Daws linear equations

Creative Gauss peculiar organic koom haum ntawm cov theoretical thiab cov tswv yim xam, ntawm qhov tob ntawm qhov teeb meem. Gauss lub chaw ua hauj lwm muaj ib tug zoo kawg li tej yam nyob rau hauv lub tsim ntawm algebra (qhia txog cov ntsiab axioms ntawm lub science), kev daws ntawm linear equations ntawm lub hom phiaj ntawm tus xov tooj (nrog geometric nto), zauv physics (Gaussian kuj), hluav taws xob kev tshawb xav thiab magnetism, geodesy (muab ib tug qauv ntawm cov me squares) thiab ze li ntawm tag nrho cov seem astronomy.

"Xam kev tshawb fawb"

Cov thawj heev ntawm nws zoo nyob rau hauv lub loj heev creation ntawm Gauss - "xam kev tshawb fawb" (luam tawm nyob rau hauv 1801), uas ntawd kub ntev li yuav luag tag nrho cov xyoo ntawm nws lub neej. Tom qab tsim - tus thawj xib fwb seem ntawm xam - kev tshawb xav tooj thiab advanced lej, uas muaj cov tshuaj ntawm linear equations.

Ntawm tus loj tus naj npawb ntawm cov me me thiab tus thawj xibfwb tau teev nyob rau hauv "xam kev tshawb fawb", nws yuav tsum tau muab sau tseg rau tag nrho cov tswv yim ntawm quadratic cov ntaub ntawv, thiab ua ntej ntawv pov thawj ntawm cov quadratic them pauj kev cai lij choj. Qhov kawg ntawm nws lub neej Gauss tau nyob rau hauv ib tug zoo meej lub vajvoog ntawm lub tswvyim ntawm kev sib cais sib npaug, cim tias seb thaum lawv muaj kev koom nrog kev pab raws qib ntawm lub tsev uas cov pov thawj twb nyob rau hauv lub ancient lub sij hawm, muaj peev xwm ntawm constructing ib lub compass thiab straightedge ncaj ncees polygon nrog qhov tseeb naj npawb ntawm cov sab.

Gauss pom tag nrho cov xov tooj nyob rau hauv uas qhov kev siv ntawm ib tug yeej muaj tseeb polygon siv ib tug pas ntsuas thiab compass yuav ua tau yooj yim. Qhov no thiaj li hu ua "tsib txawv Gaussian qub xov tooj", peb thiab tsib, kaum xya, thiab ob puas tsib caug xya thiab 65.237, thiab txawm khoo nyob rau hauv ntau theem ntawm ob Gaussian zauv. Piv txwv li, tsim nrog kev pab los ntawm lub siab ntseeg chaw ua hauj lwm cov khoom (3h5h17) - Gon yog tso cai thiab qhov tseeb 7-gon yog tsis yooj yim sua, txij li thaum daim duab yog tsis Gaussian, nws muaj li ib txwm tooj.

Tsev algebra axiom

Nrog rau cov npe ntawm Gauss tseem kev cob cog rua lub ntsiab axiom ntawm algebra, raws li uas tus naj npawb ntawm cov hauv paus hniav ntawm tus polynomial (tiag tiag thiab complex) yog tib yam (nrog rau cov zauv hauv paus hniav txia complex paus yuav tsum tau noj mus rau hauv tus account raws li ntau lub sij hawm raws li nws cov theem). Thawj qhia txog cov ntsiab axioms ntawm algebra Gauss ua nyob rau hauv 1799, thiab tom qab ntawd ua ib qho kev tsis tau qhov nqi ntawm cov pov thawj.

ua tswvyim

Kev txiav txim zoo rau tag nrho cov sciences soj ntsuam nrog xws li ib tug system, raws li cov hau kev rau kev daws systems sib npaug, tsim los ntawm Gauss, muaj peev xwm sawv ntawm tau txais ntau tej zaum qhov tseem ceeb ntawm cov kev ntsuam. Tshwj xeeb ntau tej chaw yog ua los ntawm Gauss nyob rau hauv 1821. txoj kev kawg squares. Zaum nteg rov qab thiab pib cov kev tshawb xav ntawm tsis.

Lub ntsiab lus ntawm cov kev tshawb fawb Gauss

Yuav luag tag nrho cov ntawm nws yog tam sim no tau tshwm sim, tus poj txoj kev tshawb no ntawm Carl Gauss tsis luam tawm thaum lub sij hawm nws lub neej. Lawv fwm nyob rau hauv daim ntawv ntawm cov sketches, tsab ntawv, uas raug theej los ntawm nws comrades. Txoj kev tshawb no cov ntaub ntawv twb koom nyob rau hauv tej hauj lwm ntawm Göttingen scientific lub zej lub zos, uas muab mus rau luam tawm kaum ob tagnrho tej hauj lwm ntawm Gauss. Ntau exciting thiab nrov ua hauj lwm "Daws linear equations" luam tawm lig li ntawd nyob nws chaw muag mis nyuj uas muaj cov ntaub ntawv no.

Qhov scientific ua hauj lwm ntawm Charles raws li nyob rau hauv kev daws linear equations. Applied lej tau siab siv nyob rau hauv lub puag ib feem ntawm cov kev kawm, nws tau muab nrog teeb meem loj. Rau cov tswv yim yuav tsum tau muab tiv thaiv, muaj ntau kev kawm ntawv uas xav mus nquam paj nquam nruas lub ntsiab ntawm lub ntsiab ntawm linear equations.

Xam txoj kev tshawb no muaj ib tug loj feem nyob rau tom ntej tsim ntawm tus xov tooj kev tshawb xav thiab algebra. Them pauj kev cai thiab rau hnub no nyob ib qho tseem ceeb qhov chaw nyob rau hauv algebra. Qhov no zoo kawg paub txog yog tsis cov ntaub ntawv, tsim nyog ua hauj lwm nyob rau hauv xws productions li "xam kev tshawb fawb", "kev txiav txim siab matrix los ntawm Gauss" thiab "tshuaj ntawm linear equations", tag nrho cov kev txawj ntse nws tau coj, raws li lawv hais, tawm ntawm kuv lub taub hau.