Ukuxazulula Linear Izibalo

Gauss inhlangano Creative eyinqaba organic phakathi izibalo theory kanye nama-practical, le izinkinga ukujula. umsebenzi Gauss sika baba nethonya elikhulu ku ukwakheka kwe-algebra (isiqinisekiso axioms eyinhloko isayensi), ikhambi of zibalo lwento of imfundiso yokuziphendukela izinombolo (yangaphakathi ebusweni Jomethri), i-physics zezibalo (isimiso Gaussian), ugesi theory kanye uzibuthe, geodesy (ukunikeza indlela tikwele letincane) futhi cishe zonke izigaba astronomy.

"Ucwaningo Aritmethikhi"

Zona ngqa ekudalweni enkulukazi Gauss - "ucwaningo Aritmethikhi" (eyanyatheliswa ngo-1801), eyathatha cishe zonke iminyaka yokuphila kwakhe. Ukulandela ukwakheka - izigaba avelele izibalo - inombolo theory kanye izibalo zezinga eliphezulu, esasihlanganisa isixazululo of zibalo lwento.

Of inombolo enkulu emiphumeleni amancane oyinhloko ezisohlwini "ucwaningo Aritmethikhi", kufanele kuphawulwe umqondo ogcwele amafomu quadratic, kanye nobufakazi lokuqala umthetho reciprocity quadratic. Ekupheleni kokuphila kwakhe Gauss imiphumela kumbuthano esiphelele nomqondo ukwehlukana zibalo, okubonisa ubudlelwane babo imisebenzi yokwakha ngemapholigoni efakazelwe kakade ezikhathini zasendulo, ikhono wokwakha ikhampasi kanye wokulinganisa ipholigoni ezithembekile enanini lelingilo kuletintfo izinhlangothi.

Gauss yabonisa zonke izinombolo lapho kwakhiwa ipholigoni kweqiniso ukusebenzisa irula lapho kusetshenzwa bese ikhampasi kungaba elula. Lokhu okubizwa ngokuthi "ezahlukene Gaussian izinombolo ezinhlanu evamile", amathathu nanhlanu, ishumi nesikhombisa, futhi ezimbili namashumi amahlanu nesikhombisa kanye 65.237, ngisho sanda ngokuphindiwe izigaba ezahlukene integers ezimbili Gaussian. Ngokwesibonelo, ukwakha ngosizo ethembekileyo zasehhovisi (3h5h17) - gon ovunyelwe futhi elungile 7-gon akunakwenzeka, kusukela sibalo akuyona Gaussian, it has inombolo evamile.

Ikhaya algebra Axiom

Nge igama Gauss namanje ixhunyiwe Axiom main algebra, owawuthi inani izimpande polynomial (yangempela futhi eziyinkimbinkimbi) kuyafana (ne izimpande zezinombolo uguqule impande sakhiwo sizoba kucatshangelwe kaningi ngokuthanda isigaba saso). isiqinisekiso lokuqala axioms main algebra Gauss benza e 1799, futhi kamuva wenza ukunikezwa okwamanje ethile ubufakazi.

ukucutshungulwa kokuma

umqondo okungafanele kuwo wonke wesayensi ekubhekaneni isimiso esinjalo, njengoba izindlela ukuxazulula izinhlelo of zibalo, akhiwa Gauss, bayakwazi ukuthola amanani engaba ngaphezulu izilinganiso. Ikakhulukazi bebaningi esenziwa Gauss e 1821. indlela okungenani izikwele. Ososayensi ukuphumula futhi bazisekela imfundiso yokuziphendukela amaphutha.

Okwakushiwo Gauss izifundo

Cishe konke lokhu kalokhu yambuliwe, isifundo esikhulu Carl Gauss akazange ukushicilela phakathi nesikhathi sokuphila kwakhe. Bayalondolozwa ngesimo imidwebo, eseyi, eyayibonakala bekopisha akanye nalo. Idatha Ucwaningo matasa emisebenzini ka Gottingen wezesayensi, okwathi kamuva laba ukushicilela amavolumu nambili yemisebenzi Gauss. umsebenzi okuningi okuthakazelisayo futhi ethandwa "Ukuxazulula Linear zibalo" eshicilelwe ngasekupheleni njengoba ngephutha wathola idayari yakhe ngala amarekhodi.

Umsebenzi yesayensi Charles esekelwe ukuxazulula zibalo lwento. wezibalo osetshenziswayo seyenziwe ngokugcwele base ingxenye isayensi, sanikwa lula. Ukuze uthole amacebiso okuthi kwadingeka izimpi kwakukhona izifundiswa abaningi ababefuna ukugubha isihloko izixazululo of zibalo lwento.

cwaningo Aritmethikhi saba nomthelela omkhulu kwi ukwakheka oluzayo inombolo theory ne-Aljibhra. imithetho reciprocity futhi kuze kube namuhla hlala ebalulekile e-algebra. Lokhu usosayensi omkhulu kwakungelona izincwadi, ezidingekayo ukuze ukusebenza imikhiqizo efana "ucwaningo Aritmethikhi", "isinqumo-matrix ngu Gauss" futhi "Isixazululo of zibalo lwento", yonke ulwazi ayeyithathile, njengoba besho, aphume ikhanda lami.