Faitatau ki te waka rererangi: te huru me ngā āhuatanga

Whakarara ki te rererangi, ko te tuatahi ka puta he ariā i roto i te āhuahanga Euclidean mō neke atu i te rua mano tau ki muri.

āhuatanga Main o āhuahanga puāwaitanga

Ko te whanau o tenei ako pūtaiao e pā ana ki mahi rongonui o te philosopho Kariki onamata Euclid, e tuhituhi i roto i te toru o nga BC rau, te buka iti "Elements". Wehea ki kotahi tekau ma toru ngā pukapuka, "Elements" Ko te paetae teitei o pāngarau tahito katoa me ata whakaatu i te haapiiraa tumu e pā ana ki te āhuatanga o tau plane.

whakatakoto huru Classical o rererangi whakarara i rite whai: kia huaina ai e rua rererangi whakarara ki te whai ratou ia kahore ngā noa. Tenei te pānui i mahi postulate tuarima Euclidean.

Āhuatanga o rererangi whakarara

Ko te āhuahanga Euclidean o taratahi, te tikanga e rima:

• Ko te taonga, ko te tuatahi (me whakamārama ana whakarara ki te waka rererangi o ratou mana āhua). Na roto i te wāhi kotahi, e takoto ki waho o tenei manureva ngā, ka taea e tatou te utu kotahi me kotahi anake pereni whakarara

• Ko te taonga tuarua (mohiotia hoki rite ngā āhuatanga triplicate). I roto i te take i reira e whakarara ki te faatura ki te toru o nga rererangi e rua, i waenganui ia ratou, e faitatau hoki ratou.

• rawa Tuatoru (i roto i te kupu atu, e kiia ana ko te raina rawa rīpeka whakarara ki te rererangi). Ki te whakawhiti rārangi wehe tika tangohia tetahi o enei rererangi whakarara, ka whiti i te reira me tetahi atu.

• rawa te wha (taonga o ngā rārangi tika whakairo i runga i rererangi faitatau ki ia atu). A, no te whakawhiti e rua rererangi whakarara te tuatoru (i tetahi koki), me o ratou aho o te whakarara pūtahitanga

• rawa te rima (te taonga e whakaahua ana i te wāhanga ngā o rārangi tika whakarara, e takoto i waenganui i nga rererangi faitatau ki ia atu). Ko te wāhanga o te rārangi whakarara, e E kopakia ana i waenganui i rua rererangi whakarara tika rite.

Whakarara ki te rererangi i roto i Euclidean-kore āhuahanga

Ko te huarahi pērā i roto i ngā te āhuahanga o Lobachevsky me Rēimāna. Ki te whakatinanahia Euclidean āhuahanga te i runga i nga wāhi papatahi, ka Lobachevsky i roto i ngā wāhi tōraro kōpiko (niao ki hoatu noa), i Rēimāna kitea e te reira i ona iteraa i roto i ngā wāhi pai kōpiko (i roto i te kupu atu - ngā wāhi). He he he tirohanga stereotypical rawa noa e Lobachevsky whakarara ki te (rārangi, me te hoki) pereni whakawhiti. Heoi, e kore te mea pono tenei. He pono e pā ana te whanau o te āhuahanga pūwerewere i ki te tohu o te postulate tuarima o Euclid me huri whakaaro ki runga reira, engari te tikanga te whakamāramatanga rawa o rererangi whakarara me ngā rārangi tika e kore e taea e ratou te whakawhiti ranei Lobachevsky ranei Rēimāna, i roto i nga mea katoa ngā wāhi e whakatinana ratou. He huringa o te ngakau, me te kupu, ko te rite whai. I roto i te wahi o te postulate e taea te unu kotahi anake rererangi whakarara i roto i te wāhi e kore i runga i te waka rererangi i homai, ka haere mai tetahi waihanga: i roto i te wāhi e kore e e takoto i runga i tenei waka rererangi ngā taea te tango e rua, i te iti rawa, tika, e te hunga i roto i kotahi rererangi ki tenei, me te kore e whiti i te reira.