Hauv kev xyaum, cov haujlwm feem ntau tshwm sim uas yuav tsum muaj peev xwm tsim cov ntu ntawm cov duab geometric ntawm ntau cov duab thiab nrhiav thaj tsam ntawm ntu. Hauv kab lus no, peb yuav saib seb qhov tseem ceeb ntawm lub prism, pyramid, cone thiab lub tog raj kheej li cas, thiab yuav ua li cas xam lawv thaj chaw.
3D nuj nqis
Los ntawm stereometry nws paub tias daim duab peb sab ntawm txhua yam yog txwv los ntawm ntau qhov chaw. Piv txwv li, rau xws li polyhedra li ib tug prism thiab ib tug pyramid, cov nto yog lub polygonal sab. Rau lub tog raj kheej thiab lub khob hliav qab, peb tab tom tham txog qhov chaw ntawm kev hloov pauv ntawm cov duab cylindrical thiab conical.
Yog tias peb nqa lub dav hlau thiab arbitrarily hla tus nto ntawm daim duab peb-dimensional, peb yuav tau ib seem. Nws cheeb tsam yog sib npaug rau thaj tsam ntawm ib feem ntawm lub dav hlau uas yuav nyob rau hauv lub ntim ntawm daim duab. Qhov tsawg kawg nkaus tus nqi ntawm cheeb tsam no yog xoom, uas yog pom tau hais tias thaum lub dav hlau kov daim duab. Piv txwv li, ib seem uas yog tsim los ntawm ib qho taw tes tau txais yog tias lub dav hlau hla mus rau sab saum toj ntawm lub pyramid lossis lub khob hliav qab. Tus nqi siab tshaj plaws ntawm qhov chaw hla ntu yog nyob ntawmqhov txheeb ze ntawm daim duab thiab lub dav hlau, nrog rau cov duab thiab qhov loj ntawm daim duab.
Hauv qab no, peb yuav xav txog yuav ua li cas xam thaj tsam ntawm cov ntu tsim rau ob daim duab ntawm lub kiv puag ncig (lub tog raj kheej thiab lub khob hliav qab) thiab ob lub polyhedra (pyramid thiab prism).
Lub tog raj kheej
Lub tog raj kheej kheej kheej yog ib daim duab ntawm kev sib hloov ntawm ib daim duab plaub nyob ib ncig ntawm nws sab. Lub tog raj kheej yog tus cwj pwm los ntawm ob qhov tsis sib xws: puag ncig r thiab qhov siab h. Daim duab hauv qab no qhia tias lub tog raj kheej kheej kheej zoo li cas.
Muaj peb ntu tseem ceeb rau daim duab no:
- ncig;
- rectangular;
- elliptical.
Elliptical yog tsim los ntawm lub dav hlau sib tshuam sab saum npoo ntawm daim duab ntawm qee lub kaum sab xis rau nws lub hauv paus. Round yog qhov tshwm sim ntawm kev sib tshuam ntawm lub dav hlau txiav ntawm sab saum toj mus rau lub hauv paus ntawm lub tog raj kheej. Thaum kawg, ib daim duab plaub tau txais yog tias lub dav hlau txiav yog sib npaug mus rau axis ntawm lub tog raj kheej.
cheeb tsam yog xam los ntawm tus qauv:
S1=pir2
Qhov cheeb tsam ntawm axial seem, piv txwv li cov duab plaub, uas dhau los ntawm axis ntawm lub tog raj kheej, txhais raws li hauv qab no:
S2=2rh
Cov ntu ntu
Ib lub khob hliav qab yog ib daim duab ntawm kev sib hloov ntawm txoj cai daim duab peb sab nyob ib ncig ntawm ob txhais ceg. Lub khob hliav qab muaj ib sab saum toj thiab ib puag ncig puag ncig. Nws cov parameters kuj yog lub vojvoog r thiab qhov siab h. Ib qho piv txwv ntawm daim ntawv lub khob yog qhia hauv qab no.
Muaj ntau hom conic seem. Cia peb sau lawv:
- ncig;
- elliptical;
- parabolic;
- hyperbolic;
- triangular.
