El lamba e, Lambar Euler ko kuma sanannen Napier akai-akai yana ɗaya daga cikin lambobi mafi dacewa da mahimmanci marasa ma'ana a fagen ilimin lissafi da algebra. Mahimmin lamba a cikin aikin juzu'i wanda lambar halitta ba za ta iya wakilta ta ba. Wannan lambar tana da manyan aikace-aikace a duniyar lissafi.
Saboda haka, za mu sadaukar da wannan labarin don gaya muku duk abin da kuke buƙatar sani game da lambar e, halaye da mahimmancinsa.
menene lamba e
Lambobi ne mara hankali kuma ba za mu iya sanin ainihin ƙimarsa ba saboda yana da wurare goma sha ɗaya mara iyaka, don haka ana ɗaukar shi lamba maras ma'ana. A cikin ilimin lissafi, zamu iya ayyana lamba e a matsayin ginshiƙi na aikin ma'auni na halitta, wani lokacin ana kiransa neper base saboda masu ilimin lissafi ne suka fara amfani da shi.
Ana kiran wannan lamba lambar da ba ta dace ba saboda ba za a iya wakilta ta a matsayin rabon lambobi biyu ba, adadin adadinsa ba shi da iyaka, haka nan kuma lamba ce mai wuce gona da iri domin ba za a iya wakilta ta a matsayin tushen algebraic equation tare da rational coefficients.
Babban fasali
Daga cikin manyan abubuwan da za mu iya ambata kamar haka:
- Wannan lamba ce mara rubutu wacce ba za a iya maimaita lambobinta akai-akai ba.
- Lambobin lambar e basa bin kowane irin tsari.
- Ana kiran shi akai-akai na Napier akai-akai ko lambar Euler.
- Ana iya amfani da shi a cikin rassa daban-daban na lissafi.
- Ba za a iya wakilta shi da lamba biyu ba.
- Hakanan ba za'a iya wakilta shi azaman ainihin lamba goma ko maimaita ƙima ba.
Shahararren masanin lissafi kuma mai mahimmanci Leonhard Euler, daya daga cikin ƙwararrun ƙwararrun ƙwararrun mathematics na kowane lokaci, ya yi amfani da alamar e a cikin ka'idar logarithms a 1727.. Daidaiton da ke tsakanin harafin farko na sunanka na ƙarshe da sunan lambar mu ta zo ɗaya kawai. Rikodi na farko ko kimanin adadin e da aka samu a cikin takardun lissafi ya samo asali ne tun a 1614, lokacin da John Napier's Mirifici Logarithmorun Canonis ya buga. Koyaya, ƙimar farko zuwa lambobin ya sami Jacob Bernoulli lokacin warware matsalar sha'awar dogon lokaci a cikin ƙayyadaddun ƙayyadaddun ƙayyadaddun farko, wanda ya sa shi fahimta da nazarin ƙayyadaddun ƙayyadaddun algebraic, kuma an daidaita ƙimarsa a 2,7182818.
Leonard Euler shine farkon wanda ya fara gane lambobi tare da alamar yanzu, wanda yayi daidai da harafin e, amma ya sami nasarar gabatar da shi kimanin shekaru 10 bayan haka a cikin Injin Lissafi. A zahiri, Leonhard Euler ne ya fara gano lambar. amma mutumin da ya gano shi a shekara ta 1614 dan kasar Scotland ne mai suna John Napier. Godiya ga bincikensa, ana iya maye gurbin ninkawa da ƙari, rarraba ta hanyar ragi da haɓaka ta samfur, sauƙaƙe aiwatar da lissafin lissafi na hannu.
Kayayyaki da aikace-aikacen lambar e
Hakanan ana iya amfani da waɗannan kaddarorin azaman ma'anar e.
- e shine jimlar juzu'i na ma'auni.
- e shine iyaka na gaba ɗaya jerin sharuɗɗan.
- Faɗawar juzu'i na e ba shi da na yau da kullun, amma a cikin ci gaba da ɓangarorin da aka daidaita, ana iya samun ci gaba ko ƙila a daidaita su.
- e rashin hankali ne kuma ya wuce gona da iri.
Wasu aikace-aikacen da za a iya amfani da wannan lambar su ne kamar haka:
- A fannin tattalin arziki, wannan shine ainihin yanki na farko na lissafin sha'awa.
