Prism yog qhov yooj yim geometric duab peb sab. Txawm li cas los xij, qee cov menyuam kawm ntawv muaj teeb meem hauv kev txiav txim siab nws cov khoom tseem ceeb, qhov ua rau, raws li txoj cai, cuam tshuam nrog cov lus siv tsis raug. Hauv tsab xov xwm no, peb yuav xav txog dab tsi prisms yog dab tsi, lawv hu ua, thiab piav qhia meej txog qhov tseeb quadrangular prism.
Prism hauv geometry
Kev kawm ntawm cov duab peb sab yog ib txoj haujlwm ntawm stereometry - ib feem tseem ceeb ntawm spatial geometry. Nyob rau hauv stereometry, ib tug prism yog to taub xws li ib tug daim duab, uas yog tsim los ntawm lub parallel txhais lus ntawm ib tug arbitrary ca polygon ntawm ib tug tej yam deb ntawm qhov chaw. Parallel translation implies ib tug txav nyob rau hauv uas kev sib hloov nyob ib ncig ntawm ib tug axis perpendicular mus rau lub dav hlau ntawm lub polygon yog kiag li cais.
Raws li qhov tshwm sim ntawm txoj kev piav qhia ntawm kev tau txais prism, ib daim duab raug tsim, txwv los ntawm obpolygons muaj tib qhov ntev, dag hauv cov dav hlau sib luag, thiab qee tus lej ntawm parallelograms. Lawv tus lej coincides nrog tus naj npawb ntawm sab (vertices) ntawm lub polygon. Zoo tib yam polygons hu ua lub hauv paus ntawm lub prism, thiab lawv qhov chaw saum npoo yog thaj tsam ntawm lub hauv paus. Parallelograms txuas ob lub hauv paus tsim ib sab saum npoo.
Prism ntsiab thiab Euler's theorem
Vim tias daim duab peb sab nyob rau hauv kev txiav txim siab yog polyhedron, uas yog, nws yog tsim los ntawm ib txheej ntawm kev sib tshuam dav hlau, nws yog tus yam ntxwv los ntawm ib tug xov tooj ntawm vertices, ntug thiab lub ntsej muag. Lawv yog tag nrho cov ntsiab lus ntawm prism.
Nyob rau hauv nruab nrab ntawm lub xyoo pua 18th, Swiss lej Leonhard Euler tau tsim kev sib txuas ntawm cov lej ntawm cov ntsiab lus ntawm polyhedron. Qhov kev sib raug zoo no yog sau nrog cov qauv yooj yim hauv qab no:
Number of edges=number of vertices + number of faces - 2
Rau ib qho prism, qhov sib npaug no muaj tseeb. Cia peb muab piv txwv ntawm nws siv. Piv txwv tias muaj ib qho quadrangular prism tsis tu ncua. Nws yog duab hauv qab no.
Nws tuaj yeem pom tau tias tus lej ntawm qhov chaw rau nws yog 8 (4 rau txhua lub hauv paus plaub). Tus naj npawb ntawm sab lossis lub ntsej muag yog 6 (2 lub hauv paus thiab 4 sab duab plaub). Ces tus naj npawb ntawm ntug rau nws yuav yog:
ntau tus tav=8 + 6 - 2=12
Txhua tus tuaj yeem suav tau yog tias koj xa mus rau tib daim duab. Yim ntug nyob ntawm lub hauv paus, thiab plaub ntug yog perpendicular rau cov hauv paus.
Kev faib tawm tag nrho ntawm prisms
Nws yog ib qho tseem ceeb kom nkag siab txog qhov kev faib tawm no kom koj tsis txhob ntxhov siab hauv cov ntsiab lus tom qab thiab siv cov qauv tsim nyog los xam, piv txwv li, thaj chaw saum npoo lossis ntim ntawm cov duab.
