Ijiyomethri yokuhlaziya iyindlela yokufunda ijometri usebenzisa i-calculus. Ku-geometry yokuhlaziya, izibalo zejometri zimelelwa izilinganiso zezibalo nemisebenzi. Lokhu kuvumela ukubalwa kwezibalo zejometri, okusiza ukutadisha ijometri.
I-geometry yokuhlaziya yaqala ngekhulu le-18, lapho isazi sezibalo esingumFulentshi u-René Descartes ethula umqondo wokumelela izibalo zejiyomethri kusetshenziswa izixhumanisi. Kusukela ngaleso sikhathi, i-geometry yokuhlaziya iye yasetshenziswa kabanzi kwizibalo, i-physics, nakwezinye izindawo zesayensi.
Ku-geometry yokuhlaziya, izibalo zejometri zimelelwa izilinganiso zezibalo nemisebenzi. Lokhu kuvumela ukubalwa kwezibalo zejometri, okusiza ukutadisha ijometri.
I-geometry yokuhlaziya yaqala ngekhulu le-18, lapho isazi sezibalo esingumFulentshi u-René Descartes ethula umqondo wokumelela izibalo zejiyomethri kusetshenziswa izixhumanisi. Kusukela ngaleso sikhathi, i-geometry yokuhlaziya iye yasetshenziswa kabanzi kwizibalo, i-physics, nakwezinye izindawo zesayensi.
Ijiyomethri yokuhlaziya - Imiqondo eyisisekelo - i-Algebra I
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Iyini i-geometry yokuhlaziya nezibonelo?
Ijiyomethri yokuhlaziya igatsha lezibalo elifunda ubudlelwano phakathi kwezinto zejiyomethri nokuguquguquka kwe-algebra. Ngamanye amazwi, ijiyomethri yokuhlaziya izama ukuthola umumo wezinto ekumeleleni kwazo kwe-algebraic.
Ezinye izibonelo zejiyomethri yokuhlaziya yilezi: ukuthola indawo yesiyingi ukusuka esilinganisweni sayo, ukuthola ukuphambana kwemigqa emibili ezilinganisweni zayo, nokunquma ukuthi iphuzu lingaphakathi noma lingaphandle kwendingilizi ukusuka esilinganisweni sayo.
I-analytic geometry ihlukaniswa kanjani?
Ijiyomethri yokuhlaziya igatsha lejometri elifunda izibalo zejometri nezinto lisebenzisa izindlela zokuhlaziya izibalo. Ingahlukaniswa ngamagatsha amathathu amancane: ijometri yendiza, ijometri yendawo kanye nejometri ye-fractal.
Uyini umgomo wejiyomethri yokuhlaziya?
Ijiyomethri yokuhlaziya isiyalo sezibalo esibandakanya ukufundwa kwezinto zejiyomethri kusetshenziswa izindlela ze-algebraic nezindlela zokuhlaziya. Le ndawo yezibalo isetshenziswa kabanzi emagatsheni ahlukahlukene esayensi, njengefiziksi nobunjiniyela. Ezinye zezinto ezifundwe ku-geometry yokuhlaziya zihlanganisa amaphuzu, imigqa, indawo, nemizimba. Izindlela ezisetshenziswa ukuhlaziya lezi zinto zingasukela ku-calculus, i-trigonometry, kanye ne-geometry yokuguqula.
Iyini i-geometry yokuhlaziya ngokusho kwababhali?
Ijiyomethri yokuhlaziya igatsha lezibalo elifunda izakhiwo zezinto zejometri lisebenzisa izindlela zokuhlaziya izibalo. Lo mkhakha wezibalo waqala ngekhulu le-17 ngomsebenzi kaRené Descartes noPierre de Fermat, futhi uthuthukiswe ongoti bezibalo abafana noLeonhard Euler, uJoseph-Louis Lagrange, uCarl Friedrich Gauss noBernhard Riemann.
Iyini ijiyomethri yokuhlaziya?
Ijiyomethri yokuhlaziya igatsha lezibalo elifunda i-geometry lisebenzisa isistimu yokuxhumanisa. Ngezinye izikhathi ibizwa nangokuthi i-Cartesian geometry, ngemva kukaRené Descartes, owethula ukusetshenziswa kwezixhumanisi emsebenzini wakhe wango-1637 othi La Géométrie.
Ziyini ukusetshenziswa kwayo okungokoqobo?
Ezinye izinhlelo ezisebenzayo zamandla omoya ukusebenzisa izinjini zomoya ukukhiqiza ugesi, kusetshenziswa imishini yomoya ukumpompa amanzi, nokusebenzisa oseyili ukuhambisa izikebhe.
Ihlobene kanjani ne-algebraic geometry?
I-algebraic geometry icwaninga ngezinto zejiyomethri ezingachazwa kusetshenziswa izibalo ze-algebraic. Isibonelo, umbuthano ungachazwa njengesethi yawo wonke amaphuzu endizeni ayibanga elithile (elibizwa ngokuthi irediyasi) ukusuka endaweni engaguquki (ebizwa ngokuthi isikhungo).
Singazibona kanjani ngeso lengqondo izinto zejiyomethri ngokuhlaziya?
Kunezindlela eziningana zokubona ngeso lengqondo izinto zejometri ngokuhlaziya. Enye indlela iwukusebenzisa amagrafu endizeni yeCartesian. Enye indlela iwukubalwa kwezindawo namapherimitha. Izibalo zingasetshenziswa futhi ukumela izinto zejiyomethri.
