Pyramid ua ke nrog lub prism yog ib qho zoo meej polyhedron hauv qhov chaw peb sab, lawv cov yam ntxwv geometric tau kawm hauv tsev kawm theem siab. Hauv kab lus no, peb yuav txiav txim siab seb cov pyramids yog dab tsi, cov ntsiab lus twg lawv muaj, thiab luv luv qhia qhov tseeb pyramids.
Geometric daim duab pyramid
Los ntawm qhov pom ntawm geometry, lub pyramid yog ib daim duab spatial, muaj xws li ib tug polygon thiab ob peb daim duab peb sab. Tau txais daim duab no yog qhov yooj yim heev. Txhawm rau ua qhov no, coj ib lub polygon nrog n sab, tom qab ntawd xaiv qhov chaw tsis txaus ntseeg hauv qhov chaw uas yuav tsis nyob hauv lub dav hlau ntawm lub polygon, thiab txuas txhua qhov vertex ntawm polygon mus rau qhov no. Obviously, daim duab tsim nyob rau hauv no txoj kev yuav muaj n daim duab peb sab txuas rau ib leeg ntawm ib vertex.
Yuav kom pom cov duab geometric ntawm daim duab piav qhia, cia peb thaij duab.
Qhov no qhia tau hais tias lub pyramid quadrangular, lub hauv paus uas yogquadrilateral, thiab sab saum npoo yog tsim los ntawm plaub daim duab peb sab uas muaj ib qho vertex.
Pyramid ntsiab
Zoo li txhua lub polyhedron, lub pyramid yog tsim los ntawm peb hom ntsiab:
- dab;
- tops;
- ribs.
Lub ntsej muag yog ib feem ntawm cov dav hlau uas cais cov ntim sab hauv ntawm daim duab los ntawm qhov chaw nyob ib puag ncig. Yog tias lub hauv paus ntawm lub pyramid muaj n-gon, ces tus naj npawb ntawm nws lub ntsej muag yeej ib txwm n + 1. Ntawm no, n sab yog daim duab peb sab thiab ib sab yog hais txog n-gonal puag.
Vertices yog cov ntsiab lus uas peb lossis ntau lub ntsej muag ntawm daim duab sib tshuam. Lub hauv paus cheeb tsam muaj n vertices, txhua tus yog tsim los ntawm ob lub ntsej muag daim duab peb sab thiab lub hauv paus. Lub ntsiab lus uas cov duab peb sab sib ntsib yog hu ua sab saum toj ntawm lub pyramid. Yog li, daim duab nyob rau hauv kev txiav txim siab muaj n + 1 vertices.
Ntug yog cov kab ncaj uas tshwm thaum ob lub ntsej muag sib tshuam. Txhua ntug yog bounded los ntawm ob vertices ntawm nws kawg. Txhua lub pyramid nrog n-gon puag muaj 2n npoo. Ib nrab ntawm tus lej no, uas yog, n, yog tsim los ntawm kev sib tshuam ntawm sab peb sab.
hom muaj peev xwm ua tau
Lub npe ntawm daim duab hauv qab kev txiav txim siab tshwj xeeb yog txiav txim siab los ntawm hom polygon ntawm lub hauv paus. Piv txwv li, yog tias nws muaj peb lub ces kaum thiab peb sab, ces lub pyramid yuav yog daim duab peb sab, yog plaub - plaub fab, thiab lwm yam.
Polygon tuaj yeem ua rau convex thiab concave, nrog rau hom tsis tu ncua thiab dav. Tag nrho cov no kuj txiav txim siab qhov tsos ntawm lub pyramid.
Ib qho tseem ceeb hauv kev txiav txim siab hom duab yog txoj hauj lwm ntawm sab saum toj ntawm lub pyramid txheeb ze rau nws lub hauv paus. Cov ntu ntu uas tau kos los ntawm sab saum toj mus rau lub hauv paus polygonal yog hu ua qhov siab ntawm daim duab. Yog tias ntu no cuam tshuam lub hauv paus ntawm nws qhov chaw geometric (rau daim duab peb sab, qhov no yog qhov kev sib tshuam ntawm cov nruab nrab, rau plaub fab, qhov sib tshuam ntawm kab pheeb ces kaum), ces daim duab hu ua kab ncaj. Tsis tas li ntawd, lawv hais txog ib lub pyramid inclined.
Yog tias n-gon ntawm lub hauv paus tsis tu ncua (sib npaug ntawm daim duab peb sab, square, thiab lwm yam), thiab daim duab ncaj nraim, ces nws hu ua pyramid tsis tu ncua.
Daim duab saum toj no qhia ntau lub pyramids, uas txawv ntawm tus naj npawb ntawm sab ntawm polygon ntawm lub hauv paus.
Khoom ntawm cov pyramids tsis tu ncua
Cov pyramids txawv ntawm lwm cov duab ntawm chav kawm no los ntawm qib siab ntawm symmetry. Hauv qhov no, nws yog qhov yooj yim rau kev ua tiav ntau yam geometric suav nrog lawv, piv txwv li, ntim lossis thaj chaw saum npoo.
Ib lub pyramid tsis tu ncua muaj ib qho n-gon ntawm nws lub hauv paus, thaj tsam ntawm qhov tshwj xeeb txiav txim siab los ntawm kev paub txog qhov ntev ntawm nws sab. Lub lateral nto ntawm daim duab yog tsim los ntawm n zoo tib yam daim duab peb sab, uas yog equilateral. Cov npoo ntawm lub pyramid tsis tu ncua nyob rau ntawm qhov chaw sab nraud yog sib npaug rau ib leeg. Tus nqi ntawm qhov ntev ntawm ntug no feem ntau yog siv thaum xam lub apothem ntawm ib daim duab thiab txiav txim siab qhov chaw saum npoo.
Qhov siab ntawm lub pyramid tsis tu ncua yog qhov tseem ceeb thib ob yam ntxwv ntawm daim duab (thawj yog qhov ntev ntawm ntughauv av). Qhov siab yog siv thaum xam ntim.
Txhua lub dav hlau sib npaug rau lub hauv paus, uas cuam tshuam rau sab ntawm lub ntsej muag ntawm lub pyramid, ua rau kev tsim ntawm ib feem ntau. Nws yog homothetic nrog rau lub hauv paus polygon. Kev piav qhia hlais ua rau kev tsim ntawm tag nrho cov chav kawm ntawm cov duab tshiab - truncated li niaj zaus pyramids.
Pyramids nto moo tshaj plaws
Tau kawg, cov no yog cov pyramids quadrangular tsis tu ncua ntawm Egyptian pharaohs. Nyob rau hauv ib qho chaw hu ua Giza, muaj ntau tshaj 100 ntawm cov pob zeb monuments, qhov zoo tshaj plaws ntawm kev tsim thiab qhov tseeb ntawm cov geometric tsis uas txuas ntxiv amaze cov kws tshawb fawb txog niaj hnub no. Qhov loj tshaj ntawm lawv yog lub Pyramid ntawm Cheops, uas yog hais txog 146 meters siab thiab txog 230 meters ntev.
Yuav ua li cas cov pyramids no tau ua haujlwm rau, nrog rau cov txheej txheem twg thiab thaum twg lawv tau tsim, tsis muaj leej twg paub txog niaj hnub no.