Rau txhua qhov prism ntawm qhov tsis txaus ntseeg, 4 cov yam ntxwv tuaj yeem paub qhov txawv uas yuav ua rau nws tus yam ntxwv. Cia peb sau lawv:
- Los ntawm cov ces kaum ntawm lub polygon ntawm lub hauv paus: daim duab peb sab, pentagonal, octagonal thiab lwm yam.
- polygon hom. Tej zaum nws yuav yog lossis tsis yog. Piv txwv li, daim duab peb sab txoj cai yog qhov tsis sib xws, tab sis daim duab peb sab sib npaug yog qhov tseeb.
- Raws li hom polygon convexity. Nws tuaj yeem yog concave lossis convex. Convex prisms yog feem ntau.
- Ntawm cov ces kaum ntawm lub hauv paus thiab sab parallelograms. Yog hais tias tag nrho cov ces kaum sib npaug zos rau 90 o, ces lawv hais txog txoj cai prism, yog tsis yog tag nrho cov ntawm lawv yog, ces xws li ib tug daim duab yog hu ua oblique.
Ntawm tag nrho cov ntsiab lus no, Kuv xav nyob hauv qhov kawg. Ib tug ncaj prism kuj hu ua ib lub prism. Qhov no yog vim qhov tseeb tias rau nws parallelograms yog cov duab plaub nyob rau hauv rooj plaub dav dav (qee zaum lawv tuaj yeem ua squares).
Piv txwv li, daim duab saum toj no qhia tau hais tias lub pentagonal concave rectangular los yog daim duab ncaj.
Regular quadrangular prism
Lub hauv paus ntawm qhov prism no yog ib qho plaub hau tsis tu ncua, uas yog, square. Daim duab saum toj no twb qhia tias qhov prism zoo li cas. Ntxiv rau ob lub squares uas nwstxwv sab saum toj thiab hauv qab, nws kuj suav nrog 4 daim duab plaub.
Cia peb qhia rau sab ntawm lub hauv paus ntawm ib lub quadrangular prism tsis tu ncua los ntawm tsab ntawv a, qhov ntev ntawm nws sab ntug yuav raug qhia los ntawm tsab ntawv c. Qhov ntev no kuj yog qhov siab ntawm daim duab. Tom qab ntawd thaj tsam ntawm tag nrho saum npoo ntawm qhov prism no qhia los ntawm tus qauv:
S=2a2+ 4ac=2a(a + 2c)
Ntawm no yog thawj nqe lus qhia txog kev koom tes ntawm lub hauv paus rau tag nrho cheeb tsam, lub sij hawm thib ob yog thaj tsam ntawm sab saum toj.
Muab tso rau hauv tus account lub npe qhia rau qhov ntev ntawm ob sab, peb sau cov mis rau qhov ntim ntawm daim duab hauv nqe lus nug:
V=a2c
Qhov ntawd yog, qhov ntim yog xam raws li cov khoom lag luam ntawm thaj tsam ntawm lub hauv paus square thiab qhov ntev ntawm sab ntug.
Cube shape
Txhua tus paub qhov zoo tshaj plaws peb-dimensional daim duab no, tab sis ob peb tus neeg xav tias nws yog quadrangular prism, sab uas yog sib npaug rau qhov ntev ntawm sab ntawm lub hauv paus square, uas yog, c=a.
Rau ib lub voos xwmfab, cov qauv rau tag nrho thaj chaw saum npoo thiab ntim yuav siv daim ntawv:
S=6a2
V=a3
Vim ib lub voos xwmfab yog ib qho prism uas muaj 6 qhov sib npaug sib npaug, txhua tus khub ntawm lawv tuaj yeem suav tias yog lub hauv paus.
Lub voos xwmfab yog ib daim duab zoo heev, uas nyob rau hauv qhov xwm txheej tau pom nyob rau hauv daim ntawv ntawm cov siv lead ua lattices ntawm ntau cov ntaub ntawv hlau thiab ionic crystals. Piv txwv li, lattices ntawm kub, nyiaj, tooj liab thiab roojntsev yog cubic.
