ibhotile ye-klein

ibhotile ye-klein

Kwi-topology, isebe lemathematika, ibhotile ye-klein ngumzekelo womphezulu ongafikelelekiyo. Yi-dimensional-dimensional manifold apho isixokelelwano singenako ukuchazwa rhoqo ukumisela ii-vectors eziqhelekileyo. Ngokungacwangciswanga, ngumhlaba ocalanye ukuba, ukuba ugqithisiwe, unokulandelwa umva kwimvelaphi njengoko umhambi ejika.

Kweli nqaku siza kukuxelela yonke into okufuneka uyazi malunga nebhotile ye-Klein, iimpawu zayo kunye nezinto ezinomdla.

Iimpawu eziphambili

happy klein

Ezinye izinto ezinxulumene non-orientable ziquka Möbius imicu kunye nenqwelomoya yokwenyani. Imicu yeMobius yimigangatho eqingqiweyo, ngelixa iibhotile zeKlein zingenamida. Xa kuthelekiswa, ingqukuva yindawo enokuqhelaniswa ngokungenasiphelo. Ibhotile yeKlein yaqala ukuchazwa ngo-1882 yingcali yezibalo yaseJamani uFelix Klein.

Ingqokelela yeebhotile zeglasi zeKlein ezivuthelwa ngesandla ziboniswa kwiMyuziyam yeSayensi eLondon, ebonisa iinguqulelo ezininzi kulo mxholo we-topological. Iibhotile zivela kwi-1995 kwaye zenziwe ngu-Alan Bennett kwimyuziyam.

Ibhotile yeKlein ngokwayo ayigqithwanga. Nangona kunjalo, kukho indlela yokubona ibhotile ye-Klein equlethwe kwimilinganiselo emine. I-self-intersections inokususwa ngokudibanisa i-dimension yesine kwindawo ye-three-dimensional space. Tyhila ngobunono icandelo letyhubhu eliqulathe indlela yokuhlangana ngaphandle kwesithuba soqobo se-3D ecaleni komlinganiselo wesine. Umzekeliso oluncedo kukuqwalasela igophe elinqumla inqwelomoya. I-self-intersections inokususwa ngokuphakamisa imicu kwinqwelomoya.

Ukucacisa, masithi sithatha ixesha njengenqanaba lesine. Cinga ngendlela yokwakha igrafu kwisithuba sexyzt. Umfanekiso oqhotyoshelweyo ("I-Evolution ngokuhamba kwexesha...") ibonisa inguqu eluncedo yalo mfanekiso. Kwi-t = 0, udonga luhluma kwindawo ethile kufuphi "ne-intersection." Emva kokuba inani likhule libe likhulu, inxalenye yokuqala yodonga yaqala ukuhla, yanyamalala njengekati yaseCheshire, kodwa eshiya ngasemva uncumo lwakhe olubanzi. Xa umphambili wokukhula ufikelela apho ihlumelo likhona, akukho nto inqumlayo kwaye ukukhula kugqibelele ngaphandle kokugqobhoza isakhiwo esikhoyo.

Iimpawu zeebhotile zeKlein

ibhotile yezibalo zeklein

I-Klein flask yindawo engenakuqhelaniswa ne-non-orientable ehlala iboniswa njengeflaski enentamo ende enentamo egobileyo egqithiswa ukusuka ngaphakathi ukuze ivuleke njengesiseko. Ubume obukhethekileyo bebhotile yeKlein ithetha ukuba inobuso obunye kuphela: ingaphakathi lilingana nangaphandle. Ibhotile ye-Klein ayinakho ukubakho kwisithuba se-Euclidean ene-dimensional-ntathu, kodwa umboniso ovuthela iglasi unokusinika ulwazi olunomdla. Le ayisiyobhotile ye-klein yokwenyani, kodwa kuyanceda ukuba nomfanekiso-ngqondweni wento eyayicingwa yingcali yezibalo yaseJamani uFelix Klein xa weza nombono webhotile yeKlein.

