Mbiri ya kukula kwa manambala. Mbiri ya kukula kwa nambala weniweni

Chitukuko cha masiku ano sichitheka kulingalira popanda nambala. Timakumana nawo tsiku ndi tsiku, timachita mazanamazana, mazana ndi zikwi pazochitika pothandizira makompyuta. Ife takhala tikuzoloŵera izi kuti mbiriyakale ya chitukuko cha nambala sichitikonda ife konse, ndipo anthu ambiri sanayambe amaganizapo za izo. Koma popanda kudziwa zammbuyo, munthu sangamvetsetse zomwe zilipo, choncho munthu ayenera kuyesetsa kumvetsetsa chiyambicho.

Nanga ndi mbiri yanji ya kukula kwa manambala? Ndi liti pamene iwo anawonekera, kodi mwamunayo wapita bwanji ku chilengedwe chawo? Tiyeni tione za izo!

Development

Mu masamu, palibe chinthu china chofunika kwambiri. Ngakhale izi, chiwerengero monga lingaliro chasintha kwa zaka zikwi zingapo, mpaka asayansi a dziko adagwirizana momwe angazindikire.

Maphunziro oyambirira, omwe adafuna kuti chidziwitso chimenechi chiwoneke, adalumikizidwa ndi ulimi, zomangamanga komanso nyenyezi. Pomwepo, kuphunzira za mlengalenga ndi chigawo cha miyeso yonse kunali kofunikira pa chitukuko cha kutumiza ndi malonda apadziko lonse, popanda popanda chikhalidwe chomwe chingakhalepo.

Kufikira pang'ono

Ngakhale anthu ambiri omwe anali achikulire anagwiritsidwa ntchito ndipo anabweretsedwera ku yunifolomu kwa zaka mazana ambiri. Ambiri a iwo anapangidwa chifukwa cha kukonzanso kubwereza mawu kapena makalata. Pythagoras wotchuka amati ziŵerengerozo ndizozizwitsa, zopanda mphamvu zomwe zimachitika m'chilengedwe chonse. Kawirikawiri, malinga ndi malingaliro amakono a sayansi, iye anali m'njira zambiri molondola.

Anthu a ku China anagawa ziwerengero ziwiri (zomwe zidapulumuka mpaka lero):

• Odd, kapena Ian. Mu filosofi yakale ya Chichina, iwo amaimira mlengalenga ndi mwangozi.
• Choncho, ngakhale (Yin). Lingaliro limeneli likuimira dziko ndi kusakhazikika.

Kuyambira kale

Ndithudi inu mwaganiza kale kuti mbiriyakale ya chitukuko cha nambala ikuyamba kuwerengera pansi kuchokera nthawi za zakuya kwambiri. Pa nthawi imeneyo, zizindikiro zodabwitsa zinali zowonjezeka kwa ansembe olemekezeka, omwe anakhala oyamba masamu m'mbiri ya dziko lathu lapansi.

Akatswiri a zaumulungu ndi akatswiri ofukula zinthu zakale amatsimikizira kuti munthu adatha kuwerengera kale mu Stone Age. Poyamba, chiwerengero choyamba chinkawonetsedwa ndi chiwerengero cha zala ndi zala. Ankawagwiritsa ntchito kuwerengera masitepe, olanda, adani ... Poyambirira munthuyu amafunikira manambala ochepa chabe, koma chitukuko cha anthu chimafuna kuwonjezeka kwa dongosolo. Izi sizinangowonjezera chitukuko cha zilembo za masamu, komanso zinathandiza kuti chitukuko chonse cha anthu chikhale chitukuko, popeza kuti nkhaniyi inkafuna ntchito yochenjera kwambiri.

Kotero mbiriyakale ya kuphulika ndi kukula kwa chiwerengerocho ndi zosagwirizana kwambiri ndi kusintha kwa malingaliro ndi chikhumbo cha makolo athu akutali kuti azisintha. Pamene adayang'ana nyenyezi, amalingalira kwambiri za masamu (ngakhale pa chikhalidwe choyambirira) m'dziko lowazungulira, nzeru zawo.

