Zovuta manambala. Ubwino ndi Evolution "mfundo kungoganiza"

Manambala - zazikulu zinthu masamu zofunika computations osiyana ndi kuwerengetsera. The ya zachilengedwe, inteja, zomveka ndi zopanda nzeru mfundo digito amati kuchuluka kwa manambala otchedwa weniweni. Koma palinso zachilendo ndithu gulu - ". Zedi kungoganiza" manambala zovuta chimafotokozera René Descartes monga Ndipo mmodzi wa masamu otchuka m'ma chakhumi ndi chisanu ndi chitatu Leonhard Euler akufuna kuti uzipereke iwo kalata i ku French mawu imaginare (kungoganiza). ndi manambala zovuta ziti?

Chotero anaitana mawu a mawonekedwe + zina kuti adzipeza, komwe ndi b ndi manambala enieni, ndipo ine ndi chizindikiro digito amtengo wapatali kwambiri amene lalikulu ndi -1. Ntchito pa manambala zovuta zimagwiridwa ndi chimodzimodzi malamulo monga zosiyanasiyana ntchito masamu pa polynomials. Izi gulu masamu sikukutanthauza zotsatira za miyezo kapena kuwerengetsera. Pakuti ichi zokwanira manambala enieni. Nanga n'chifukwa chiyani ayenera?

manambala zovuta lingaliro masamu, zofunika chifukwa chakuti ena maikwezhoni ndi koefishienti weniweni ndi njira m'munda wa manambala "wamba". Choncho, kukuza kuchuluka kwa kuthetsa kusiyana adanyamuka kufunika kuyambitsa magulu atsopano masamu. manambala zovuta ndi umboni makamaka ongolankhula n'zotheka kuthetsa maikwezhoni izi monga ² × 1 = 0. Iwo ananena kuti, ngakhale mwambo wake akuoneka gulu manambala mwachangu ndipo chimagwiritsidwa ntchito kwambiri, mwachitsanzo, chifukwa njira zosiyanasiyana zothandiza mavuto chiphunzitso elasticity, zamagetsi, aerodynamics ndi hydromechanics, atomiki sayansi ndi khalidwe ena a sayansi.

Gawo ndi mkangano wa nambala zovuta ntchito ndandanda yomanga. mawonekedwe kulemba otchedwa trigonometric. Komanso, kutanthauzira geometrical a manambala awa zina kukodzedwa kuchuluka kwa ntchito yawo. Inasanduka zotheka kugwiritsa ntchito iwo zosiyanasiyana kompyuta mapu.

Masamu wabwera kutali ndi manambala yosavuta zachilengedwe kachitidwe zovuta Integrated ndi ntchito zawo. Pa nkhani imeneyi akhoza kulemba osiyana phunziro. Apa ife tione zina chabe mwa zinthu zamoyo zinachita chiphunzitso nambala bwino zonse mbiri ndi sayansi maziko chowaloleza wa gulu masamu.

Greek masamu kuti "zoona" okha zachilengedwe manambala, amene angagwiritsidwe ntchito kuwerengera chilichonse. Kale lachiwiri Zakachikwi BC. e. Aiguputo ndi a ku Babulo zosiyanasiyana kuwerengetsera othandiza mwakhama ntchito ting'onoting'ono. Yotsatira zofunika wofunika kwambiri pa chitukuko cha masamu anali kuoneka manambala sizabwino China wakale zaka mazana awiri pamaso yathu ino. Iwo anali ntchito akale Greek masamu Diophantus ankadziwa malamulo a ntchito yosavuta pa iwo. Mothandizidwa ndi manambala zoipa, kunakhala kotheka polongosola kusintha zosiyanasiyana makhalidwe, osati ndege positive.

Mu chiwiri m'ma AD, izo bwino anakhazikitsa kuti mizu lalikulu la manambala zabwino nthawi zonse makhalidwe awiri - kuwonjezera zabwino, komanso negative. Ku otsiriza kuchotsa muzu lalikulu la alipidwa njira algebraic nthawi kuti ankaganiza zosatheka palibe chofunika kwambiri kwa × kuti × ² = ─ 9. Kwa nthawi yaitali zinalibe kanthu. Izo zinali kokha m'zaka za m'ma chakhumi ndi chisanu ndi chimodzi, pamene panali ndipo mwakhama kuphunzira maikwezhoni kiyubiki, kufunika kuchotsa mizu lalikulu la manambala zoipa, monga mwa chilinganizo za njira mawu awa lili osati kyubu, komanso mizu lalikulu.

chilinganizo Izi wangwiro, ngati anthu aone kuti pali ali pa ambiri chimodzi muzu weniweni. Pankhani ya kukhalapo mu aone kuti pali mizu atatu chenicheni cha mankhwala awo anali analandira ndi chiwerengero cha mtengo negative. Iwo likukhalira kuti njira kuchira umadutsa mizu atatu a zosatheka pamaso pa masamu a nthawi ntchito.

Kuti mudziwe chifukwa chododometsa algebraists Italy J. Cardano anali akufuna kuyambitsa gulu latsopano la chikhalidwe osaka manambala, amene amatchedwa zovuta. Ine ndikudabwa zimene Cardano amaona kuti chilibe ntchito ndipo anachita zonse kupewa kuwagwiritsa ntchito kuti akufuna siyana masamu. Koma kale mu 1572 buku anaonekera wina algebraist Italy Bombelli, amene anali malamulo zambiri chifukwa ntchito pa manambala zovuta.

M'zaka za chakhumi ndi chisanu ndi chiwiri anapitiriza kukambirana za chikhalidwe masamu ya manambala deta ndi mphamvu ya kutanthauzira awo zojambula. Komanso pang'onopang'ono kukhala ndi bwino njira wogwira nawo ntchito limodzi. Ndipo kumapeto kwa zaka 17 ndi 18, chiphunzitso ambiri a manambala zovuta analengedwa. Amathandiza kwambiri kuti chitukuko ndi kusintha kwa chiphunzitso cha ntchito za zosintha zovuta polima Russian ndi asayansi Soviet. N. I. Muskhelishvili zikugwira ntchito kwake kwa mavuto ndi chiphunzitso cha elasticity, Keldysh ndi Lavrentiev manambala zovuta zomwe zagwiritsidwa ntchito mu munda wa hydro- ndi aerodynamics, ndi Vladimir Bogolyubov - chiphunzitso kwadzidzidzi kumunda.