Yuav ua li cas ua ib lub polyhedron tawm ntawm daim ntawv. Daim ntawv polyhedra - schemes

2024 Tus sau: Sierra Becker | [email protected]. Kawg hloov kho: 2024-02-26 05:10

paper crafts tsis tsuas yog ntau yam ntawv tshaj tawm thiab daim ntawv thov ua nyob rau hauv daim ntawv ntawm cov khoom tiaj tus. Volumetric qauv ntawm cov duab yog heev qub (duab 1). Piv txwv li, koj tuaj yeem tsim ib lub polyhedron tawm ntawm daim ntawv. Cia peb saib qee txoj hauv kev ua nws siv cov duab kos thiab duab.

History of figures

Ancient lej science muaj nws cov hauv paus hniav nyob rau yav dhau los, thaum lub sij hawm txoj kev vam meej ntawm Ancient Rome thiab tim Nkij teb chaws. Tom qab ntawd nws yog ib qho kev cai rau kev koom tes nrog kev xav nrog cov tswv yim. Yog li ntawd, raws li cov lus qhia ntawm Plato (ib qho ntawm cov neeg Greek thaum ub xav), txhua tus ntawm polyhedra, muaj qee tus lej ntawm cov dav hlau zoo ib yam, cim ib lub caij. Cov duab los ntawm daim duab peb sab - octahedron, icosahedron thiab tetrahedron - yog txuam nrog huab cua, dej thiab hluav taws, feem, thiab tuaj yeem hloov mus rau ib leeg vim tib hom ntsej muag, txhua tus uas muaj peb lub vertices. Lub ntiaj teb yog cim los ntawm hexahedron ntawm squares. Thiab lub dodecahedron, ua tsaug rau lub ntsej muag pentagonal tshwj xeeb, ua lub luag haujlwm zoo nkauj thiab yog tus qauv ntawm kev sib haum xeeb thiab kev thaj yeeb.

Nws tseem paub tias yog ib tus kws ua lej Greek, Euclid, tau ua pov thawj hauv nws cov lus qhuab qhia ntawm "Pib pib" qhov tshwj xeeb ntawm Platonic cov khib nyiab thiab lawv cov khoom kom "haum" rau hauv qhov chaw (duab 2). Lub polyhedron pom los ntawm daim ntawv yog tsim los ntawm folding nees nkaum isosceles daim duab peb sab kaw ua ke. Daim duab qhia meej meej ua qauv rau kev ua ib daim duab. Cia peb saib ze dua ntawm txhua theem ntawm kev tsim ib qho icosahedron.

Ua nees nees

Lub icosahedron muaj qhov sib npaug ntawm daim duab peb sab isosceles. Nws tuaj yeem yooj yim folded siv lub unfolding qhia hauv daim duab 2. Nqa ib daim duab plaub. Kos rau nws nees nkaum daim duab peb sab ntawm tib qhov loj thiab cov duab, muab tso rau hauv plaub kab. Hauv qhov no, txhua lub ntsej muag ntawm ib lub sijhawm yuav yog ib sab ntawm lwm tus. Siv cov qauv tsim los ua ib qho khoob. Nws yuav txawv ntawm lub hauv paus-scan los ntawm qhov muaj cov nyiaj pub dawb rau gluing raws tag nrho cov kab sab nraud. Tom qab txiav ib qho khoob ntawm daim ntawv, khoov nws raws kab. Ua ib lub polyhedron los ntawm daim ntawv, kaw cov kab huab nrog ib leeg. Hauv qhov no, qhov vertices ntawm daim duab peb sab yuav txuas rau ib qho taw tes.

Regular polyhedra

Tag nrho cov duab txawv ntawm ib leeg los ntawm ntau lub ntsej muag thiab lawv cov duab. Tsis tas li ntawd, qee cov qauv tuaj yeem tsim los ntawm ib daim ntawv (raws li tau piav qhia hauv qhov piv txwv ntawm kev ua icosahedron), lwm tus tuaj yeem sib sau ua ke los ntawm ntau lub modules. Tsis tu ncua polyhedra yog suav tias yog classical. Lawv yog tsim los ntawm daim ntawv, adhering rauTxoj cai tseem ceeb ntawm symmetry yog qhov muaj lub ntsej muag zoo tib yam hauv cov qauv. Muaj tsib yam tseem ceeb ntawm cov duab zoo li no. Lub rooj muaj cov ntaub ntawv hais txog lawv lub npe, tus lej thiab cov duab ntawm lub ntsej muag:

Npe	Ntau lub ntsej muag	Suab ntawm txhua lub ntsej muag
tetrahedron	4	peb
hexahedron	6	square
octahedron	8	peb
dodecahedron	12	pentagon
Ikosahedron Y	20	peb