Chidziwitso cha chiwerengero

Mwamsanga pokhapokha pokhapokha, munthu anayamba kuphunzira kuyerekezera chiwerengero cha zinthu zomwe zili ndi malingaliro ofanana ndi katundu omwe waperekedwa kwa iye. Panali ziganizo "zambiri", "zochepa", "zofanana", "zambiri". Kudziwa mofulumira kunakhala kovuta kwambiri, ndipo posakhalitsa kunkafunikira dongosolo la akaunti.

Tiyenera kukumbukira kuti mbiri ya kukula kwa manambala m'choonadi inayamba ndi maonekedwe a munthu woyamba. Anadziŵa mosadziŵika kuyerekezera chiŵerengero cha anthu, nyama, zinthu, ngakhale popanda ngakhale ngakhale pang'ono chabe masamu. Koma izi zinali zosamvetsetseka: chinthu chilichonse chingakhudzidwe, ndipo zina mwaziganizidwe mosavuta.

Mawerengero, omwe amafotokoza zinthu za zinthu zomwezi, alipo, koma zinali zosatheka kuzikhudza kapena kuzifanizitsa. Nyumbayi inachititsa anthu mantha kwambiri, iwo amati ziwerengerozo ndi zamatsenga, makhalidwe apamwamba.

Umboni wina wa zifukwa

Akatswiri asayansi akhala akuganiza kuti poyamba anthu amagwiritsa ntchito mfundo zitatu zokha: "mmodzi", "awiri" ndi "ambiri." Mfundo imeneyi imatsimikiziridwa momveka bwino kuti m'zinenero zambiri zakale muli mitundu itatu (mwachi Greek chakale): osakwatira, awiri ndi ochuluka. Pambuyo pake, mwamuna adaphunzira kusiyanitsa, mwachitsanzo, njuchi ziŵiri kuchokera ku zitatu. Poyamba, nkhaniyi inkagwirizanitsidwa ndi zinthu zinazake.

Mpaka posachedwa, Achimwenye a ku Australia ndi a Polynesiya anali ndi ziwerengero ziwiri zokha: "chimodzi" ndi "ziwiri", ndi nambala zina zonse zinapezedwa mwa kuziphatikiza. Mwachitsanzo, nambala zitatu ndi ziwiri, imodzi, zinayi ndi ziwiri. Izi n'zosadabwitsa kukumbutsanso za njira ya chiwerengero yomwe ikugwiritsidwa ntchito ndi makompyuta. Komabe, moyo wowawa wa nthawi imeneyo unakakamiza iwo kuti aphunzire, ndipo chotero nkhani yakaleyo inadzangokhala masayansi a masamu.

Babulo ndi Mesopotamia

Kale ku Babulo, masamu anayamba kukula kwambiri, popeza mudziko lino lalikulu, nyumba zovuta kwambiri zinalengedwa, zomwe popanda kuziwerengera sizikanakhoza kumangidwa. Zokongola ngati zikhoza kuoneka, Abababulo sankachita mantha kwambiri chifukwa cha chiwerengero chawo, kotero mbiriyakale ya chiwerengero cha chiwerengero cha mawuwo idayamba mwachindunji nawo.

Ababulo anadutsa anthu onse a m'nthaŵi yawo kuti amatha kulemba kuchuluka kwa zinthu, anthu kapena zinyama okhala ndi zizindikiro zochepa. Iwo adayambitsa ndondomeko ya dongosolo, yomwe imatenga nambala yosiyana ya chiwerengero chomwecho chokhala ndi maudindo osiyanasiyana.

Kuphatikiza apo, kayendedwe kake ka zowerengera kanakhazikitsidwa pa njira yakugonana, imene Ababulo, monga asayansi amati, adabwerekera ku chitukuko cha Sumerian. Musaganize kuti mbiri ya chitukuko cha chiwerengero cha manambala chaima m'dera lino. Timagwiritsabe ntchito lingaliro la maminiti 60, masekondi 60, madigiri 360 pambali yoyesa chozungulira.

