Wāhi Euclidean: definition, āhuatanga, tohu

Ahakoa i roto i te kura, kua whakaurua ngā ākonga katoa ki te ariā o "āhuahanga Euclidean", nga tikanga matua o e E arotahi ana a tawhio noa te torutoru axioms e hāngai ana i runga i ngā āhuatanga āhuahanga pērā i ngā, rererangi, kaupapa rārangi tika. Katoa o ratou ngatahi hanga te mea e mohiotia kua e te wā "wāhi Euclidean".

Euclidean wāhi, te whakamāramatanga o i hāngai te i runga i te tūranga o te whakareatanga scalar o pere ko te take motuhake o te rārangi (affine) wāhi, e makona he maha o ngā whakaritenga. Tuatahi, ko te hua i roto o pere tino hangarite, arā te vector ki taunga (x: y) i roto i ngā o te rahinga he ōrite ki te pere ki te taunga (y: x), engari te ritenga i roto i te aronga.

Tuarua, i roto i te hui i hanga te hua scalar o te pere ki ano, ka kia pai te hua o tenei mahi. e kia te okotahi anake te take, ina he rite ki te kore te tīmatanga, me te mutu taunga o tenei pere: i roto i tenei take, me ona hua ki ano te taua, ka kia kore.

Te toru, i reira he he tohatoha he hua scalar, arā, te taea o whakawhānui tetahi o ona taunga i runga i te moni o te uara e rua e kore e e uta e tetahi huringa i roto i te hua whakamutunga o te whakareatanga scalar o pere. I te pae hopea, i roto i te tuawha, i roto i te whakarea o pere i te taua uara tūturu o ratou hua scalar te hoki nui haere e te tauwehe taua.

I roto i taua take, ki te enei tikanga katoa e wha, tatou e nehenehe e humarie mea e ko te wāhi Euclidean tenei.

wāhi Euclidean i te wāhi mahi o te tirohanga, e taea te āhuatanga e te tauira motuhake e whai ake nei:

1. Ko te take māmā - ko te wātea o te huinga o pere ki etahi o nga ture taketake o āhuahanga, te hua scalar.
2. whiwhi wāhi Euclidean te i roto i te take, ki te e pere tikanga matou he tetahi huinga fakataimí o tau tūturu me te tātai i homai, whakaahua ratou moni scalar hua ranei.
3. he tika te take motuhake o te wāhi Euclidean ki ite i te kore wāhi pera-ka karanga, i whiwhi nei te i roto i te kaupapa e te roa o e rua pere scalar ko te kore.

wāhi Euclidean he maha o ngā āhuatanga motuhake kua. Tuatahi, kia mau ai take scalar mo e rua te taiapa tuatahi, me te take tuarua o te hua scalar, te hua o tenei e kore e amohia e tetahi huringa. Tuarua, me te mema tuatahi i te tohatoha o te hua scalar, mahi me Distributivity huānga tuarua. I tua atu ki te moni scalar o pere, he wahi i roto i te take o te tangohanga o pere Distributivity. I te pae hopea, tuatoru, i roto i te whakarea scalar o te pere ki te kore, te hua ka hoki kia kore.

Ko te kupu, ko te wāhi Euclidean - ko te ariā āhuahanga tino nui whakamahia mō te whakaoti rapanga ki te whakaritenga tahi o pere whanaunga ki tahi i te tahi, mo te āhuatanga o i whakamahia taua ariā kei te rite te hua i roto.