Klein mole: He aha ia mea

Geometric mea, hope kapaia "Klein hue", i ho'ākāka 'ia ma mua i loko o 1882 ma ka German mathematician Feliksom Kleynom. He aha ka mea? Keia mea (a oi kaʻoi loa, ka geometric a me ka topological ili) aole wale mea,ʻaʻole i loko o mākou ekolu-dimensional honua. A pau i nā ana hoʻohālike i mea no ka kuai i loko o ka haawina pōʻeleʻele loa, i ka nana aku, akā, e hāʻawi mai ai uuku manaʻo e pili ana i ka mea Klein mole he. No ka nui mōakaaka, ka mea, ua ho'ākāka 'ia e like keia: hoi i noonoo ai i ka hue me ka'ā'ī lōʻihi loa. A laila, mentally e ia lua elua: hoʻokahi i loko o ka pā, a me ka lua ma ka lalo. A laila, lena i ka'ā'ī, hookomo ia i loko o ka puka i loko o ka pā pōhaku, a mawaho ma ke auoiaea puka i loko o ka lalo. Ke kūpono kiʻi, a me ka wānana o ka mea e e eha-dimensional kahua, a mea he Klein hue maoli, ma keia ekolu-dimensional ka lewa.

Klein omole hōʻikeʻano Hawaiʻi o ka makemakika hua'ōlelo a me nā papakuhikuhi e ole e olelo aku i kekahi mea i ka nonprofessional. He nui ka poe e panai ai i kēia ho'ākāka 'ana: Klein hue - Ua orientable lokomaikaʻi he (' ole 'ilikai) i loaa i ka helu o ka waiwai. Ma hope o ka hua'ōlelo "waiwai" oe ke kūkulu i ka lōʻihi moʻo iloko olaila o trigonometric oihana, helu, a me ka Helene, a Roma palapala. Akā, ka mea hiki wale nō i hookahuli ai i ka untrained kanaka, ua loaa i ka manaʻo o ka mea i ka wānana o na hue i loko o ka ekolu-dimensional ka lewa.

Mea mea: ka inoa "Klein hue", keia mea ua loa paha no i ka hewa a me ka misspelling unuhi. Ka nui, e hoike i Klein, i loko o kona manao paa ia e hoʻohana i ka olelo Fläche,ʻo ia hoʻi, "ili honua" i loko o Kelemānia. Ma ka "huakai" mai Kelemania, a hiki i nā aupuni i ka olelo iho i loko o like ma Flasche kākau (mole). Alaila, ua hoi aku la i ka manawa a hiki i ka aina o ke kumu i loko o ka hou, Hoʻololi 'palapala, ae, a noho ai ka wa pau ole.

No ka nui 'o Puʻohala (oi' epekema fiction kākau) ikea uʻi i ka manawa "Klein mole". Kona hoʻohana me he kaila, a me kekahi manawa i ka papa kuhikuhiE "maka" i ka hoailona o ka " 'imi naʻauao" fiction. Oia, no ka mea hoike, o ka moʻolelo "Ka Last Illusionist", no a hiki i ka peni o Bruce Elliot. Ma ka moʻolelo o ke kilo i ka hope crushes me kona hoa, ka poe i hana ia paena me ka Klein hue eha-dimensional. E koho i ka hue illusionist, a koe hapalua submerged i loko o laila. E like me ka mea kākau, hiki ole e uhaʻiʻia kēia hue me ā 'inoʻino kekahi kahi. No laila, inā paha ka mea, 'o maoli - ole i kekahi ke olelo mai. Ma ka liʻiliʻi loa makemakika, a hiki o hiki mai pane i kēia nīnau, ka mea, ua ole e pāhaʻohaʻo ana, ia mea pili 'ole i ka' epekema.

Kēlā wā i kēia wā pela i Klein hue no Promotional hana hue waina. Eia naʻe, e hana pela i kekahi hue mea technically paʻakikī ke aniani, keia pono luna-papa aniani wau. Nolaila, ia mea he pipiʻi, a ua i hoʻohana infrequently. A ikea ai o ka 'ike loea hou a me ka-i? Iecaianoaaiiuo o? Iecaianoaaiiuo o na hue ma luna o ke kahe' aʻole ole e ke aloha, no ka mea, e hoopai auanei hana ano o ka hoʻopiha omole me ka wai ( 'aneʻi, hoi, eia complexities). A me ka manao o ka strangeness a me His e koke, eia ka hana a he leo ACCIDENTAL waina, mai kekahi hue waina makaaniani.