Klein ibhodlela: ukuthi kuyini

into e-Jomethri, kamuva owabizwa ngokuthi "Klein ibhodlela", labonakala okokuqala ezichazwe 1882 by sezibalo German Feliksom Kleynom. Kuyini lokhu? Lokhu into (noma ngaphezulu ngokunembile, ebusweni be-Jomethri topological) lapho nje alikho izwe lethu ngakuthathu. Zonke amamodeli yilezi ukudayiswa ezitolo isipho, bheka, kodwa linikeza umqondo kancane ngalokho kuyinto ibhodlela Klein. Ukuze okuvula, sichazwe kanje: cabanga ibhodlela nge intamo eside kakhulu. Khona-ke ukwenza ngengqondo ke izimbobo ezimbili: elilodwa odongeni, kanti eyesibili ezansi. Khona-ke bend entanyeni, ufaka bayifaka nanso imbobo ogangeni futhi olubonakalayo ngembobo okukhipha phansi. Into okuholela kanye lelivakalako into kuyoba isikhala ezine-ntathu, okuyinto ngempela Klein ibhodlela, kule isikhala ezintathu-ntathu.

Klein incazelo ibhodlela ulimi imigomo zezibalo kanye namafomula ngeke uthi yini nonprofessional. Abaningi bayokuthi ukwanelisa le ncazelo: Klein ibhodlela - kuyinto ezininginingi orientable (noma ngaphezulu) ukuba eziningana izakhiwo. Ngemva igama elithi "umhlaba" ungakha uhide ehlanganisa imisebenzi Trigonometric, izinombolo, isiGreki izinhlamvu wamaRoma. Kodwa kungaba kuphela ukudida umuntu ongaqeqeshiwe, sengisilethe umbono kuyini projection amabhodlela endaweni ezintathu-ntathu.

Eqinisweni ezithakazelisayo: Igama elithi "Klein ibhodlela", le nto kwaba cishe ngenxa yephutha noma Ukupela notolika. Iqiniso lokuthi Klein abase bekhulile, ekuzimiseleni kwakhe ukusebenzisa izwi Fläche, okungukuthi, "ubuso" ngesiJalimane. Esikhathini "uhambo" eJalimane aya kwamanye amazwe ukuthi izwi siguqulelwa ezifanayo Flasche ngokubhala (ibhodlela). Khona-ke leli gama liye wabuyela ezweni lendabuko entsha, ifomu Ushintshe, yebo futhi waqhubeka phakade.

Ukuze abaculi abaningi (ikakhulukazi isayensi abalobi emaciniso) uvele ezikhangayo igama elithi "Klein ibhodlela". Ukusetshenziswa Its njengenhlangano ngemfanelo, futhi ngezinye izikhathi main "ubuso" kwakuzoba uphawu lokuthi "nongqondongqondo 'eqanjiwe. Enjalo, isibonelo, indaba "The Last Illusionist", okuqondene ngothi Bruce Elliot. Ngo indaba umsizi Bili ubulala nge abavikela bakhe abenza namaqhinga nge ezine-ntathu Klein ibhodlela. Sithathe illusionist ibhodlela futhi ihlezi isigamu kwamanzi kulo. Ngokusho umbhali, lokhu ibhodlela ayikwazi ngobugebengu ngaphandle kokulimaza okuqukethwe. Ngakho noma ngabe empeleni - akekho ongasho. Okungenani wezibalo, okungase ukuphendula mhlawumbe lo mbuzo, it is hhayi onemibuzo, ke asihlobene isayensi.

Ngezikhathi ezithile ngokukhethekile Klein amabhodlela zokutusa bevalela iwayini. Nokho, ukwenza igabha ngokomthetho nzima ingilazi, lokhu kudinga eseqophelweni eliphezulu ingilazi Blower. Ngakho-ke, ngempela eqolo futhi isetshenziswa njalo. A ukuhlolwa ubuchwepheshe kanye ukukhiqizwa ukukhiqizwa amabhodlela ezinjalo ku ukugeleza akwenzi mqondo, ngoba uma kudinga umsebenzi indlela yokugcwalisa amabhodlela nge uketshezi (lapha, futhi, kukhona eziyinkimbinkimbi). Futhi umuzwa strangeness futhi igugu uzoshesha ngelinye ngokuphazamisa iwayini ngephutha kusuka ibhodlela lewayini izibuko.