Stereometry yog ib feem ntawm geometry uas kawm cov duab uas tsis nyob hauv tib lub dav hlau. Ib qho ntawm cov khoom ntawm kev kawm ntawm stereometric yog prisms. Nyob rau hauv tsab xov xwm peb yuav muab ib tug txhais ntawm ib tug prism los ntawm ib tug geometric taw tes ntawm view, thiab kuj qhia luv luv cov khoom uas yog yam ntxwv ntawm nws.
duab geometric
Lub ntsiab lus ntawm prism hauv geometry yog raws li nram no: nws yog ib tug spatial daim duab uas muaj ob zoo tib yam n-gons nyob rau hauv parallel dav hlau, txuas rau ib leeg los ntawm lawv vertices.
Tau txais prism yog ib qho yooj yim. Xav txog tias muaj ob qhov zoo tib yam n-gons, qhov twg n yog tus naj npawb ntawm sab lossis vertices. Cia peb muab lawv tso kom lawv sib npaug. Tom qab ntawd, lub vertices ntawm ib tug polygon yuav tsum tau txuas mus rau cov coj vertices ntawm lwm tus. Daim duab tsim yuav muaj ob sab n-gonal, uas yog hu ua bases, thiab n quadrangular sab, uas nyob rau hauv cov ntaub ntawv dav dav yog parallelograms. Cov txheej txheem ntawm parallelograms ua rau sab saum npoo ntawm daim duab.
Muaj ib txoj hauv kev kom tau txais cov duab hauv nqe lus nug. Yog li, yog tias peb coj ib qho n-gon thiab hloov mus rau lwm lub dav hlau uas siv cov ntu sib npaug ntawm qhov sib npaug, ces nyob rau hauv lub dav hlau tshiab peb tau txais tus thawj polygon. Ob qho tib si polygons thiab tag nrho cov kab sib txuas uas tau kos los ntawm lawv cov vertices tsim lub prism.
Daim duab saum toj no qhia tau tias muaj peb sab prism. Nws yog hu ua li ntawd vim nws lub hauv paus yog daim duab peb sab.
Cov ntsiab lus uas tsim cov duab
Lub ntsiab lus ntawm prism tau muab los saum toj no, los ntawm qhov tseeb tias cov ntsiab lus tseem ceeb ntawm daim duab yog nws lub ntsej muag lossis sab, txwv tag nrho cov ntsiab lus sab hauv ntawm prism los ntawm qhov chaw sab nraud. Txhua lub ntsej muag ntawm daim duab nyob rau hauv kev txiav txim siab yog ib qho ntawm ob hom:
- sib;
- qhov chaw.
Muaj n sab daim, thiab lawv yog parallelograms lossis lawv cov hom tshwj xeeb (duab plaub, squares). Feem ntau, sab ntsej muag txawv ntawm ib leeg. Tsuas muaj ob lub ntsej muag ntawm lub hauv paus, lawv yog n-gons thiab sib npaug ntawm ib leeg. Yog li, txhua qhov prism muaj n + 2 sab.
Dhau li ntawm ob sab, daim duab yog tus cwj pwm los ntawm nws cov vertices. Lawv yog cov ntsiab lus uas peb lub ntsej muag kov tib lub sijhawm. Ntxiv mus, ob ntawm peb lub ntsej muag ib txwm nyob rau sab saum toj, thiab ib qho - rau hauv paus. Yog li, nyob rau hauv lub prism tsis muaj tshwj xeeb xaiv ib vertex, xws li, piv txwv li, nyob rau hauv lub pyramid, tag nrho cov ntawm lawv yog sib npaug. Tus naj npawb ntawm vertices ntawm daim duab yog 2n (n daim rau txhuavim).
Thaum kawg, qhov tseem ceeb thib peb ntawm lub prism yog nws cov npoo. Cov no yog ntu ntawm ib qho ntev, uas yog tsim los ntawm kev sib tshuam ntawm ob sab ntawm daim duab. Zoo li lub ntsej muag, cov npoo kuj muaj ob hom sib txawv:
- los yog tsim los ntawm ob sab;
- los yog tshwm sim ntawm qhov sib txuas ntawm qhov parallelogram thiab sab ntawm n-gonal puag.
