翻訳と辞書 Words near each other ・ Hermund Nygård ・ Hermunduri ・ Hermus ・ Hermite constant ・ Hermite distribution ・ Hermite interpolation ・ Hermite Islands ・ Hermite normal form ・ Hermite number ・ Hermite polynomials ・ Hermite reciprocity ・ Hermite ring ・ Hermite spline ・ Hermite's cotangent identity ・ Hermite's identity ・ Hermite's problem ・ Hermite–Hadamard inequality ・ Hermite–Minkowski theorem ・ Hermitian adjoint ・ Hermitian connection ・ Hermitian function ・ Hermitian hat wavelet ・ Hermitian manifold ・ Hermitian matrix ・ Hermitian symmetric space ・ Hermitian variety ・ Hermitian wavelet ・ Hermits of Saint William ・ Hermits of St. John the Baptist ・ Hermits of the Most Blessed Virgin Mary of Mount Carmel 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 Hermite's problem ： ウィキペディア英語版 Hermite's problem Hermite's problem is an open problem in mathematics posed by Charles Hermite in 1848. He asked for a way of expressing real numbers as sequences of natural numbers, such that the sequence is eventually periodic precisely when the original number is a cubic irrational. ==Motivation== A standard way of writing real numbers is by their decimal representation, such as: :$x=a\_0.a\_1a\_2a\_3\backslash ldots\backslash$ where ''a''0 is an integer, the integer part of ''x'', and ''a''1, ''a''2, ''a''3… are integers between 0 and 9. Given this representation the number ''x'' is equal to :$x=\backslash sum\_^\backslash infty\; \backslash frac.$ The real number ''x'' is a rational number only if its decimal expansion is eventually periodic, that is if there are natural numbers ''N'' and ''p'' such that for every ''n'' ≥ ''N'' it is the case that ''a''''n''+''p'' = ''a''''n''. Another way of expressing numbers is to write them as continued fractions, as in: :$x=(),\backslash$ where ''a''0 is an integer and ''a''1, ''a''2, ''a''3… are natural numbers. From this representation we can recover ''x'' since :$x=a\_0\; +\; \backslash cfrac\}\}.$ If ''x'' is a rational number then the sequence (''a''''n'') terminates after finitely many terms. On the other hand, Euler proved that irrational numbers require an infinite sequence to express them as continued fractions.〔(【引用サイトリンク】url=http://math.dartmouth.edu/~euler/pages/E101.html )〕 Moreover, this sequence is eventually periodic (again, so that there are natural numbers ''N'' and ''p'' such that for every ''n'' ≥ ''N'' we have ''a''''n''+''p'' = ''a''''n''), if and only if ''x'' is a quadratic 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「Hermite's problem」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.