Ntau yam duab

Raws li tsib yam uas tau muab, siv kev txawj ntse thiab kev xav, cov kws ua haujlwm tau yooj yim tsim ntau hom ntawv sib txawv. Lub polyhedron tuaj yeem sib txawv kiag li ntawm tsib daim duab tau piav qhia saum toj no, tau tsim ib txhij los ntawm lub ntsej muag ntawm cov duab sib txawv, piv txwv li, los ntawm squares thiab triangles. Qhov no yog li cas Archimedean solids tau txais. Thiab yog tias koj hla ib lossis ntau lub ntsej muag, koj tau txais daim duab qhib, saib ob qho tib si sab nraud thiab sab hauv. Rau kev tsim cov qauv peb-seem, cov qauv tshwj xeeb yog siv, txiav tawm ntawm cov ntawv tuab tuab, zoo-zoo li daim ntawv. Lawv kuj ua tshwj xeeb polyhedrons los ntawm ntawv. Schemes ntawm xws li cov khoom muablub xub ntiag ntawm ntxiv, protruding modules. Wb saib txoj hauv kev los tsim ib daim duab zoo nkauj heev uas siv dodecahedron ua piv txwv (duab 3).

Yuav ua li cas ua ib lub polyhedron nrog kaum ob vertices tawm ntawm daim ntawv: thawj txoj kev

Cov duab zoo li no tseem hu ua stellate dodecahedron. Txhua qhov ntawm nws cov vertices yog lub pentagon tsis tu ncua ntawm nws lub hauv paus. Yog li ntawd, xws li ntawv polyhedra yog ua nyob rau hauv ob txoj kev. Cov txheej txheem rau kev tsim khoom yuav txawv me ntsis ntawm ib leeg. Hauv thawj kis, qhov no yog ib feem (daim duab 4), vim tias cov khoom tiav tau dov. Ntxiv nrog rau lub ntsej muag tseem ceeb, daim duab kos muaj cov khoom sib txuas rau gluing, ua tsaug rau cov duab kaw rau hauv ib qho tag nrho. Ua ib lub polyhedron nyob rau hauv txoj kev thib ob, koj yuav tsum tau ua ob peb tus qauv sib cais. Cia peb xav txog cov txheej txheem ua haujlwm kom ntxaws ntxiv.

Yuav ua li cas ua ib daim ntawv polyhedron: txoj kev thib ob

Ua ob lub ntsiab qauv (Pic 5):

- Ua ntej. Kos ib lub voj voog ntawm daim ntawv thiab muab faib ua ob ntu. Ib qho yuav yog lub hauv paus rau tus qauv, tshem tawm qhov thib ob arc tam sim ntawd kom yooj yim. Faib ib feem rau hauv tsib qhov sib npaug thiab txwv tag nrho cov radii nrog cov ntu ntu. Qhov tshwm sim yog tsib zoo tib yam isosceles daim duab peb sab koom ua ke. Kos ib sab ntawm ntu nruab nrab raws nraim tib lub voj voog, tsuas yog hauv daim iav duab. Qhov tshwm sim, thaum folded, zoo li ob lub cones. Ua cov qauv zoo li no hauv tag nrho rau rau daim. Rau gluing lawvqhov thib ob yog siv, uas yuav muab tso rau hauv.

- Thib ob. Cov qauv no yog lub hnub qub tsib-taw tes. Ua tib yam li kaum ob qhov khoob. Ua ib lub polyhedron, txhua lub hnub qub nrog qhov xaus khoov tau muab tso rau hauv lub khob zoo li qhov chaw thiab ua rau cov npoo.

Kev ua tiav ntawm daim duab yog tau los ntawm kev sib txuas ob chav thaiv nrog cov ntawv ntxiv, tig lawv sab hauv. Modeling cov khoom, nws yog ib qho teeb meem heev ua rau lawv sib txawv loj. Npaj ua qauv ntawm daim ntawv polyhedra tsis yog yooj yim kom loj. Ua li no, nws tsis txaus tsuas yog ua nyiaj pub dawb rau txhua tus ciam teb sab nraud. Koj yuav tsum ntsuas txhua lub ntsej muag sib cais. Nov yog tib txoj hauv kev kom tau txais daim ntawv loj ntawm tus qauv qub. Siv txoj kev thib ob ntawm kev tsim cov polyhedron, nws yog qhov yooj yim dua los ua qhov no, vim nws yuav txaus los ua kom qhov pib qhov khoob, uas yuav tsum tau ua tus naj npawb ntawm cov neeg siv khoom twb tau ua lawm.