Pythagoras ankayembekezera

Olemba akale a ku Babulo anali atadziŵa bwino kale zinthu zamakona achilendo. Kuphatikiza apo, iwo anachita mawerengedwe a voliyumu ya piramidi ya truncated. Masiku ano zikudziwika bwino kuti mbiri ya chitukuko cha nambala yeniyeni imayambira ndendende kuyambira nthawi imeneyo: akatswiri a masamu a Mesopotamiya ndi Babeloni samangogwiritsa ntchito tizigawo ting'onoting'ono, koma ngakhale akhoza kuthetsa mavuto omwe akugwiritsa ntchito, kuphatikizapo atatu osadziwika!

M'zaka zaposachedwa, akatswiri a masamu a masiku ano adadabwa kumva kuti akale awo akale sankatulutsa zowonongeka koma ngakhale mizu ya cubic. Ayeneranso kuyandikira chiwerengero cha Pi, pafupifupi kuzungulira mpaka atatu. Tiyenera kukumbukira kuti Aigupto adatha kuwerengera molondola (3.16).

Nambala zachilengedwe

Zakale zakale ndi mbiri ya kukula kwa chiwerengero cha chirengedwe. Pakalipano, akukhulupirira kuti woyamba kugwiritsa ntchito mawu amenewa m'ntchito zake anali wasayansi wakale wachiroma Boethius (480-524), koma kale kwambiri, Nikomach wa Geraz analemba mu ntchito zake za chilengedwe, zachilengedwe.

Komabe, kumvetsa kwamakono mawu akuti "chiwerengero cha chirengedwe" ankagwiritsidwa ntchito ndi D'Alembert (1717-1783). Koma simukuyenera kuzimitsa: phunziro lomwelo la nkhaniyo linayamba ndi iwo. Pambuyo pake, chiwerengero cha chilengedwe ndi 1, 2, 3, 4, ...

Ndi maonekedwe awo, sitepe yofunika kwambiri inatengedwa kuti apange masamu ndi algebra mwa mawonekedwe omwe timawadziwa lero. Akatswiri a masamu amakhulupirira mwachidwi kuti pali chiŵerengero chochepa cha chilengedwe. Inde, nthawi zakale munthu samadziwa za izi. Ndalama zomwe anthu sangathe kuziganizira zinkawonetsedwa ndi mawu akuti "mdima", "legion", "kuika" ndi zina zotero. Kotero mbiriyakale ya chitukuko cha nambala ya nambala ndi yakale kwambiri ...

Chiphunzitso chayikidwa

Poyamba, chiŵerengero cha chirengedwe chinali chochepa kwambiri. Koma wotchuka Archimedes (m'zaka za zana lachitatu BC BC) adatha kuwonjezera kwambiri lingaliro limeneli. Anali katswiri wa sayansi yemwe analemba buku la Psammite, limene anthu ake nthawi zambiri ankalitcha: "Kuwerengera mchenga". Iye anawerengera molondola chiwerengero cha tinthu tating'onoting'ono tomwe timakhulupirira kuti tikhoza kutenga lonse lonse la mpira ndi makilomita 15,000,000,000,000.

Asanafike Archimedes Agiriki adakwanitsa kufika pa zikwi khumi ndi zikwi khumi. Ambiri, koma adatcha chiwerengerochi pa 10 000. Dzina lomweli limachokera ku Chigiriki "miros", kutanthauza "lalikulu kwambiri", "chachikulu kwambiri" mu Chirasha. Archimedes anapitirira: anayamba kugwiritsa ntchito mawerengedwe ake akuti "zikwi zambirimbiri", zomwe zinachititsa kuti adzipange yekha, kachitidwe ka wolembayo.

Mtengo wokwanira umene wasayansi anganene ndi 80,000,000,000,000,000 zero. Ngati mumasindikiza nambalayi pa tepi yautali, ndiye kuti mukhoza kumanga dziko lonse pa equator nthawi zoposa 2 miliyoni.

Motero, chiwerengero cha chilengedwe chonse chili ndi ntchito ziwiri zofunika kwambiri:

• Amatha kupanga chiwerengero cha zinthu zilizonse.
• Ndi chithandizo chawo, zizindikiro za zinthu mu mndandanda wa mayina akufotokozedwa.

Manambala enieni

Nanga bwanji mbiri ya kukula kwa nambala yeniyeni? Ndipotu, masamu, iwo amakhala ndi malo ochepa kwambiri! Choyamba tidzatsitsimutsa kukumbukira. Nambala iliyonse yabwino, yolakwika, komanso zero ikhoza kutchedwa yowona. Kuika kwawo kumagawidwa kukhala zomveka komanso zopanda nzeru.

