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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Proof that e is irrational ： ウィキペディア英語版 Proof that e is irrational The number ''e'' was introduced by Jacob Bernoulli in 1683. More than half a century later, Euler, who had been a student of Jacob's younger brother Johann, proved that ''e'' is irrational, that is, that it can not be expressed as the quotient of two integers. ==Euler's proof== Euler wrote the first proof of the fact that ''e'' is irrational in 1737 (but the text was only published seven years later). He computed the representation of ''e'' as a simple continued fraction, which is :$e\; =\; (1,\; 2,\; 1,\; 1,\; 4,\; 1,\; 1,\; 6,\; 1,\; 1,\; 8,\; 1,\; 1,\; \backslash ldots,\; 2n,\; 1,\; 1,\; \backslash ldots).\; \backslash ,$ Since this continued fraction is infinite and rational numbers can't be written as infinite continued fractions, ''e'' is irrational. A short proof of the previous equality is known. Since the simple continued fraction of ''e'' is not periodic, this also proves that ''e'' is not a root of second degree polynomial with rational coefficients; in particular, ''e''2 is irrational. 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「Proof that e is irrational」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.