El inombolo e, inombolo ka-Euler noma i-Napier constant eyaziwa kakhulu ingenye yezinombolo ezifanele nezibalulekile ezingenangqondo emkhakheni wezibalo ne-algebra. Inombolo eyisisekelo kumsebenzi womchazi ongakwazi ukumelwa inombolo engokwemvelo. Le nombolo inezinhlelo zokusebenza ezinhle emhlabeni wezibalo.
Ngenxa yalesi sizathu, sizonikezela lesi sihloko ukuze sikutshele konke okudingeka ukwazi mayelana nenombolo u-e, izici zayo nokubaluleka kwayo.
yini inombolo e
Inombolo engenangqondo futhi ngeke sazi inani layo eliqondile ngoba inezindawo zamadesimali ezingapheli, ngakho ithathwa njengenombolo engenangqondo. Kumathematika, singachaza inombolo u-e njengesisekelo somsebenzi womchazi wemvelo, ngezinye izikhathi ibizwa ngokuthi i-neper base ngenxa yokuthi ochwepheshe bezibalo abangabokuqala abayisebenzisa.
Le nombolo ibizwa ngokuthi inombolo engenangqondo ngenxa yokuthi ayikwazi ukumelwa njengenani lama-integer amabili, inombolo yayo yedesimali ayinamkhawulo, futhi iyinombolo ye-transcendental ngoba ayikwazi ukumelwa njengomsuka we-algebraic equation enama-rational coefficients.
Izici eziyinhloko
Phakathi kwezici eziyinhloko singabala okulandelayo:
- Lena inombolo ye-nondescript izinombolo zayo ezingakwazi ukuphindaphinda njalo.
- Izinombolo zenombolo u-e azilandeli noma yiluphi uhlobo lwephethini.
- Ivamise ukubizwa ngenombolo ka-Napier noma inombolo ka-Euler.
- Ingasetshenziswa emagatsheni ahlukene ezibalo.
- Alikwazi ukumelwa ngamanani aphelele amabili.
- Futhi ayikwazi ukumelwa njengenombolo yedesimali okuyiyonayona noma amadesimali aphindayo.
Isazi sezibalo esidumile nesibalulekile uLeonhard Euler, omunye wezazi zezibalo ezake zachuma kakhulu, wasebenzisa uphawu u-e kuyinkolelo-mbono ye-logarithms ngo-1727.. Ukuqondana phakathi kohlamvu lokuqala lwesibongo sakho kanye negama lenombolo yethu kumane kwaqondana. Irekhodi lokuqala noma ukulinganiselwa kwenombolo e etholakala emaphepheni ezibalo ihlehlela emuva ku-1614, lapho i-Mirifici Logarithmorun Canonis ka-John Napier ishicilelwa. Kodwa-ke, ukulinganisa kokuqala kwezinombolo kutholwe nguJacob Bernoulli lapho exazulula inkinga yenzalo yesikhathi eside enanini elinqunyiwe lokuqala, okwamholela ekuqondeni nasekufundeni umkhawulo we-algebraic oyisisekelo, futhi inani lawo lahlelwa ku-2,7182818.
U-Leonard Euler waba ngowokuqala ukuqala ukubona izinombolo ngophawu lwamanje, oluhambisana nohlamvu u-e, kodwa wakwazi ukuyethula cishe eminyakeni eyi-10 kamuva ku-Mathematical Mechanics. Eqinisweni, inombolo yatholwa okokuqala nguLeonhard Euler, kodwa indoda eyayithola ngo-1614 kwakungu-Scotsman ogama lakhe linguJohn Napier. Ngenxa yokutholakala kwakhe, ukuphindaphinda kungashintshwa ngokuhlanganisa, ukuhlukaniswa ngokususa nokuphindaphinda ngomkhiqizo, okwenza kube lula ukwenza izibalo zezibalo.
Izakhiwo kanye nokusetshenziswa kwenombolo e
Lezi zakhiwo ezilandelayo zingasetshenziswa futhi njengezincazelo ze-e.
- e isamba sokubuyelana kwamafekthri.
- e umkhawulo wokulandelana okuvamile kwamatemu.
- Ukunwetshwa okuyingxenyana kuka-e akunakho ukujwayela, kodwa kumafrakhishini aqhubekayo ajwayelekile, kungase kube nokujwayelekile noma kungenzeki amafrakshini aqhubekayo.
- u-e akanangqondo futhi udlulele.
Ezinye izinhlelo zokusebenza lapho le nombolo ingasetshenziswa yilezi ezilandelayo:
- Kwezomnotho, lena empeleni indawo yokuqala yokubala inzuzo eyinhlanganisela.
