Prism yog ib qho ntawm cov neeg paub zoo kawm hauv chav kawm ntawm cov duab kos duab hauv cov tsev kawm theem nrab. Yuav kom suav tau ntau yam ntxwv rau cov duab ntawm chav kawm no, koj yuav tsum paub tias hom prisms muaj dab tsi. Cia wb mus saib qhov teeb meem no.
Prism hauv stereometry
Ua ntej ntawm tag nrho, cia peb txhais cov chav kawm hais txog cov duab. Lub prism yog ib qho polyhedron uas muaj ob qho tib si polygonal hauv paus, uas yog sib cuam tshuam los ntawm parallelograms.
Koj tuaj yeem tau txais daim duab no raws li hauv qab no: xaiv ib qho kev txiav txim siab ntawm lub dav hlau, thiab tom qab ntawd txav nws mus rau qhov ntev ntawm ib qho vector uas tsis yog lub dav hlau qub ntawm lub polygon. Thaum lub sij hawm xws li ib qho kev txav mus los, ob sab ntawm lub polygon yuav piav qhia txog sab ntawm lub ntsej muag ntawm lub prism yav tom ntej, thiab txoj hauj lwm kawg ntawm lub polygon yuav dhau los ua lub hauv paus thib ob ntawm daim duab. Raws li tau piav qhia, hom prism tuaj yeem tau txais. Daim duab hauv qab no qhia tau hais tias peb lub prism.
Dab tsi yog hom prisms?
Nws yog hais txog kev faib cov duabchav kawm nug. Hauv cov ntaub ntawv dav dav, qhov kev faib tawm no yog nqa mus rau hauv tus account cov yam ntxwv ntawm lub hauv paus polygonal thiab sab ntawm daim duab. Feem ntau, peb hom prisms hauv qab no yog qhov txawv:
- Ncaj thiab oblique (oblique).
- Right and wrong.
Ib lub prism ntawm ib qho ntawm cov npe ntawm kev faib tawm tuaj yeem muaj plaub fab, pentagonal, …, n-gonal puag. Raws li rau hom triangular prism, nws tsuas yog muab faib raws li thawj ob lub ntsiab lus hais. Daim duab peb sab prism ib txwm convex.
Nyob hauv qab no, peb yuav ua tib zoo saib txhua yam ntawm cov kev faib tawm no thiab muab qee cov qauv tsim nyog rau kev suav cov geometric khoom ntawm lub prism (qhov chaw saum npoo, ntim).
Ncaj thiab Oblique Shapes
Nws tuaj yeem paub qhov txawv ntawm qhov ncaj qha prism los ntawm ib qho oblique ntawm ib sab. Nov yog daim duab sib thooj.
Ntawm no ob lub prisms tau qhia (hexagonal ntawm sab laug thiab pentagonal ntawm sab xis). Txhua leej txhua tus yuav hais nrog kev ntseeg siab tias lub hexagonal yog ncaj, thiab lub pentagonal yog oblique. Dab tsi geometric feature distinguishes cov prisms? Tau kawg, hom ntsej muag sab.
Ib qho ncaj ncaj, tsis hais nws lub hauv paus, txhua lub ntsej muag yog duab plaub. Lawv tuaj yeem sib npaug rau ib leeg, lossis lawv tuaj yeem sib txawv, qhov tseem ceeb yog tias lawv yog cov duab plaub, thiab lawv cov kaum sab xis nrog cov hauv paus yog 90o.
Hais txog daim duab oblique, nws yuav tsum tau hais tias tag nrho lossis qee qhov ntawm nws sab ntsej muag yogparallelograms uas tsim indirect dihedral ces kaum nrog lub hauv paus.
Rau txhua hom ncaj prisms, qhov siab yog qhov ntev ntawm sab ntug, rau oblique cov duab, qhov siab ib txwm tsawg dua lawv cov npoo. Paub qhov siab ntawm prism yog ib qho tseem ceeb thaum xam nws qhov chaw thiab ntim. Piv txwv li, tus qauv ntim yog:
V=Soh
qhov twg yog qhov siab, So yog thaj tsam ntawm ib lub hauv paus.
Prisms raug thiab tsis raug
Txhua yam prism tsis raug yog tias nws tsis ncaj lossis nws lub hauv paus tsis raug. Cov lus nug ntawm ncaj thiab inclined prisms tau tham saum toj no. Ntawm no peb xav txog dab tsi cov lus qhia "piv txwv li polygonal puag" txhais tau tias.
Ib tug polygon tsis tu ncua yog tias tag nrho nws sab sib npaug (cia peb qhia lawv qhov ntev los ntawm tsab ntawv a), thiab tag nrho nws cov ces kaum kuj sib npaug. Piv txwv ntawm cov polygons tsis tu ncua yog daim duab peb sab sib npaug, ib lub xwmfab, lub hexagon nrog rau lub kaum ntawm 120o thiab lwm yam. Qhov cheeb tsam ntawm ib txwm n-gon suav nrog cov qauv no:
S=n/4a2ctg(pi/n)
Nyob hauv qab no yog ib tug schematic sawv cev ntawm ib txwm prisms nrog peb sab, square, …, octagonal bases.
Siv cov qauv saum toj no rau V, peb tuaj yeem sau cov lus qhia sib xws rau cov duab tsis tu ncua:
V=n/4a2ctg(pi/n)h
Raws li tag nrho thaj chaw saum npoo av, rau cov prisms li niaj zaus nws yog tsim los ntawm thaj chaw ntawm obzoo tib yam bases thiab n zoo tib yam duab plaub nrog sab h thiab a. Cov lus tseeb no tso cai rau peb sau cov qauv rau thaj tsam ntawm ib qho prism li niaj zaus:
S=n/2a2ctg(pi/n) + nah
Ntawm no yog thawj lub sij hawm sib raug rau thaj tsam ntawm ob lub hauv paus, lub sij hawm thib ob txiav txim siab thaj tsam ntawm thaj chaw sab nraud nkaus xwb.
Ntawm txhua hom prisms li niaj zaus, tsuas yog quadrangular prisms muaj lawv lub npe. Yog li, lub quadrangular prism tsis tu ncua, uas a≠h, hu ua rectangular parallelepiped. Yog tias daim duab no muaj a=h, ces lawv tham txog lub voos xwmfab.
Concave shapes
Txog tam sim no, peb tau txiav txim siab tsuas yog hom convex ntawm prisms. Nws yog rau lawv tias lub ntsiab tseem ceeb yog them rau hauv kev kawm ntawm cov chav kawm ntawm cov nuj nqis raws li kev xav. Txawm li cas los xij, tseem muaj concave prisms. Lawv txawv ntawm cov convex uas lawv cov hauv paus yog concave polygons, pib los ntawm plaub fab.
Daim duab qhia txog ob lub concave prisms, uas yog ua los ntawm ntawv, ua piv txwv. Sab laug ib tug nyob rau hauv daim ntawv ntawm ib tug tsib-taw lub hnub qub yog ib tug decagonal prism, txoj cai ib tug nyob rau hauv daim ntawv ntawm ib tug rau-taw lub hnub qub yog hu ua ib tug dodecagonal concave ncaj prism.