- A ilmin halitta, iya kwatanta girmar tantanin halitta yana da mahimmanci.
- An kwatanta fitar da capacitor a cikin kayan lantarki.
- Yana bayyana haɓakar ƙididdiga na ionic ko halayen a fagen ilmin sunadarai.
- Gudanar da hadaddun lambobi, galibi tsarin Euler.
- Carbon 14 Dating na burbushin halittu a ilmin burbushin halittu.
- Auna asarar zafi daga abubuwan da ba su da aiki a cikin likitan likitanci don tantance lokacin mutuwa.
- A cikin ƙididdiga, ka'idar yuwuwa da ayyuka masu fa'ida
- A cikin zinariya rabo da logarithmic karkace.
Domin ya bayyana a cikin ayyuka masu ma'ana waɗanda ke kwatanta girma, kasancewarsa yana da mahimmanci lokacin da muka yi nazarin girma ko raguwa, kamar su. yawan kwayoyin cuta, yaduwar cututtuka, ko rubewar rediyoaktif, kuma yana da amfani wajen saduwa da burbushin halittu.
Mahimmanci da son sani
Lambar e tana kusan daidai da 2.71828 kuma yawanci ana rubuta shi azaman ≈2718. Wannan lambar tana da mahimmanci sosai a fannin lissafi da sauran fannonin da suka shafi samarwa, kimiyya da rayuwar yau da kullun. Wannan lambar tana taka muhimmiyar rawa a fagen lissafi. kuma yana daga cikin sakamako na asali da yawa kamar iyaka, abubuwan da aka samo asali, abubuwan haɗin kai, jerin, da sauransu. Bugu da ƙari kuma, yana da ƙayyadaddun kaddarorin da ke ba da damar amfani da shi don ayyana maganganun da ke da aikace-aikace masu mahimmanci a yawancin fannoni na ilimin ɗan adam.
Wasu abubuwan sha'awa masu alaƙa da lambar e sune kamar haka:
- Lambar e tana aiki azaman tushe na tsarin logarithmic na halitta ko na halitta.
- Lambar tana wakiltar lnx = t, inda x ta kasance tabbataccen lamba ta gaske, t tana da inganci ga x>1 da korau ga x <1.
- Ya wanzu a cikin ma'anar aiki y (x) = ex ko y (x) = exp(x) wanda saitin CVA na ƙimar da aka yarda shine saitin R na duk lambobin gaske.
Wasu tarihin
Maganar farko kai tsaye ga wannan adadin ya zo ne a cikin shahararren aikin John Napier na 1614, Mirifici Logarithmorum Canonis Descriptio, wanda a cikinsa aka fara bayyana ra'ayoyinsa game da logarithms, antilogarithms, sakamako, da teburin lissafin su; duk da haka, Jacob Bernoulli zai sami kusantar farko ta hanyar warware matsalar farkon ƙayyadadden adadin sha'awa na dogon lokaci, wanda ke kai ku zuwa iyakar da aka sani a yanzu bayan maimaita maimaitawa.
Saita ƙimar sa zuwa 2,7182818. Masanin ilimin lissafi kuma masanin falsafa Gottfried Leibniz daga baya ya yi amfani da wannan darajar a wasiƙu zuwa ga Kirista Huygens a 1690 da 1691, yana nuna ta da harafin b. Leonard Euler ya fara gano lambobi a cikin 1727 tare da alamar yanzu, harafin e, amma sai bayan shekaru goma ya gabatar da lambar ga jama'ar lissafi a cikin littafinsa Mechanics.
Daga baya masana za su yi amfani da a, b, c da e har sai na ƙarshe ya yi nasara don lambobi marasa ma'ana. Charles Hermite ya tabbatar da cewa wannan babbar lamba ce a cikin 1873. Su approximation ya fara da aikin Bernoulli, sa'an nan Euler sanya wani approximation na 18 matsayi bayan wakafi, don haka suka samar, dangane da kayyade matsayi na pi, da latest version na gasar ya kasance a 2010 Shigeru Kondo da Alexander J. Yee ƙaddara. e zuwa biliyan daidai wuraren goma.
Ina fatan cewa tare da wannan bayanin zaku iya ƙarin koyo game da lambar e da halayensa.