翻訳と辞書 Words near each other ・ Eulima lactea ・ Eulima langleyi ・ Eulima lapazana ・ Eulima latipes ・ Eulima leachi ・ Eulima legrandi ・ Eulima leptostoma ・ Eulima leptozona ・ Eulima lodderae ・ Euler's Disk ・ Euler's equations (rigid body dynamics) ・ Euler's factorization method ・ Euler's flycatcher ・ Euler's formula ・ Euler's four-square identity ・ Euler's identity ・ Euler's laws of motion ・ Euler's pump and turbine equation ・ Euler's rotation theorem ・ Euler's sum of powers conjecture ・ Euler's theorem ・ Euler's theorem (differential geometry) ・ Euler's theorem in geometry ・ Euler's three-body problem ・ Euler's totient function ・ Eulerian matroid ・ Eulerian number ・ Eulerian path ・ Eulerian poset ・ Euler–Bernoulli beam theory Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Euler's identity ： ウィキペディア英語版 Euler's identity In mathematics, Euler's identity,〔Dunham, 1999, (p. xxiv ).〕 and the Euler product formula. | group=n}} (also known as Euler's equation) is the equality :$e^\; +\; 1\; =\; 0$ where : is Euler's number, the base of natural logarithms, : is the imaginary unit, which satisfies 2 = −1, and : is pi, the ratio of the circumference of a circle to its diameter. Euler's identity is named after the Swiss mathematician Leonhard Euler. It is considered an example of mathematical beauty. == Explanation == Euler's identity is a special case of Euler's formula from complex analysis, which states that for any real number , : $e^\; =\; \backslash cos\; x\; +\; i\backslash sin\; x$ where the inputs of the trigonometric functions ''sine'' and ''cosine'' are given in ''radians''. In particular, when  = ', or one half-turn (180°) around a circle: : $e^\; =\; \backslash cos\; \backslash pi\; +\; i\backslash sin\; \backslash pi.$ Since :$\backslash cos\; \backslash pi\; =\; -1\; \backslash ,\; \backslash !$ and :$\backslash sin\; \backslash pi\; =\; 0,$ it follows that : $e^\; =\; -1\; +\; 0\; i,$ which yields Euler's identity: : $e^\; +1\; =\; 0.$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Euler's identity」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.