Kunzwisisa Kwakatangira Nhamba Dzakaoma
Nzvimbo yemasvomhu yakazara nepfungwa dzinoita sedzisinganzwisisike uye dzisinganyatsonzwisisiki, dzichizongozviratidza senzira dzakakosha dzekunzwisisa nyika. Imwe pfungwa yakadaro ndeyenhamba dzakaoma kunzwisisa. Nhamba idzi, dzinosanganisira chikamu chaicho nechikamu chekufungidzira, pakutanga dzinogona kuita sedzisingazivikanwe nevanhu. Asi, dzine midzi yakadzika munhoroondo yemasvomhu uye dzinoita mabasa akakosha munzvimbo dzakasiyana-siyana dzakadai seinjiniya, fizikisi, uye kugadzirisa zviratidzo. Kuti unzwisise kukosha kwadzo, zvakakosha kutsvaga kwadzakabva uye kunzwisisa kukura kwadzo.
Kutanga kweNhamba dzekufungidzira
Nyaya yenhamba dzakaoma inotanga ne quadratic equation. Kubva kare, masvomhu akagadzirisa ma equation echimiro \(x^2 + bx + c = 0\). Zvisinei, mhinduro dzinosanganisira square roots dze negative numbers dzichiri kuomera uye dzinonetsa. Semuenzaniso, nyanzvi yemasvomhu yechiGiriki chekare Diophantus akataura nezvemhinduro dzaibatanidza negative square roots asi akazviramba sezvisingagoneki. Saizvozvowo, panguva imwe cheteyo, masvomhu muIndia neChina vakaongorora ma polynomial equation, vachiona kuti negative roots dzaiva nedambudziko.
Zvakatoitika muzana remakore rechi16 apo nyanzvi yemasvomhu yekuItaly Gerolamo Cardano akaita kufambira mberi kunoshamisa. Mubhuku rake guru rinonzi Ars Magna (1545), Cardano akapa nzira yekugadzirisa ma cubic equations. Paaishanda pama equation aya, akasangana ne square roots ye negative numbers. Kunyangwe aizeza kugamuchira mhinduro idzi zvizere, haana kudziramba zvachose. Pane kudaro, akataura nezvekuvapo kwadzo uye akatodzishandisa pa algebra, achiisa hwaro hwekuti nyanzvi dzemasvomhu dzakazotevera dziongorore nhamba idzi 'dzekufungidzira' zvakakomba.
Kubudirira mu17th uye 18th Century
Izwi rekuti "fungidziro" rakatangwa naRené Descartes muna 1637, pakutanga raishandiswa seshoko rekunyomba kutsanangura huwandu uhwu hwairatidzika sehwekunyepedzera. Zvisinei, izwi iri rakaramba richingoramba richirasikirwa nepfungwa dzaro dzekuzvidza. Panguva iyi, kufambira mberi kwakaramba kuripo sezvo nyanzvi dzemasvomhu dzakadai saRafael Bombelli dzakatanga kutsanangura nekushanda nenhamba idzi zvakasimba.
Basa raBombelli raive rinokosha. Mubhuku rake rinonzi Algebra (1572), Bombelli akatsanangura mitemo yekushandura nhamba dzekufungidzira. Akaratidza nzira yekuwedzera, kubvisa, uye kunyange kuwanza nhamba idzi, achigadzira algebra yekutanga yenhamba dzakaoma. Basa raBombelli raive rakakosha mukuita kuti pfungwa yenhamba dzekufungidzira ive nyore kune vemasvomhu.
Kugamuchirwa nekunzwisiswa kwenhamba dzakaoma kwakawedzerwa zvikuru muzana remakore rechi18 kuburikidza nemabasa enyanzvi dzemasvomhu dzakadai saLeonhard Euler naCarl Friedrich Gauss. Euler akabatsira zvikuru mukumiririra nhamba dzakaoma muchimiro che exponents. Akaunza notation \(i\) ye square root ye -1 uye akagadzira fomura yakakurumbira yaEuler \(e^{ix} = \cos(x) + i\sin(x)\), zvichiratidza hukama hwakadzama pakati pe trigonometry ne complex exponentiation.
