Puas yog cov kab sib txuas sib txuas hauv hyperbolic geometry?
Puas yog cov kab sib txuas sib txuas hauv hyperbolic geometry?

Video: Puas yog cov kab sib txuas sib txuas hauv hyperbolic geometry?

Video: Puas yog cov kab sib txuas sib txuas hauv hyperbolic geometry?
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Hauv hyperbolic geometry , muaj ob hom kab sib npaug . Yog ob kab ua tsis yog sib tshuam nyob rau hauv ib tug qauv ntawm hyperbolic geometry tab sis lawv sib tham ntawm nws ciam teb, ces tus kab hu ua asymptotically thaum uas tig mus los yog hyperparallel.

Ib yam li ntawd, tib neeg nug, puas cov kab sib txuas sib txuas ntawm ib qho chaw?

Parallel kab ua tsis muaj nyob hauv kheej kheej geometry. Tej yam ncaj kab los ntawm qhov point P ntawm a kheej kheej yog los ntawm txhais lub voj voog loj. Ob lub voj voog loj yuav sib tshuam ntawm ob lub ntsiab lus ntawm ib ntu Euclidean, uas yog txoj kab uas hla kheej kheej . Tsis muaj sib npaug hauv kheej kheej geometry.

Tsis tas li ntawd, cov kab sib txuas puas tuaj yeem cuam tshuam? Hauv qhov projective geometry, ib khub ntawm kab ib txwm kev sib tshuam ntawm qee qhov taw tes, tab sis kab sib npaug tsis txhob sib tshuam nyob rau hauv lub dav hlau tiag. Cov kab ntawm infinity yog ntxiv rau lub dav hlau tiag. Qhov no ua tiav lub dav hlau, vim tam sim no parallel kab sib tshuam nyob rau hauv ib qho chaw uas lies ntawm lub kab ntawm infinity.

Tsis tas li ntawd, muaj pes tsawg kab sib luag nyob hauv hyperbolic geometry?

Lej Tom Qab Qhov Tseeb: Ob kab hais tias yog thaum uas tig mus yog lawv tsis sib tshuam. Hauv Euclidean geometry , muab a kab L muaj raws nraim ib kab dhau ib yam muab point Pthas yog thaum uas tig mus rau L ( thaum uas tig mus postulate). Txawm li cas los nyob rau hauv hyperbolic geometry , muaj infinitely ntau kab sib npaug rau L hla P.

Vim li cas ho tsis cov kab sib luag nyob hauv elliptical geometry?

Nyob rau hauv spherical Geometry Parallel kab TSIS TAU EXIST . Hauv Euclidean geometry ib postulate muaj nyob hais tias los ntawm ib qho point, muaj muaj nyob tsuas yog 1 thaum uas tig mus rau ib tug muab kab . Yog li ntawd, Parallel kab tsis txhob muaj txij li txhua lub voj voog loj ( kab ) los ntawm ib qho taw tes yuav tsum hla peb lub voj voog qub.

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