Tus lej ntawm cov npoo yog li 3n, thiab 2n ntawm lawv yog hom thib ob.
Prism yam
Muaj ntau ntau txoj hauv kev los faib prisms. Txawm li cas los xij, lawv txhua tus ua raws li ob yam ntawm daim duab:
- ntawm hom n-coal puag;
- rau sab hom.
Ua ntej, cia peb tig mus rau qhov thib ob thiab txhais lub prism ncaj thiab oblique. Yog tias tsawg kawg ib sab yog parallelogram ntawm ib hom dav dav, ces daim duab hu ua oblique lossis oblique. Yog hais tias tag nrho cov parallelograms yog cov duab plaub los yog squares, ces cov prism yuav ncaj.
Lub ntsiab lus ntawm lub prism ncaj qha kuj tuaj yeem muab rau hauv ib txoj kev sib txawv me ntsis: daim duab ncaj yog ib qho prism uas nws sab ntug thiab lub ntsej muag yog perpendicular rau nws cov hauv paus. Daim duab qhia ob daim duab plaub fab. Sab laug yog ncaj, sab xis yog oblique.
Tam sim no cia peb mus rau qhov kev faib tawm raws li hom n-gon dag hauv lub hauv paus. Nws tuaj yeem muaj tib sab thiab kaum sab xis lossis txawv. Nyob rau hauv thawj rooj plaub, lub polygon yog hu ua tsis tu ncua. Yog hais tias daim duab nyob rau hauv kev txiav txim siab muaj ib tug polygon nrog sib npaugsab thiab cov ces kaum thiab yog ib txoj kab ncaj, ces nws yog hu ua raug. Raws li cov ntsiab lus no, lub prism tsis tu ncua ntawm nws lub hauv paus tuaj yeem muaj qhov sib npaug ntawm daim duab peb sab, square, ib txwm pentagon, lossis hexagon, thiab lwm yam. Cov lej uas raug teev tseg yog qhia hauv daim duab.
Linear parameters of prisms
Cov kev txwv hauv qab no yog siv los piav qhia qhov ntau thiab tsawg ntawm cov duab raws li kev txiav txim siab:
- siab;
- pab sab;
- sab tav ntev;
- 3D kab pheeb ces kaum;
- kab pheeb ces kaum sab thiab hauv paus.
Rau cov prisms li niaj zaus, tag nrho cov npe muaj feem cuam tshuam rau ib leeg. Piv txwv li, qhov ntev ntawm sab tav yog tib yam thiab sib npaug rau qhov siab. Rau ib tug tshwj xeeb n-gonal daim duab tsis tu ncua, muaj cov qauv uas tso cai rau koj los txiav txim tag nrho cov seem los ntawm ob qho kev tsis sib xws.
Suab nto
Yog tias peb xa mus rau cov ntsiab lus saum toj no ntawm lub prism, ces nws yuav tsis yooj yim to taub dab tsi ntawm daim duab sawv cev. Qhov saum npoo yog thaj tsam ntawm txhua lub ntsej muag. Rau ib tug ncaj prism, nws yog xam los ntawm cov mis:
S=2So + Poh
qhov So yog thaj chaw ntawm lub hauv paus, Po yog thaj tsam ntawm n-gon ntawm lub hauv paus, h yog qhov siab (qhov nrug ntawm lub hauv paus).
ntim ntawm daim duab
Nrog rau qhov chaw rau kev xyaum, nws yog ib qho tseem ceeb kom paub qhov ntim ntawm prism. Nws tuaj yeem txiav txim siab los ntawm cov qauv hauv qab no:
V=Soh
Qhov noqhov kev qhia no muaj tseeb rau txhua yam ntawm prism, suav nrog cov uas yog oblique thiab tsim los ntawm tsis xwm yeem polygons.
Rau cov prisms li niaj zaus, qhov ntim yog qhov ua haujlwm ntawm qhov ntev ntawm sab ntawm lub hauv paus thiab qhov siab ntawm daim duab. Rau qhov sib thooj n-gonal prism, cov qauv rau V muaj ib daim ntawv pob zeb.
