Euler tus qauv siv pes tsawg lub ntsej muag ntawm tetrahedron muaj vertices li 4 thiab 6 ntug?
Euler tus qauv siv pes tsawg lub ntsej muag ntawm tetrahedron muaj vertices li 4 thiab 6 ntug?

Video: Euler tus qauv siv pes tsawg lub ntsej muag ntawm tetrahedron muaj vertices li 4 thiab 6 ntug?

Video: Euler tus qauv siv pes tsawg lub ntsej muag ntawm tetrahedron muaj vertices li 4 thiab 6 ntug?
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Nplooj ntawv no teev cov pov thawj ntawm cov Euler formula : rau tej convex polyhedron, lub tus lej ntawm ntsug thiab ntsej muag ua ke yog raws nraim ob ntau tshaj qhov tus lej ntawm ntug . Symbolically V-E+F=2. Rau np., a tetrahedron muaj plaub vertices , plaub lub ntsej muag , thiab six ntug ; 4 - 6 + 4 =2.

Yog li ntawd, dab tsi yuav yog tus naj npawb ntawm lub ntsej muag yog tias muaj 6 vertices thiab 12 ntug?

Ib lub voos xwmfab lossis ib lub cuboid yog peb qhov loj me uas muaj 12 ntug , 8 kaum los yog ntsug , thiab 6 ib fim.

Ib tug kuj yuav nug, Euler cov qauv ua haujlwm li cas? Euler's formula , Ob qho ntawm ob qho tseem ceeb theorems ntawm Leonhard Euler . Qhov thib ib yog qhov sib txawv ntawm qhov sib txawv (saib topology) hais txog tus naj npawb ntawm lub ntsej muag, vertices, thiab cov npoo ntawm ib qho polyhedron. Nws yog sau F + V = E + 2, qhov twg F yog tus naj npawb ntawm lub ntsej muag, V tus naj npawb ntawm vertices, thiab E tus naj npawb ntawm cov npoo.

Dab tsi yog tus qauv rau kev sib raug zoo ntawm tus naj npawb ntawm cov ntsej muag vertices thiab cov npoo ntawm lub voos xwmfab?

V - E + F = 2; los yog, hauv cov lus: cov tus lej ntawm ntsug , rho tawm tus lej ntawm ntug , plus cov tus naj npawb ntawm lub ntsej muag , yog sib npaug rau ob.

Euler's polyhedron formula yog dab tsi?

Qhov theorem no suav nrog Euler's polyhedral formula (qee zaum hu Euler's formula ). Niaj hnub no peb yuav hais qhov tshwm sim no xws li: Tus naj npawb ntawm vertices V, ntsej muag F, thiab ntug E hauv ib qho convex 3-dimensional polyhedron , txaus siab V + F - E = 2.

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