Ngokunxusene moya: meko kunye neempawu

Eyayingqalene moya a ingqiqo yokuqala ukuvela kwi geometry Euclidean iminyaka engaphezu kwama engamawaka amabini eyadlulayo.

iimpawu eziphambili geometry lakudala

Ukuzalwa olu qeqesho zenzululwazi ezinxulumene nemisebenzi adumileyo sobulumko yamandulo yamaGrike Euclid, owabhala le BC ngenkulungwane yesithathu, iphamflethi "Elements". Yahlulwe iincwadi ezilishumi, "Elements" yeyona mpumelelo iphezulu kuwo onke nemathematika yamandulo ukumcacisela ngokuchane iinkolelo ezibalulekileyo ezinxulumene iimpawu yamanani moya.

imeko Classical iinqwelo-moya parallel laliqulunqwe ngolu hlobo lulandelayo: moya ezimbini kubizwa ngaxeshanye ukuba nganye ke akukho manqaku eqhelekileyo. Oku funda Euclidean yabasebenzi postulate wesihlanu.

Iimpawu moya parallel

I Euclidean geometry angawodwa, ngokuqhelekileyo ezintlanu:

• Lo mhlaba ke lokuqala (kwaye ichaza eyayingqalene moya lwabo). Ngokusebenzisa ingongoma enye, edulusele ngaphandle kwale moya ethile, sinokwenza omnye kuphela moya ukufana

• Ipropati yesibini (eyaziwa ngokuba iipropati triplicate). Kwimeko apho iinqwelomoya babini ngaxeshanye kunye malunga wesithathu, phakathi kwabo, ukuba ibuye zifana.

• impahla lesithathu (ngamanye amagama, ibizwa ngokuba umgca ipropati ezidibanayo eyayingqalene moya). Ukuba ithathwa umgca ngokwahlukileyo ngqo iqabele enye yezi iinqwelomoya parallel, uya kuwela nenye.

• impahla wesine (impahla imigca ethe ngqo wazikrola moya kufana kwesinye). Xa moya ezimbini ngaxeshanye phambana wesithathu (nakweyiphi engile), kunye umgca yazo yonqumlo ukuba ukufana

• impahla Fifth (yempahla uchaza inxalenye ezahlukeneyo imigca parallel ngqo, leyo kulala phakathi iinqwelomoya kufana kwesinye). Ezi ziqwempu yemida parallel, leyo afakwe phakathi moya ezimbini ezinxuseneyo ngokuyimfuneko ngokulinganayo.

Eyayingqalene moya kwi non-Euclidean geometry

Loo ndlela ingakumbi geometry we Lobachevsky kunye Riemann. Ukuba Euclidean geometry kuphunyezwa kwi kwizikhewu tyaba, ngoko Lobachevsky nakwizikhewu kakubi egosogoso (kujikwa kalula), lo gama Riemann oko lifezekiswa yayo izithuba kakuhle egosogoso (ngamanye amagama - imimandla). Kukho imbono ukungaphangalali eqheleke kakhulu ukuba Lobachevsky onxusene moya (kwaye kwakhona line) i phambana. Noko ke, oku akuyonyaniso. Eneneni ukuzalwa geometry itanjenti edityaniswa isiqinisekiso postulate yesihlanu Euclid kwaye ukutshintsha izimvo kulo, kodwa acaciswa iinqwelo-moya enxuseneyo kunye imigca ethe kuthetha ukuba abakwazi ukuwela okanye Lobachevsky okanye Riemann, phantsi kwazo naziphi na izithuba kokuba ziphunyezwe. Ukutshintsha kwentliziyo kunye namagama imi ngolu hlobo. Endaweni postulate ukuba kuphela moya ukufana singa zotywa ngokusebenzisa ingongoma hayi kwi moya elinikiweyo, kwafika omnye kuqulunqo: ngokusebenzisa ingongoma oko ongenakuxoka kule moya ethile ingathatha ezimbini, ubuncinane, ngqo, abakuwe enye moya nale kwaye musa uyihambisa.