Okhunye okukhambisana indiza: isimo nezakhiwo

Okuhambisana indiza ngumqondo bavela okokuqala geometry Euclidean iminyaka engaphezu kwezinkulungwane ezimbili edlule.

izici eziyinhloko geometry classical

Ukuzalwa lesi siyalo yesayensi elihlobene ne imisebenzi abadumile sefilosofi yamaGreki asendulo Euclid, owabhala BC, leli pheshana "Imisuka" lesithathu leminyaka. Ihlukaniswe yaba ezincwadini eziyishumi nantathu, "Imisuka" impumelelo kunazo zonke wezibalo lasendulo futhi uchazwe naletintfo eliyisisekelo elihlobene ne izakhiwo indiza izibalo.

isimo Classical izindiza parallel ukuthi zavela ngale ndlela: izindiza ezimbili kusengathiwa parallel uma ngamunye abanalo amaphuzu ezivamile. Lokhu ukufunda Euclidean yesihlanu postulate zabasebenzi.

Izakhiwo izindiza parallel

I Euclidean geometry ka elingalodwa, ngokuvamile amahlanu:

• Impahla ungowokuqala (futhi kuhambisana indiza uchaza ulimi lwawo luhluke). Ngokusebenzisa iphuzu elilodwa, okuyinto amanga ngaphandle kwalo indiza ethile, singathola esisodwa futhi esisodwa kuphela indiza parallel

• Eyesibili impahla (owaziwa nangokuthi izakhiwo triplicate). Esimweni lapho izindiza ezimbili kukhona parallel mayelana eyesithathu, phakathi kwabo, basuke ibuye zifana.

• Impahla ingeyesithathu (ngamanye amagama, ibizwa ngokuthi umugqa impahla intersecting kuhambisana indiza). Uma kuthathwe umugqa eceleni ngqo kweqa esinye salezi izindiza okufanayo, kuyoba ukuwela nomunye.

• impahla Okwesine (impahla imigca lecondzile ezibaziweyo ezindizeni zifana kuya komunye nomunye). Lapho izindiza ezimbili okuhambisana aphambana wesithathu (kusuka kunoma iyiphi i-engeli), futhi umugqa kwabo empambana kokuba parallel

• impahla wesihlanu (impahla echaza izingxenye ezahlukene imigqa parallel iqonde, okuyinto amanga phakathi izindiza zifana kuya komunye nomunye). Amazenge imigca parallel, okuyinto okuvalelwe phakathi izindiza ezimbili okuhambisana ngempela alinganayo.

Okuhambisana indiza e-non-Euclidean geometry

le ndlela yokukhuluma ikakhulukazi geometry ka Lobachevsky futhi Riemann. Uma Euclidean geometry ukusebenza izikhala flat ke Lobachevsky ezikhaleni omubi lwalugobile (engonxantathu nje ukubeka), kuyilapho Riemann ithola Ukuqaphela yayo izikhala kahle lwalugobile (ngamanye amagama - izindawo). Kukhona umbono ovamile kakhulu stereotypical ukuthi Lobachevsky kuhambisana indiza (futhi umugqa) aphambana. Nokho, lokho akulona iqiniso. Ngempela ukuzalwa geometry ephambene kwakuhambisana nezinga eliphansi ubufakazi postulate Euclid sika yesihlanu nokushintsha ukubukwa kuso, kodwa kakhulu incazelo izindiza kuqondane and imigqa eqondile lisho ukuthi abakwazi ukuwela noma Lobachevsky noma Riemann, nganoma iluphi izikhala bona ziyasetshenziswa. A bashintshe izinhliziyo zabo futhi okubekwe ngayo kanje. Esikhundleni postulate ukuthi indiza parallel eyodwa kuphela kungenziwa shi ngokusebenzisa iphuzu hhayi indiza unikezwa, kwafika nomunye ekwakhiweni: ngokusebenzisa iphuzu ukuthi akuncikile kule indiza ethile kungathatha ezimbili, okungenani, iqonde, enisezweni omunye indiza nale futhi ungaweqi ke.