Ntau yam nthuav dav tuaj yeem pom rau koj tus kheej hauv cov cheeb tsam ntawm kev tshawb fawb uas, zoo li, yuav tsis muaj txiaj ntsig zoo hauv lub neej niaj hnub ntawm ib tus neeg yooj yim. Piv txwv li, geometry, uas feem ntau cov neeg tsis nco qab txog sai li sai tau thaum lawv hla lub tsev kawm ntawv. Tab sis nyob rau hauv ib txoj kev coj txawv txawv, thaj chaw tsis paub ntawm kev tshawb fawb ua rau zoo siab heev thaum koj ntsib lawv los ze zog. Yog li kev txhim kho geometric ntawm polyhedron - ib yam uas tsis tsim nyog hauv lub neej txhua hnub - tuaj yeem yog qhov pib ntawm kev muaj tswv yim zoo siab uas tuaj yeem ntes ob tus menyuam yaus thiab cov neeg laus.
Zoo nkauj geometry
Kho kom zoo nkauj sab hauv tsev, tsim cov khoom txawv txawv, stylish nrog koj tus kheej tes, yog ib qho kev kos duab ntxim nyiam. Ua ntau yam polyhedrons koj tus kheej los ntawm cov ntawv tuab txhais tau hais tias tsim cov khoom tshwj xeeb uas tuaj yeem dhau los ua haujlwm rau ib hnub lossis ob hnub, lossis tuaj yeem tig mus rau hauv kev tsim kho vaj tsev sab hauv. Tsis tas li ntawd, nrog rau kev txhim kho cov cuab yeej muaj peev xwm ntawm spatial qauv ntawm txhua yam, nws tau dhau los ua qauv 3D stylish thiab niaj hnub. Muaj cov tswv uassiv kev tsim kho ntawm cheb raws li txoj cai ntawm geometry, cov qauv ntawm cov tsiaj thiab ntau yam khoom yog ua los ntawm cov ntawv. Tab sis qhov no yog ib qho nyuaj ua lej thiab kos duab. Txhawm rau pib ua haujlwm hauv cov txheej txheem zoo sib xws, kev txhim kho ntawm polyhedron yuav pab tau.
Different faces - txawv cov duab
Polyhedra yog thaj chaw tshwj xeeb ntawm geometry. Lawv yog cov yooj yim - piv txwv li, blocks uas cov menyuam yaus ua si los ntawm lub hnub nyoog thaum ntxov - thiab muaj ntau heev, nyuaj heev. Kev tsim lub cheb ntawm polyhedra rau gluing yog suav hais tias yog ib qho nyuaj heev ntawm kev tsim thiab kev muaj tswv yim: koj yuav tsum tsis tsuas yog kom paub cov hauv paus ntawm kev kos duab, geometric nta ntawm qhov chaw, tab sis kuj yuav tsum muaj lub tswv yim spatial uas tso cai rau koj los soj ntsuam cov duab. qhov tseeb ntawm qhov kev daws teeb meem ntawm theem tsim. Tab sis fantasy ib leeg tsis txaus. Txhawm rau ua scans ntawm polyhedra tawm ntawm daim ntawv, nws tsis txaus tsuas yog xav txog yuav ua li cas cov haujlwm yuav tsum saib thaum kawg. Koj yuav tsum muaj peev xwm xam nws kom raug, tsim nws, thiab kos kom raug.
thawj polyhedron yog lub voos xwmfab
Feem ntau, txhua tus neeg uas tau mus kawm ntawv, txawm tias nyob rau qib pib, tau ntsib kev ua haujlwm hauv kev ua haujlwm, qhov tshwm sim ntawm qhov yuav tsum yog daim ntawv lub voos xwmfab. Feem ntau, tus kws qhia ntawv tau muab qhov khoob - kev txhim kho ntawm lub voos xwmfab polyhedron ntawm cov ntawv tuab nrog cov hnab ris tshwj xeeb tsim los ua kom lub ntsej muag ntawm tus qauv rau hauv ib qho tag nrho. Cov tub ntxhais kawm theem pib tuaj yeem txaus siab rau txoj haujlwm no, vim tias nrog kev pab ntawmdaim ntawv, txiab, kua nplaum thiab lawv cov kev siv zog tig los ua ib qho khoom siv tes ua - lub voos xwmfab peb sab.
