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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 Vedic square ： ウィキペディア英語版 Vedic square In ancient Indian mathematics, a Vedic square is a variation on a typical 9 × 9 multiplication table. The entry in each cell is the digital root of the product of the column and row headings i.e. the remainder when the product of the row and column headings is divided by 9 (with remainder 0 represented by 9). Numerous geometric patterns and symmetries can be observed in a Vedic square some of which can be found in traditional Islamic art. ==Algebraic Properties== This table can be viewed as the multiplication table of the monoid $((\backslash mathbb/9\backslash mathbb)^,\; \backslash )$ where $\backslash mathbb/9\backslash mathbb$ is the set of positive integers partitioned by the residue classes modulo nine. Also, the operator ''$\backslash circ$'' means the abstract "multiplication" between the elements of this monoid. If $a,b$ are elements of $((\backslash mathbb/9\backslash mathbb)^,\; \backslash )$ then $a\; \backslash circ\; b$ can be defined as $(a\; \backslash times\; b)\; \backslash mod$ by using the modulus operator mod, where we take the element 9 as the representative of the residue class of 0 rather than the traditional choice of 0. This does not form a group not every non-zero element has a corresponding inverse element, for example $6\backslash circ\; 3\; =\; 9$ but there is no $a\; \backslash in\; \backslash$ such that $9\backslash circ\; a\; =\; 6.$. If we consider the subset $\backslash$, however, this does form a group. It forms a cyclic group with 2 as one choice of generator. In fact, this is just the group of multiplicative units in the ring $\backslash mathbb/9\backslash mathbb$. We can see the every columns and rows has all six cells. It shows that $\backslash$ forms a Latin square. 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「Vedic square」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.