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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 Squared triangular number ： ウィキペディア英語版 Squared triangular number In number theory, the sum of the first cubes is the square of the th triangular number. That is, :$1^3+2^3+3^3+\backslash cdots+n^3\; =\; \backslash left(1+2+3+\backslash cdots+n\backslash right)^2.$ The same equation may be written more compactly using the mathematical notation for summation: :$\backslash sum\_^n\; k^3\; =\; \backslash left(\backslash sum\_^n\; k\backslash right)^2.$ This identity is sometimes called Nicomachus's theorem. ==History== Many early mathematicians have studied and provided proofs of Nicomachus's theorem. claims that "every student of number theory surely must have marveled at this miraculous fact". finds references to the identity not only in the works of Nicomachus in what is now Jordan in the first century CE, but also in those of Aryabhata in India in the fifth century, and in those of Al-Karaji circa 1000 in Persia. mentions several additional early mathematical works on this formula, by Alchabitius (tenth century Arabia), Gersonides (circa 1300 France), and Nilakantha Somayaji (circa 1500 India); he reproduces Nilakantha's visual proof. 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「Squared triangular number」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.