Ibhotile Klein: yintoni

into Geometric, kamva ngokuba "ibhotile Klein", echazwe okokuqala ngo-1882 yi sezibalo waseJamani Feliksom Kleynom. Yintoni na? Le into (okanye ngaphezulu ncam, umphezulu zeijiyometri topological) apho yinto nje kwihlabathi lethu-ntathu. Zonke imifuziselo ukuba ezithengiswayo ezivenkileni isipho, jonga, kodwa abazi malunga yintoni ibhotile Klein. Ecacileyo omkhulu, nto ichazwa ngolu hlobo: zicamange ibhotile kunye nentamo ende kakhulu. Ngoko ngengqondo kube imingxuma ezimbini: omnye eludongeni, kwaye eyesibini ezantsi. Emva koko Wayitsala entanyeni, ukuyifakela umngxuma eludongeni kwaye ngokwangaphandle ngokusebenzisa imveliso umngxuma ezantsi. Into ngenxa kunye ezayo le into aya kuba isithuba-mbini amane, nto leyo ibhotile wokwenene Klein, kule isithuba-ntathu.

Klein inkcazelo Ibhotile ulwimi amagama zemathematika kunye neefomula abayi kuthi nantoni na ingumsebenzi ongenabugcissa. Abaninzi baya ukwanelisa le nkcazelo: Klein ibhotile - bayinto orientable (okanye umgangatho) ukuba inani iipropati. Emva kokuba elithi "propati" ungakha uthotho elide eziquka netrigonometri, amanani, nangesiGrike kunye neeleta zamaRoma. Kodwa kungaba ukudida kuphela umntu abangaqeqeshelwanga, ndasisa sinengcamango yokuba yintoni na ezayo iintsuba kwindawo-ntathu.

Interesting Eneneni: Igama "ibhotile Klein", le nto kakhulu mhlawumbi ngenxa imposiso okanye Ukupela itoliki. Inyaniso yokuba Klein, xa ukuzimisela kwakhe ukusebenzisa igama Fläche, oko kukuthi, "ubuso" in German. Xa "uhambo" baseJamani kwamanye amazwe ukuba igama similise efanayo Flasche ukubhala (ibhotile). Ngoko ke ixesha yabuyela kwilizwe imvelaphi ngendlela entsha, iguqulwe, ewe wahlala njalo ngonaphakade.

Amaciko ezininzi (ingakumbi ababhali yesayensi) wabonakala enomtsalane elithi "ibhotile Klein". ukusetyenziswa kwayo lophawu, yaye ngamanye amaxesha omkhulu othi "ubuso" waba ngumqondiso yamabali "ingqondo". Ezinjalo, umzekelo, ibali, "Le Illusionist Last", ukubayinxalenye lulusiba uBruce Elliot. Kwibali umncedisi Bili xa ezitshayela kunye umxhasi wakhe, owenza amaqhinga ngebhotile Klein-mbini emine. Sithathe le illusionist ibhotile sihlale isiqingatha batywiliselwe kuyo. Ngokutsho umbhali, ebhotileni singenakwaphulwa ngaphandle kokonakalisa imixholo. Ngoko ke, enoba ndikuxelela - akukho mntu uthi. Ubuncinane imathematika, nto leyo ukuphendula lo mbuzo, akuyi eliyinkohla, kuba awungeni kwinzululwazi.

Ngamanye amaxesha ngokukodwa wenza iibhotile Klein ngeenjongo zokukhuthaza Ukuvalela iwayini. Noko ke, ukuba lalinawo loo manzi kuba ngendlela kunzima iglasi, oku kufuna top-class yeglasi blower. Ngoko ke, oko eninzi kakhulu yaye usetyenziswa kungeyonto ayenza rhoqo. A kuvavanyo ubuchwepheshe kunye nokuveliswa kwemveliso Iibhotile ezinjalo kwi flow akwenzi ngqiqo, kuba oko kwakuya kufuna umsebenzi indlela yokuzalisa iibhotile kunye ulwelo (apha, kananjalo, kukho nobunzima). Kunye nokuziva ngokungaqheleki kunye entsha ngokukhawuleza uya andigweqe inkxamleko iwayini ngengozi evela ibhotile iiglasi zewayini.