Tshwj xeeb, ntau yam kev paub txog lub ntiaj teb nyob ib puag ncig peb tau nthuav tawm tsis yog hauv tsev kawm ntawv, tab sis tsuas yog thaum koj tuaj yeem pom qee yam ntxim nyiam hauv nws uas tuaj yeem muab qee yam tshiab, txawv txawv hauv lub neej niaj hnub. Tsis muaj coob tus neeg laus nco ntsoov tias tib lub polyhedra tau muab faib ua ntau hom thiab subspecies. Piv txwv li, muaj cov khoom hu ua Platonic solids - convex polyhedra, tsuas yog muaj cov polygons tsis tu ncua. Tsuas muaj tsib lub cev: tetrahedron, octahedron, hexahedron (lub voos xwmfab), icosahedron, dodecahedron. Lawv yog cov duab convex tsis muaj kev nyuaj siab. Lub hnub qub polyhedra yog tsim los ntawm cov duab yooj yim no hauv ntau qhov kev teeb tsa. Tias yog vim li cas txoj kev loj hlob ntawm ib qho yooj yim polyhedron tso cai rau koj los kos, los yog kos, thiab tom qab ntawd nplaum lub hnub qub polyhedron tawm ntawm daim ntawv.
Ntau thiab tsis xwm yeem lub hnub qub polyhedra
Los ntawm folding Platonic cov khib nyiab ua ke hauv ib qho kev txiav txim, koj tuaj yeem tsim tau ntau lub stellate polyhedrons - zoo nkauj, complex, multicomponent. Tab sis lawv yuav raug hu ua "irregular stellated polyhedra". Muaj tsuas yog plaub lub hnub qub polyhedra: lub me stellate dodecahedron, lub zoo stellate dodecahedron, tus yawm dodecahedron, thiab zoo icosahedron. Polyhedral nets rau gluing yuav tsis yooj yim kos duab. Lawv, zoo li cov duab, yuav muajlos ntawm ntau yam. Yog li, piv txwv li, me me dodecahedron yog tsim los ntawm 12 pentagonal isosceles pyramids, folded zoo li ib txwm dodecahedron. Ntawd yog, pib nrog, koj yuav tsum tau kos thiab nplaum 12 daim zoo tib yam ntawm cov pyramids li niaj zaus, suav nrog 5 lub ntsej muag sib npaug. Thiab tsuas yog tom qab ntawd tuaj yeem tsim lub hnub qub zoo li polyhedron los ntawm lawv. Reaming lub hnub qub me tshaj plaws zoo li dodecaer yog ib txoj haujlwm nyuaj thiab yuav luag ua tsis tau. Txhawm rau tsim nws, koj yuav tsum muaj peev xwm ua kom haum rau tib lub dav hlau 13 qhov ntsuas ntawm qhov sib txawv geometric volumetric lub cev txuas rau ib leeg.
Kev zoo nkauj nyob hauv qhov yooj yim
Txhua lub cev ntim tau ua raws li cov cai ntawm geometry yuav zoo li ntxim nyiam, suav nrog lub hnub qub zoo li polyhedron. Txoj kev loj hlob ntawm txhua lub ntsiab ntawm ib lub cev zoo li no yuav tsum tau ua kom raug raws li qhov ua tau. Thiab txawm tias qhov yooj yim tshaj plaws volumetric polyhedra, pib nrog Platonic tetrahedron, yog qhov zoo nkauj zoo nkauj ntawm kev sib haum xeeb ntawm lub ntiaj teb thiab tib neeg kev ua haujlwm embodied hauv daim ntawv qauv. Ntawm no, piv txwv li, ntau yam ntawm Platonic convex polyhedra yog dodecahedron. Daim duab geometric no muaj 12 lub ntsej muag zoo ib yam, 30 npoo thiab 12 vertices. Yuav kom nthuav tawm cov polyhedra tsis tu ncua rau gluing, koj yuav tsum tau siv qhov tseeb tshaj plaws thiab kev saib xyuas. Thiab qhov loj dua daim duab hauv qhov loj, qhov tseeb dua txhua qhov kev ntsuas yuav tsum yog.
