Isikhala Euclidean: definition, izakhiwo, izimpawu

Ngisho esikoleni, bonke abafundi baziswa welithi "geometry Euclidean", izihlinzeko eyinhloko okuyinto bagxile bezungeza axioms ambalwa esekelwe izakhi weJiyomethri ezifana amaphuzu, izindiza, iqonde umugqa ukunyakaza. Bonke kwakha lokho kakade aziwa elithi "isikhala Euclidean".

Euclidean isikhala, kwencazelo ogxile yokuma ukubuyabuyelela scalar ka zithwala icala olukhethekile komugqa (affine) isikhala, okuyinto kwanelisa eziningi izidingo. Okokuqala, umkhiqizo wangaphakathi zithwala nakanjani ziyalingana, ie Vector nge izixhumanisi (x; y) ngokuya ubuningi nsé vector nge izixhumanisi (y; x), kodwa obuhlukile isiqondiso.

Okwesibili, uma kwenzeka ukuthi wenza umkhiqizo scalar we-vector nge uqobo, umphumela lesi senzo uzokhombisa ukuthi unalo igciwane. Okuwukuphela kube njalo lapho yokuqala kanye izixhumanisi ophela le-vector ilingana zero: kulesi simo futhi umkhiqizo wawo nazo uqobo okufanayo kuyoba zero.

Okwesithathu, kukhona umkhiqizo scalar kuyinto wokusakaza, okusho ukuthi kungenzeka wokwandisa omunye izixhumanisi zayo ku isamba amanani amabili ukuthi musa kuhilelani ushintsho ku yi yokugcina ukubuyabuyelela scalar ka zithwala. Ekugcineni, yesine, e ukuphindwaphindwa zithwala ngu elifanayo ukubaluleka kwangempela komkhiqizo wabo scalar nakho kuyanda yi isici esifanayo.

Kuleso simo, uma zonke lezi izimo ezine, singasho umlomo ukuthi lesi isikhala Euclidean.

isikhala Euclidean kusukela iphuzu eliwusizo umbono, kungenziwa libhekene izibonelo ezithile ezilandelayo:

1. Icala elula - kuyinto ukutholakala iqoqo zithwala amanye ngemithetho eyisisekelo yakulelo geometry, umkhiqizo scalar.
2. isikhala Euclidean is etholwe kunjalo, uma zithwala sisho iqoqo elithile ezilinganiselwe izinombolo sangempela ifomula unikezwa, echaza scalar yabo sum noma umkhiqizo.
3. Ikesi olukhethekile isikhala Euclidean kuyadingeka ukuba aqaphele okuthiwa isikhala zero, okuyinto etholakala uma kwenzeka ukuthi ubude kokubili zithwala scalar zero.

isikhala Euclidean enezinto eziningi izakhiwo ezithile. Okokuqala, kungase scalar isici kuthathwe kokubili ubakaki lokuqala kanye isici komkhiqizo scalar yesibili, umphumela lokhu ngeke ibhekane noma yiziphi izinguquko. Okwesibili, eduze ilungu lokuqala kusuka ukusatshalaliswa umkhiqizo scalar, izenzo kanye Distributivity Isici sesibili. Ngaphezu isamba scalar ka zithwala, Distributivity unendawo esimweni ukukhupha zithwala. Ekugcineni, okwesithathu, e ukubuyabuyelela scalar we-vector zero, umphumela beyoba zero.

Ngakho, isikhala Euclidean - umqondo obaluleke kakhulu yejeyomethri esetshenziswa ukuxazulula izinkinga nelungiselelo mutual zithwala isihlobo komunye nomunye, ukuze izici okuyinto nomqondo onjalo isetshenziswa njengoba umkhiqizo kwangaphakathi.