Lawv hloov ib leeg yog tias koj ua kom lub kaum sab xis ntawm inclination ntawm lub dav hlau secant txheeb ze rau puag ncig. Txoj hauv kev yooj yim tshaj plaws yog sau cov qauv rau thaj tsam ntu ntu ntawm lub voj voog thiab daim duab peb sab.
Ib ntu ncig yog tsim los ntawm kev sib tshuam ntawm lub conical nto nrog lub dav hlau uas yog sib npaug rau lub hauv paus. Rau nws thaj chaw, cov qauv hauv qab no siv tau:
S1=pir2z2/h 2
Ntawm no z yog qhov kev ncua deb ntawm sab saum toj ntawm daim duab mus rau seem tsim. Nws tuaj yeem pom tau tias yog z=0, ces lub dav hlau hla dhau ntawm vertex, yog li thaj tsam S1 yuav sib npaug rau xoom. Txij li z < h, thaj tsam ntawm ntu hauv kev kawm yuav ib txwm tsawg dua nws cov nqi rau lub hauv paus.
Daim duab peb sab tau txais thaum lub dav hlau hla tus duab raws nws txoj kev sib hloov. Cov duab ntawm qhov tshwm sim yuav yog daim duab peb sab isosceles, ob sab ntawm cov kab uas hla ntawm lub hauv paus thiab ob lub tshuab hluav taws xob ntawm lub khob hliav qab. Yuav ua li cas thiaj nrhiav tau qhov chaw hla ntawm ib daim duab peb sab? Cov lus teb rau lo lus nug no yuav yog cov qauv hauv qab no:
S2=rh
Qhov kev sib npaug no yog tau los ntawm kev siv cov qauv rau thaj tsam ntawm daim duab peb sab ntawm qhov ntev ntawm nws lub hauv paus thiab qhov siab.
Prism sections
Prism yog ib chav loj ntawm cov duab uas yog qhov muaj ob lub hauv paus zoo tib yam polygonal sib npaug rau ib leeg,txuas nrog parallelograms. Txhua seem ntawm lub prism yog ib tug polygon. Nyob rau hauv kev saib ntawm ntau haiv neeg ntawm cov duab nyob rau hauv kev saib xyuas (oblique, ncaj, n-gonal, tsis tu ncua, concave prisms), ntau yam ntawm lawv cov seem kuj zoo heev. Hauv qab no, peb tsuas yog txiav txim siab qee qhov tshwj xeeb xwb.
Yog hais tias lub dav hlau txiav yog parallel mus rau lub hauv paus, ces qhov cross-sectional cheeb tsam ntawm lub prism yuav muab sib npaug zos rau thaj tsam ntawm lub hauv paus.
Yog tias lub dav hlau hla dhau qhov chaw geometric ntawm ob lub hauv paus, uas yog, nws yog qhov sib npaug rau sab ntug ntawm daim duab, ces ib qho parallelogram yog tsim nyob rau hauv seem. Nyob rau hauv cov ntaub ntawv ntawm ncaj thiab tsis tu ncua prisms, qhov pom seem saib yuav yog ib daim duab plaub.
Pyramid
Pyramid yog lwm lub polyhedron uas muaj n-gon thiab n daim duab peb sab. Ib qho piv txwv ntawm daim duab peb sab pyramid yog qhia hauv qab no.
Yog hais tias seem yog kos los ntawm lub dav hlau mus rau lub n-gonal puag, ces nws cov duab yuav zoo ib yam li cov duab ntawm lub hauv paus. Cov cheeb tsam ntawm cov ntu no suav nrog cov qauv:
S1=So(h-z)2/h 2
Z yog qhov kev ncua deb ntawm lub hauv paus mus rau ntu dav hlau, So yog thaj tsam ntawm lub hauv paus.
Yog hais tias lub dav hlau txiav muaj lub sab saum toj ntawm lub pyramid thiab hla nws lub hauv paus, ces peb tau txais ib daim duab peb sab. Txhawm rau xam nws thaj chaw, koj yuav tsum xa mus rau kev siv cov qauv tsim nyog rau daim duab peb sab.
