Klein pounamu: he aha te mea te reira

ahanoa āhuahanga, i muri i huaina "pounamu Klein", i whakaahuatia tuatahi i roto i 1882 i te mathematician Tiamana Feliksom Kleynom. He aha te mea te reira? Tenei ahanoa (atu ïa, te mata āhuahanga me topological ranei) i reira e kore te mea i roto i to tatou ao e toru-ahu noa. nga tauira katoa e te hunga hoki hoko i roto i te toa homai, i te titiro, engari homai iti whakaaro e pā ana ki te mea ko te pounamu Klein. Hoki te mārama nui, kua whakaahuatia te reira rite tenei: whakaaro he pounamu ki te kaki rawa roa. Na hinengaro hanga reira rua e rua: kotahi i roto i te taiepa, me te tuarua i te raro. Na ka whakapiko i te kaki, kōkuhu reira ki te poka i te taiepa, me te waho i roto i te poka putanga i roto i te raro. Ko te ahanoa hua me te ngä o te ahanoa ka hei wāhi-ahu wha, i te mea he pounamu Klein tūturu, i roto i tenei wāhi e toru-ahu.

Klein whakaahuatanga pounamu reo o ngā pāngarau me ngā tātai e kore e mea tetahi ki te nonprofessional. He tokomaha e makona tenei definition: Klein pounamu - he maha orientable (ranei mata) he maha o ngā āhuatanga. I muri i te kupu "taonga" ka taea e koe te hanga i te raupapa roa arā, o ngā pānga pākoki, tau, a Kariki me pukapuka Roma. Otiia anake e taea whakapoauau reira te tangata mohoao, kua ka te whakaaro o te mea ko te ngä o te ipu i roto i te wāhi e toru-ahu.

meka Interesting: Ko te ingoa "pounamu Klein", ko tenei ahanoa tino pea e tika ana ki te hapa Takikupu ranei kaiwhakamaori. Ko te meka e Klein, i roto i tona faaotiraa ki te whakamahi i te kupu Fläche, e ko, "mata" i roto i te German. I roto i te "ara" i Tiamana ki ētahi atu whenua puta taua kupu ki rite i roto i Flasche tuhituhi (pounamu). Na kua hoki te wā ki te whenua o te take i roto i te hou, puka whakarerekē, ae, ka noho pera ake.

Hoki toi maha (rawa pūtaiao kaituhi pakimaero) puta ātaahua te wā "pounamu Klein". Ko tōna whakamahi hei huanga, a te tahi mau taime te "mata" matua ko te tohu o "hinengaro" pakimaero. Taua, mo te tauira, te kōrero "Ko te Illusionist Last", no ki te pene o Bruce Elliot. I roto i te kōrero o te kaiāwhina o te makutu wawahi ki tona kaiwhakaruruhau, nei i tinihanga ki te pounamu Klein-ahu wha. Tangohia ake te illusionist pounamu me tonu hawhe ngaro i roto i reira. E ai ki te kaituhi, e kore e taea te whakakahore tenei pounamu kopiro ano i nga tirotiro. Na ahakoa te reira mau - e kore tetahi e taea te mea. I te iti rawa te pāngarau, pea i taea e nei te whakahoki kupu tenei pātai, e kore e manganga reira, he reira kotiti ki te pūtaiao.

Taime rawa hanga ipu Klein mō ngā take whakatairanga pātara waina. Heoi, ki te hanga he tū uaua ki te karaihe i te pounamu taua, titau tenei runga-te piha pupuhi karaihe. Na reira, ko te reira tino utu me te te whakamahia pinepine. E kore te whakamātautau o te hangarau, me te hanga o te hanga o taua ipu i runga i te rere hanga tikanga, no te mea e rapu utu i te reira tikanga mahi o te whakakī ipu ki wai (konei, rawa, i reira he hōhonutanga). Na te mana'o o te strangeness me minamina ana ka hohoro mamingatanga raruraru waina kōpeka i te pounamu o mōhiti waina.