ntawm cov kab no.
Qee lub quadrilaterals tuaj yeem muaj ob lub axes ntawm symmetry. Tab sis qhov thib ob yuav tsum yog perpendicular. Qhov no tshwm sim nyob rau hauv rooj plaub ntawm lub rhombus thiab lub duab plaub. Nyob rau hauv thawj axis ntawm symmetry - lub diagonals, thiab nyob rau hauv lub thib ob - cov kab nruab nrab. Cov txheej ntawm cov axes no tsuas yog rau square.
Symmetry hauv xwm
Xwm amazes nrog ntau yam piv txwv ntawm symmetry. Txawm peb tib neeg lub cev yog symmetrical. Ob lub qhov muag, ob lub pob ntseg, qhov ntswg thiab qhov ncauj yog nyob symmetrically txog lub hauv paus axis ntawm lub ntsej muag. Caj npab, ceg thiab tag nrho lub cev feem ntau yog teem symmetrically rau lub axis hla nruab nrab ntawm peb lub cev.
Thiab pes tsawg tus piv txwv nyob ib puag ncig peb txhua lub sijhawm! Cov no yog paj, nplooj, paj, zaub thiab txiv hmab txiv ntoo, tsiaj thiab txawm honeycombs ntawm muv muaj ib tug pronounced geometric duab thiab symmetry. Txhua yamteem caij kom zoo, txhua yam muaj nws qhov chaw, uas ib zaug lees paub qhov zoo tshaj plaws ntawm cov kev cai ntawm xwm, nyob rau hauv uas symmetry yog lub ntsiab mob.
Zoo kawg
Peb nyob ib puag ncig los ntawm qee qhov tshwm sim thiab cov khoom, xws li zaj sawv, poob, paj, paj, thiab lwm yam. Lawv symmetry yog pom tseeb, rau qee qhov nws yog vim lub ntiajteb txawj nqus. Feem ntau nyob rau hauv qhov xwm txheej, lub tswv yim ntawm "symmetry" yog to taub raws li kev hloov tsis tu ncua ntawm nruab hnub thiab hmo ntuj, caij, thiab lwm yam.
Cov khoom zoo sib xws raug pom nyob qhov twg muaj kev txiav txim thiab kev sib npaug. Tsis tas li ntawd, cov kev cai ntawm cov xwm txheej - astronomical, tshuaj, lom thiab txawm noob caj noob ces - yog nyob rau hauv tej lub hauv paus ntsiab lus ntawm symmetry, raws li lawv muaj ib tug zoo meej system, uas txhais tau hais tias qhov nyiaj tshuav muaj ib tug tag nrho-encompassing scale. Yog li ntawd, axial symmetry yog ib qho ntawm cov kev cai tseem ceeb ntawm lub ntiaj teb tag nrho.