Basa Rokutanga raGauss
Kunyange zvazvo Euler akatanga, Gauss ndiye akapa hwaro hwakasimba hwenhamba dzakaoma. Mukutanga kwezana remakore rechi19, Gauss akaratidza dzidziso huru yeAlgebra, iyo inoti equation yega yega yepolynomial isingachinji ine mudzi mumwe chete wakaoma. Dzidziso iyi yakasimbisa kukwana kwenhamba dzakaoma mukugadzirisa equation dzepolynomial uye yakasimbisa nzvimbo yadzo mudzidziso yemasvomhu.
Gauss akatangawo kududzirwa kwejometri yenhamba dzakaoma. Airatidza nhamba dzakaoma semapoinzi ari mundege, yava kuzivikanwa sendege yakaoma kana kuti plane yeArgand (yakatumidzwa zita raJean-Robert Argand uyo akaitsanangurawo akazvimirira). Nhamba yakaoma \(a + bi\) inogona kuratidzwa sepoinzi ine macoordinates (a, b), apo \(a\) iri chikamu chaicho uye \(b\) iri chikamu chekufungidzira. Kumiririrwa uku kwejometri kwakapa nzira isinganzwisisike yekunzwisisa mashandiro enhamba dzakaoma, senge kuwedzera, kubvisa, uye kuwanda.
Nhamba Dzakaoma Mumazuva Ano
Nekutanga kwakaitwa naEuler naGauss, nhamba dzakaoma dzakava chikamu chakakosha chemasvomhu uye dzakawana mashandisirwo muzvikamu zvakasiyana zvesainzi. Mufizikisi, kunyanya mumagetsi emagetsi uye quantum mechanics, nhamba dzakaoma dzinokosheswa. Semuenzaniso, basa remafungu muquantum mechanics rinotsanangurwa uchishandisa nhamba dzakaoma, zvichiita kuti kuve nekuverenga mikana uye kutsanangurwa kwehunhu hwemafungu muzvikamu.
Muinjiniya, kunyanya muinjiniya yemagetsi, nhamba dzakaoma dzinoshandiswa kuongorora macircuit eAC. Mainjiniya anoshandisa pfungwa yephasors, ayo ari nhamba dzakaoma dzinomiririra mabasa e sinusoidal, kuti zvive nyore uye kugadzirisa ma differential equations anodzora maitiro ecircuit. Maitiro aya akakosha pakugadzira nekunzwisisa masisitimu akadai seredhiyo, materevhizheni, uye ma power grids.
Uyezve, mukugadzirisa masaini, nhamba dzakaoma dzinoshandiswa muFourier analysis—nzira yemasvomhu inoparadzanisa mashandiro kana masaini kuita mafrequency. Izvi zvakakosha kune matekinoroji mazhinji, kusanganisira maalgorithms ekudzvanya manzwi nemifananidzo akadai seMP3s neJPEGs.
Rwendo Runoenderera Mberi
Rwendo rwenhamba dzakaoma kubva pakusanzwisisika kwemasvomhu kuenda kupfungwa huru yesainzi yemazuva ano neinjiniya humbowo hwesimba rekufunga kusinganzwisisike. Zvakatanga sekuyedza kugadzirisa maequation airatidzika seasingabviri zvakaita kuti pave nehurongwa hwemasvomhu hune zvahunoreva zvakawanda.
Nhasi uno, kudzidza nezvenhamba dzakaoma kuchiri kuramba kuchichinja, kuchipesvedzera nzvimbo dzakadai sedzidziso yenyonganyonga, mafambiro emvura, uye dzidziso yenhamba. Kuongorora hunhu hwadzo hakungopi ruzivo rwezviitiko zvemasvomhu chete asiwo nezvenyika dzechisikigo nedzakagadzirwa. Nhamba dzakaoma dzinotiyeuchidza kuti kutsvaga ruzivo kunowanzotanga nekugamuchira zvisingazivikanwi uye kubvunza zvisingagoneki.
Muchidimbu, mavambo nekukura kwenhamba dzakaoma kunzwisisa chiratidzo cherwendo rwakakura rwekufunga kwemasvomhu. Kubva pamatambudziko evanyanzvi vemasvomhu vekare vachitarisana nemidzi yakaipa kusvika kupfungwa dzakasimba dzaEuler naGauss avo vakadzitsanangura, nhamba dzakaoma dzinoratidza kuti pfungwa dzisinganzwisisike dzinogona sei kutungamira kukushandiswa kwakadzama. Nekunzwisisa kwadzakabva, tinonzwisisa kusvetuka kubva 'kwekufungidzira' kuenda kune kunoshamisa mune zvese dzidziso nemaitiro.