Ngati mwawerenga mosamala nkhaniyo, mungaganize kuti mbiri ya chitukuko cha nambala chenicheni imayamba kuyambira pachiyambi cha anthu. Popeza lingaliro la zero linali loyamba (zowonjezereka kapena zowonjezeka zowonjezera) zomwe zinalembedwa mu 876 kuchokera ku kubadwa kwa Khristu ndipo zinayambitsidwa ku India, tikhoza kulemba tsikuli ngati tsiku lapakati.

Ponena za tanthawuzo loipa, iwo anali oyamba kufotokozedwa ndi Diophantus (Greece) m'zaka za zana lachitatu AD, koma "adaloledwa" ku India kokha, panthawi imodzimodzimodzi ndi lingaliro la "zero."

Tiyenera kukumbukira kuti mbiri ya kukula kwa manambala mu masamu yatsimikiziranso kukhalapo kwawo ngakhale ku Igupto wakale, chifukwa chifukwa cha kuwerengera iwo nthawi zambiri ankawonekera. Koma panthaŵi imeneyo iwo ankatengedwa kuti ndi "osatheka" ndi "unreal", ngakhale kuti nthawi zina ankagwiritsidwa ntchito mofanana.

Manambala osamveka

Kumbukirani kuti nambala yeniyeni ndi yochepa. Mu mawonekedwe a nambala, chiwerengero chimagwiritsidwira ntchito mmenemo, ndipo nambala yachirengedwe ndi chipembedzo. Sitidzadziwa kuti ndi liti, komanso kuti ndi liti pamene lingaliroli linayambira, koma linagwiritsidwa ntchito mwakhama ndi a Summer kwa zaka zikwi zingapo zisanafike. Chitsanzo chawo chinatsatiridwa ndi Agiriki ndi Aigupto.

Manambala ovuta

Koma adapezeka posachedwa, atangotulukira njira zopezera mizu ya equic equation. Izi zinachitika ndi Italy ya Niccolo Fontana Tartaglia (1499-1557) kumayambiriro kwa zaka khumi ndi zisanu ndi chimodzi. Kenaka adapeza kuti sizingatheke kugwiritsa ntchito nambala chabe kuti athetse mavuto osiyanasiyana.

Zinali mu 1572 okha zomwe zodabwitsazi zinkafotokozedwa. Iwo unatha kuchita izi Raphael Bombelli, kumene mbiri ya chitukuko cha nambala yovuta ikuyamba. Koma zotsatira zomwe adapeza kwa iye kwa nthawi yaitali zinkayengedwa "zopangidwa ndi charlatan", ndipo m'zaka za m'ma 1800 katswiri wamasamu Carl Friedrich Gauss anatsimikizira kuti woyang'anira wake wam'tsogolo anali wolondola.

Mfundo ina

Akatswiri ena amanena kuti nthawi yoyamba zoganiza zatchulidwa kale mpaka 1545. Izi zinachitika pa tsamba la wotchuka pa nthawi imeneyo "Great Art, kapena On Algebraic Rules," lomwe linalembedwa ndi Gerolamo Cardano. Kenaka adayesa kupeza njira yothetsera vuto la nambala ziwiri, zomwe zikawonjezeka, zimapereka 10, ndipo zikawonjezeka, mtengo wawo umawonjezeka kufika 40.

Kwa nthawi yayitali asanakhale a masamu panali funso loti ngati malo awo akhoza kutsekedwa. Tiyeni tifotokoze: kodi machitidwe pa zovuta zimapereka zovuta, zotsatira zenizeni, kapena kodi kufufuza kwina kumabweretsa kupezeka kwa chinthu chatsopano? Komabe, yankho la vutoli liri mu ntchito ya Abraham de Moivre (iwo anafika ku 1707), kuphatikizapo ntchito za Roger Cotes, zomwe zinafalitsidwa mu 1722.

Ndiyo nkhani yonse ya kukula kwa chiwerengero. Mwachidule, ndithudi, koma nkhaniyi imalingalira zofunikira kwambiri zafukufuku m'munda uno.