Ukuba isimboli sincanyathiselwe kwindawo enokuqhelaniswa nayo, njengangaphandle kwendawo, iya kugcina i-orientation efanayo kungakhathaliseki ukuba uyihambisa njani. Ubume obukhethekileyo bebhotile ye-Klein ikuvumela ukuba usilayidi isimboli kwiindlela ezahlukeneyo: inokuvela njengomfanekiso wesibuko sayo kumphezulu ofanayo. Le propati yebhotile ye-Klein yenza kube nzima ukuyiqhelanisa.

Ibhotile yeKlein ithiywe ngengcali yezibalo yaseJamani uFelix Klein. Umsebenzi kaFelix Klein kwimathematika wamenza waqhelana kakhulu nemicu kaMöbius. Umcu we-Möbius liphepha elijikeleziswa isiqingatha sokujika kunye nokudibanisa ekupheleni ukuya ekupheleni. Le twist ijika iphepha eliqhelekileyo libe yindawo engajongekiyo. UFelix Klein waqiqa ngelithi ukuba udibanisa imicu emibini yeMöbius ecaleni kwayo, uya kudala uhlobo olutsha lomphezulu oneempawu ezifanayo ezingaqhelekanga: umphezulu weKlein okanye ibhotile yeKlein.

Ibhotile ye-Klein ichazwa njengendawo engajongekiyo kuba ukuba isimboli sincanyathiselwe kumphezulu, siyakwazi ukutyibilika ngendlela enokuthi ibuyele kwindawo efanayo nomfanekiso wesipili.

Ngaba ibhotile yeKlein inokwenziwa ebomini bokwenyani?

ibhotile engapheliyo

Ngelishwa kuthi thina bafuna ukubona iibhotile zeKlein zokwenyani, azinakwakhiwa kwindawo ye-Euclidean enemigangatho emithathu esihlala kuyo. Qhagamshela imiphetho yezintlu ezimbini zeMöbius ukwakha iflaski yeKlein yenza iindlela zokuhlangana ezingekhoyo kwiimodeli zethiyori. Imodeli yokwenyani yebhotile yeKlein kwafuneka ihambe phezu kwayo xa intamo isuka ecaleni. Oku kusinika into engeyiyo ibhotile yeKlein esebenzayo, kodwa kusemnandi ukuyihlola.

Ekubeni iiflaski ze-Klein zabelana ngeempawu ezininzi ezingaqhelekanga kunye nemicu ye-Möbius, abo bethu bangenalwazi lunzulu lwezibalo ukuze baqonde ngokwenene ukuntsonkotha kweeflasks ze-Klein banokuzama imicu ka-Felix Klein ka-Moebius Ukufumana okuthakazelisayo.

Umphezulu weKlein

UClifford Stoll yindoda esemva koyilo lwebhotile enkulu yeKlein, enobude obuyi-106cm, 62,2cm ububanzi kunye ne-163,5cm kwisangqa. Yakhiwa yiKildee Scientific Glass phakathi kuka-2001 kunye no-2003.

Igama lokuqala le nto yayingekho i-Klein Flask (i-German Kleinsche Flasche), kodwa i-Klein Surface (i-German Kleinsche Fläche). Ukuguqulelwa kwento yokuqala yereferensi ukusuka kwisiJamani ukuya kwisiNgesi amagama abhidekile. Ngenxa yenkangeleko ye-3D yonikezelo olukhumbuza ibhotile, akukho mntu waqaphela ibug.

Ukuba sahlulahlula ibhotile ye-Klein kubini kunye neplani yayo yokulinganisa, senza imicu emibini yeMöbius, nganye ibe ngumfanekiso wesibuko somnye (ngokungathi omnye ujonge esipilini). Emva koko, ibhotile ye-Klein ngumzekelo womgangatho ongenakufikeleleka, njengoluhlu lweMöbius. Ayinamsebenzi wumbi ngaphandle kokuyimela. Imiphezulu eqhelanisiweyo okanye engajongekiyo ziingqikelelo ze-topological. Yomibini yimizekelo yomgangatho ocalanye, kuba ayihambelani. Umlingo wayo ulele ekukwazini ukuyigubungela ngokupheleleyo ngendlela eqhubekayo ngokupheleleyo, egubungela zonke iingongoma eziyilayo.

Ndiyathemba ukuba ngolu lwazi unokufunda ngakumbi malunga nebhotile ye-Klein kunye neempawu zayo.


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