- Ku-biology, ukukwazi ukuchaza ukukhula kwamangqamuzana kubaluleke kakhulu.
- Ukukhishwa kwe-capacitor kuchazwa ku-electronics.
- Ichaza ukuthuthukiswa kokugxila kwe-ionic noma ukusabela emkhakheni wekhemistri.
- Ukuphathwa kwezinombolo eziyinkimbinkimbi, ikakhulukazi ifomula ka-Euler.
- I-Carbon 14 dating yezinsalela ze-paleontology.
- Linganisa ukulahlekelwa ukushisa okuvela ezintweni ezingasebenzisi emithini yomthetho ukuze unqume isikhathi sokufa.
- Ezibalweni, ithiyori yamathuba kanye nemisebenzi ye-exponential
- Ngokwesilinganiso segolide kanye ne-logarithmic spiral.
Ngenxa yokuthi ibonakala emisebenzini e-exponential elingisa ukukhula, ukuba khona kwayo kubalulekile uma sifunda ukukhula okusheshayo noma ukwehla, njenge ukwanda kwamagciwane, ukusabalala kwezifo, noma ukubola kwe-radioactive, futhi iwusizo futhi ekupholeni izinsalela.
Ukubaluleka kanye nelukuluku
Inombolo u-e icishe ilingane no-2.71828 futhi ngokuvamile ibhalwa ngokuthi ≈2718. Le nombolo ibaluleke kakhulu kwizibalo nakweminye imikhakha eminingi ehlobene nokukhiqiza, isayensi kanye nempilo yansuku zonke. Le nombolo idlala indima ebaluleke kakhulu emkhakheni wokubala. futhi iyingxenye yemiphumela eminingi eyisisekelo njengemikhawulo, okuphuma kokunye, okuhlanganisayo, uchungechunge, njll. Ngaphezu kwalokho, inesethi yezakhiwo ezivumela ukusetshenziswa kwayo ukuchaza izinkulumo ezinezinhlelo zokusebenza ezibalulekile ezizindeni eziningi zolwazi lomuntu.
Okunye okuthakazelisayo okuhlobene nenombolo u-e okulandelayo:
- Inombolo u-e isebenza njengesisekelo sesistimu ye-logarithmic yemvelo noma yemvelo.
- Inombolo imelelwa ngu-lnx = t, lapho u-x eyinombolo yangempela ephozithivu, u-t uphozithivu ku-x>1 kanye negethivu ethi x <1.
- Itholakala encazelweni yomsebenzi y(x) = ex noma y(x) = exp(x) isethi yawo ye-CVA yamanani avunyelwe isethi R yazo zonke izinombolo zangempela.
Umlando othile
Ukubhekisela kokuqala okungaqondile ngale nombolo kwenzeka emsebenzini ka-John Napier odumile wango-1614, uMirifici Logarithmorum Canonis Descriptio, lapho imibono yakhe ngama-logarithms, ama-antilogarithms, imiphumela, kanye namathebula abo okubala ichazwa kuqala; Nokho, uJacob Bernoulli uzothola isilinganiso sokuqala ngokuxazulula inkinga yenani elingaguquki lokuqala lenzalo yesikhathi eside, okukuyisa emkhawulweni owaziwayo manje ngemva kokuphindaphinda okulandelanayo.
Setha inani layo ku-2,7182818. Isazi sezibalo nesazi sefilosofi uGottfried Leibniz kamuva wasebenzisa leli gugu ezincwadini eziya kuChristian Huygens ngo-1690 no-1691, elichaza ngohlamvu u-b. ULeonard Euler waqala ukukhomba izinombolo ngo-1727 ngophawu lwamanje, uhlamvu u-e, kodwa kwaze kwaba ngemva kweminyaka eyishumi lapho ethula khona inombolo emphakathini wezibalo encwadini yakhe ethi Mechanics.
Kamuva ochwepheshe bazosebenzisa u-a, b, u-c kanye no-e kuze kube yilapho sekunqoba izinombolo ezingenangqondo. UCharles Hermite wafakazela ukuthi leli kwakuyinani elibalulekile ngo-1873. Ukulinganisa kwabo kwaqala ngomsebenzi kaBernoulli, kwase kuthi u-Euler wenza isilinganiso sezikhundla eziyi-18 ngemuva kwekhefana, ngakho-ke bakhiqiza, ngokunquma indawo ye-pi, inguqulo yakamuva yomncintiswano yayingo-2010 uShigeru Kondo no-Alexander J. Yee banquma. e kuya ezindaweni zamadesimali eziyibhiliyoni.
Ngithemba ukuthi ngalolu lwazi ungafunda kabanzi mayelana nenombolo ye-e nezici zayo.