Geometric cov duab hauv qhov chaw yog qhov khoom ntawm kev kawm stereometry, cov chav kawm uas tau dhau los ntawm cov menyuam kawm ntawv hauv tsev kawm theem siab. Kab lus no tau mob siab rau xws li lub zoo meej polyhedron li prism. Cia peb xav paub ntau ntxiv txog cov khoom ntawm prism thiab muab cov qauv uas ua haujlwm los piav txog lawv ntau npaum li cas.
Prism yog dab tsi?
Txhua tus xav txog lub thawv lossis lub voos xwmfab zoo li cas. Ob daim duab yog prisms. Txawm li cas los xij, cov chav kawm ntawm prisms muaj ntau yam sib txawv. Hauv geometry, daim duab no tau muab cov ntsiab lus hauv qab no: lub prism yog ib qho polyhedron nyob rau hauv qhov chaw, uas yog tsim los ntawm ob qho tib si thiab zoo tib yam polygonal sab thiab ob peb parallelograms. Cov ntsej muag sib luag zoo tib yam ntawm daim duab yog hu ua nws cov hauv paus (sab sauv thiab qis). Parallelograms yog sab ntsej muag ntawm daim duab, txuas ob sab ntawm lub hauv paus nrog ib leeg.
Yog tias lub hauv paus tau sawv cev los ntawm n-gon, qhov twg n yog tus lej, ces daim duab yuav muaj 2 + n ntsej muag, 2n vertices thiab 3n npoo. Lub ntsej muag thiab ntug hais txogib qho ntawm ob hom: ob qho tib si lawv nyob rau sab nraud, lossis rau hauv paus. Raws li cov vertices, lawv txhua tus sib npaug thiab koom rau hauv lub hauv paus ntawm prism.
Nyob ntawm cov duab ntawm chav kawm hauv kev kawm
Kawm txog cov khoom ntawm prism, koj yuav tsum sau cov hom ua tau ntawm daim duab no:
- Convex thiab concave. Qhov sib txawv ntawm lawv yog nyob rau hauv cov duab ntawm polygonal puag. Yog hais tias nws yog concave, ces nws kuj yuav yog ib tug peb-dimensional daim duab, thiab vice versa.
- Ncaj thiab oblique. Rau ib qho ncaj prism, sab ntsej muag yog cov duab plaub los yog squares. Hauv daim duab oblique, sab ntsej muag yog parallelograms ntawm hom dav lossis rhombuses.
- Yuav thiab yog. Nyob rau hauv thiaj li yuav kawm tau cov duab kom raug, nws yuav tsum ncaj thiab muaj lub hauv paus raug. Ib qho piv txwv ntawm cov tom kawg yog cov duab tiaj tus xws li daim duab peb sab sib npaug lossis square.
Lub npe ntawm prism yog tsim los ntawm kev muab cov npe teev npe. Piv txwv li, txoj cai-angled parallelepiped los yog lub voos xwmfab uas tau hais los saum no yog hu ua quadrangular prism. Tsis tu ncua prisms, vim lawv cov symmetry siab, yooj yim rau kev kawm. Lawv cov khoom raug qhia nyob rau hauv daim ntawv ntawm cov qauv lej tshwj xeeb.
Prism cheeb tsam
Thaum xav txog tej yam khoom ntawm prism raws li nws cheeb tsam, lawv txhais tau tias tag nrho cheeb tsam ntawm tag nrho nws lub ntsej muag. Nws yog qhov yooj yim tshaj plaws los xav txog tus nqi no yog tias koj nthuav tawm daim duab, uas yog, nthuav txhua lub ntsej muag rau hauv ib lub dav hlau. Hauv qab noDaim duab qhia ib qho piv txwv ntawm cheb ntawm ob lub prisms.
Rau qhov kev txiav txim siab tsis ncaj ncees, cov qauv rau thaj tsam ntawm nws qhov cheb hauv daim ntawv dav dav tuaj yeem sau raws li hauv qab no:
S=2So+ bPsr.
