Mätäpono o Dirichlet. Mārama me te tapatahi i roto i te otinga o ngā raruraru o rerekē whīwhiwhi

mathematician German Gustava Lezhona Dirichlet, Pita (13.02.1805 - 05.05.1859) mohiotia te rite i te kaiwhakarewa o te parau tumu, te taitara o tona ingoa. Otiia i roto i te tua ki te ariā, ngā faataa e te hi'oraa o "manu me ngā pūtau", i runga i te pūkete o te mema ke ōrite o te St Petersburg Academy o Sciences, mema o te Royal Society o London, te Paris Academy o Sciences, te Berlin Academy o Sciences, Ahorangi o Berlin me te University o Göttingen he maha pepa i runga i te tātari pāngarau me te tau ariā .

Ia e kore e anake whakaurua ki te pāngarau i te parau tumu pai-mohiotia, ano i taea e Dirichlet whakamatau te ture tauwehe i runga i te maha mure ore o te tau pirimia e tīariari i roto i tetahi haereraa tauhanga o tau tōpū ki etahi tikanga. He huru hoki tenei ko e te wā tuatahi o ia me te rerekētanga - te maha o ngā pirimia.

riro ia he ako tino o te ture o te tohatoha o ngā tau o mau, e te hunga i rawe ki ki te tauhanga ahu. Dirichlet whakaurua he raupapa o ngā mahi e whai he tirohanga ngā, i muri ia i roto i te wahi o te tātari pāngarau mō te wā tuatahi tika whakapuaki, me te tūhura i te ariā o te pūtahitanga here me ki whakapumautia te pūtahitanga o te tau, e hoatu i te tohu pakari o te pea whänui ki te raupapa Fourier o te mahi e he tau tahuti, rite nga piki me ngā heke . e kore ahau e waiho i waho whakarongo ki nga mahi o ngā pātai Dirichlet o rehe me te ahupūngao pāngarau (te parau tumu Dirichlet mō ngā mahi hawarite ariā).

tikanga pūtaiao ahurei hangaia German ko tona tapatahi ataata, e taea ki tatou ako te parau tumu Dirichlet i roto i te haapiiraa tuatahi. taputapu pūkenga mō te whānui o ngā tono ngā, e kua whakamahia rite taunakitanga mo te theorems ohie i roto i te āhuahanga, me mo te whakaoti rapanga arorau, me te pāngarau matatini.

Kua whakaaetia te wātea me te noho pai o te whakamahi o te tikanga ki te whakamārama i te reira āta tākaro i te ara. faaiteraa matatini, me te ahua manganga hanga parau tumu Dirichlet kua te puka: "hoki te huinga o ngā huānga N pakaru ki te maha o ngā wāhanga ritua - n (he mea motu āhuatanga noa), ngā N> n, ka i roto i te iti rawa kia kotahi wahi neke atu i te kotahi huānga. " I pai te whakaritea e te reira faahou mō tenei i roto i te tikanga ki te whiwhi mārama, i matou ki te whakakapi i te N i roto i "hea", me n i te "whare herehere", me whakapuaki ākahukahu ki te tiki i te titiro: "Engari e te räpeti hoki i te iti rawa kia kotahi neke atu i te pūtau, ki reira he tonu i iti kotahi pūtau, e whiwhi ake atu i te rua me te hea. "

Tenei tikanga o te whakaaroaro ana ake mohiotia te i runga i te anga ke, ka whānui mohiotia ia rite te parau tumu Dirichlet. Tūmahi e taea te whakatika, ina te whakamahia reira, he momo whanui. Te kore te haere ki te whakamārama taipitopito o te rongoā, ngāue'aki tatau pē pai te parau tumu Dirichlet mō tohu mahi āhuahanga, me te arorau ohie, me waha te pūtake mō te hīkaro ka whakaaro teitei pāngarau raruraru.

kī kaiwhakahau o tenei tikanga e te fifi matua o te tikanga, ko te ki te whakatau he aha hipokina e raraunga raro i te whakamāramatanga o "hea", me e kia i titiro rite te "pūtau."

I roto i te raruraru o hāngai me te tapatoru e takoto ana i roto i te manureva i taua, ki te whakamatau e kore e taea e whiti i te reira noa e toru taha, iti ki te whakamahi i tetahi huru, ki te tika - e kore e raina tika na waenganui i tetahi tapatoru teitei. Ka rite ki te "hares" whakaaro te teitei o te tapatoru, me "pūtau" e rua hawhe-rererangi, e takoto ki tetahi taha o te raina. Ko reira mārama e ka i te iti rawa e rua tiketike i roto i tetahi o te hawhe-rererangi, aua, e kore e tāmia tika te roa o te wa e fakangatangata ratou, rite hiahiatia.

Ka rite ki noa a mahino whakamahia reira te parau tumu Dirichlet ki te raruraru arorau o karere me pennants. I te tepu a tawhio noa Kei te awa o te ngā āhua e, engari kei te haki o nga whenua me te paenga kia e ko muri ki te tohu o te whenua ke ia karere. He mea tika ki te whakamatau i te oraraa o te āhuatanga taua, ina e kia i te iti rawa e rua o te haki i muri ki te māngai o te whenua mo. Ki te manako tatou te karere mo te "manu" me "pūtau" ki te tautapa i te toe tūranga i roto i te huringa o te tepu (e kua waiho ratou tetahi iti), ka te raruraru mai ki te whakatau i tahaki.

E hoatu ēnei tauira e rua ki te whakaatu pēhea te ngāwari ki te whakaoti rapanga rauangi te whakamahi i te tikanga whakawhanakehia e te mathematician Tiamana.