Yuav ua li cas cheb koj tus kheej?
Tej zaum, ntxiv rau gluing polyhedron - tsawg kawg lub hnub qub zoo li, tsawg kawgPlatonic, nws yog qhov nthuav ntau dua los tsim kev txhim kho ntawm tus qauv yav tom ntej ntawm koj tus kheej, ntsuas koj lub peev xwm rau kev kos duab, tsim qauv thiab spatial kev xav. Tej yam yooj yim Platonic solids muaj cov polygons yooj yim, uas zoo ib yam rau ib leeg hauv ib daim duab. Yog li, tetrahedron yog peb daim duab peb sab isosceles. Ua ntej tsim ib lub cheb, koj yuav tsum xav txog yuav ua li cas kom folds tiaj tus polygons ua ke kom tau ib lub polyhedron. Daim duab peb sab tuaj yeem txuas rau ib leeg raws cov npoo los ntawm kos ib sab ntawm ib sab. Txhawm rau txhawm rau txhim kho polyhedrons, cov tswv yim yuav tsum tau nruab nrog cov hnab ris tshwj xeeb lossis cov li qub uas yuav tso cai rau koj txuas txhua qhov chaw rau hauv ib qho tag nrho. Lub tetrahedron yog qhov yooj yim tshaj plaws nrog plaub lub ntsej muag. Ib qho octahedron tuaj yeem sawv cev ua ob lub tetrahedron, nws muaj yim garni - isosceles daim duab peb sab. Lub hexahedron yog lub voos xwmfab uas paub txhua tus neeg txij thaum yau. Ib qho icosahedron yog qhov sib xyaw ntawm 20 isosceles daim duab peb sab rau hauv ib qho convex polyhedron. Ib tug dodecahedron yog ib daim duab peb sab ntawm 12 lub ntsej muag, txhua tus uas yog ib txwm pentagon.
Subtleties ntawm kev ua haujlwm
Tsim ib lub vas ntawm polyhedron thiab gluing ib daim ntawv qauv tawm ntawm nws yog ib qho teeb meem. Lub scan, ntawm chav kawm, tuaj yeem nqa tau npaj lawm. Thiab koj tuaj yeem, nrog qee qhov kev siv zog, tsim nws tus kheej. Tab sis txhawm rau ua kom tiav peb-dimensional qauv ntawm polyhedron, koj yuav tsum tau sib sau ua ke. Lub polyhedron yog qhov zoo tshaj plaws ua los ntawm cov ntawv tuab, uas tuav nws cov duab zoo thiab tsis warp los ntawm cov kua nplaum. Tag nrho cov kab ntawdyuav tsum tau khoov, nws yog qhov zoo tshaj rau pre-punch, siv, piv txwv li, ib tug tsis-sau ntawv ballpoint cwj mem los yog tom qab ntawm ib tug riam hniav. Qhov nuance no yuav pab txhawm rau quav tus qauv kom raug, hwm qhov ntev thiab cov lus qhia ntawm cov npoo.
Yog tias koj ua cov polyhedrons sib txawv los ntawm cov ntawv xim, ces cov qauv zoo li no tuaj yeem siv los ua cov khoom dai kom zoo nkauj hauv chav - me nyuam chav, chav ua haujlwm, chav nyob. Los ntawm txoj kev, polyhedra tuaj yeem raug hu ua qhov kev pom tshwj xeeb ntawm cov khoom dai. Cov ntaub ntawv niaj hnub tso cai tsim cov khoom qub sab hauv raws li cov duab geometric.