Cia peb piav cov lus. Tus nqi So yog thaj tsam ntawm ib lub hauv paus, b yog qhov ntev ntawm sab ntug, Psr yog qhov ntu ntu, uas yog perpendicular rau sab parallelograms ntawm daim duab.
Cov qauv sau feem ntau yog siv los txiav txim qhov chaw ntawm inclined prisms. Nyob rau hauv cov ntaub ntawv ntawm ib txwm prism, cov lus qhia rau S yuav siv rau ib tug tshwj xeeb daim ntawv:
S=n/2a2ctg(pi/n) + nba.
thawj lo lus nyob rau hauv cov lus qhia sawv cev rau thaj tsam ntawm ob lub hauv paus ntawm ib txwm prism, lub sij hawm thib ob yog thaj tsam ntawm cov duab plaub sab. Ntawm no yog qhov ntev ntawm sab ntawm ib txwm n-gon. Nco ntsoov tias qhov ntev ntawm sab ntug b rau ib txwm prism kuj yog nws qhov siab h, yog li hauv cov qauv b tuaj yeem hloov tau los ntawm h.
Yuav ua li cas xam qhov ntim ntawm daim duab?
Prism yog ib qho yooj yim polyhedron nrog siab symmetry. Yog li ntawd, txhawm rau txiav txim siab nws qhov ntim, muaj cov qauv yooj yim heev. Nws zoo li no:
V=Soh.
Xaiv cheeb tsam thiab qhov siab tuaj yeem ua kom yuam kev thaum saib oblique tsis xwm yeem. Qhov teeb meem no tau daws los ntawm kev soj ntsuam geometric txuas ntxiv uas muaj cov ntaub ntawv hais txog lub dihedral kaum sab xis ntawm sab parallelograms thiab lub hauv paus.
Yog tias qhov prism yog lawmtus qauv rau V ua tau zoo heev:
V=n/4a2ctg(pi/n)h.
Raws li koj tuaj yeem pom, thaj tsam S thiab ntim V rau lub prism tsis tu ncua yog qhov tshwj xeeb txiav txim siab yog tias ob qho ntawm nws cov kab tsis raug paub.
Daim duab peb sab prism
Cia peb ua kom tiav cov kab lus los ntawm kev xav txog cov khoom ntawm daim duab peb sab prism. Nws yog tsim los ntawm tsib lub ntsej muag, peb ntawm uas yog cov duab plaub (squares), thiab ob yog daim duab peb sab sib npaug. Ib tug prism muaj rau vertices thiab cuaj npoo. Rau qhov prism no, cov qauv ntim thiab qhov chaw saum npoo yog sau hauv qab no:
S3=√3/2a2+ 3ha
V3=√3/4a2h.
Dhau li ntawm cov khoom no, nws kuj tseem muaj txiaj ntsig los muab cov qauv rau lub apothem ntawm lub hauv paus ntawm daim duab, uas yog qhov siab ha ntawm daim duab peb sab sib npaug:
ha=√3/2a.
Ob sab ntawm lub prism yog cov duab plaub zoo tib yam. Qhov ntev ntawm lawv kab pheeb ces kaum yog:
d=√(a2+ h2).
Kev paub txog cov khoom geometric ntawm daim duab peb sab prism tsis yog tsuas yog theoretical xwb tab sis kuj muaj txiaj ntsig zoo. Qhov tseeb yog tias daim duab no, ua los ntawm cov iav kho qhov muag, yog siv los kawm cov hluav taws xob spectrum ntawm lub cev.
Dhau los ntawm lub iav prism, lub teeb yog decomposed rau hauv ib tug xov tooj ntawm cov xim xim raws li qhov tshwm sim ntawm dispersion phenomenon, uas tsim tej yam kev mob rau kev kawm cov spectral muaj pes tsawg leeg ntawm ib tug electromagnetic flux.
