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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 Vinculum (symbol) ： ウィキペディア英語版 Vinculum (symbol) A vinculum is a horizontal line used in mathematical notation for a specific purpose. It may be placed as an overline (or underline) over (under) a mathematical expression to indicate that the expression is to be considered grouped together. For most of its uses it has been replaced by parentheses in modern notational style. ''Vinculum'' is Latin for "bond", "fetter", "chain", or "tie", which is suggestive of some of the uses of the symbol. A vinculum can indicate a line segment where ''A'' and ''B'' are the endpoints: *$\backslash overline.$ A vinculum can indicate the repetend of a repeating decimal value: * = 0. = 0.1428571428571428571... Similarly, it is used to show the repeating terms in a periodic continued fraction. Quadratic irrational numbers are the only numbers that have these. Its main use was as a notation to indicate a group (a bracketing device serving the same function as parentheses): :$(a-\backslash overline),$ meaning to add ''b'' and ''c'' first and then subtract the result from ''a'', which would be written more commonly today as . Parentheses, used for grouping, are only rarely found in the mathematical literature before the eighteenth century. The vinculum was used extensively, usually as an overline, but Chuquet in 1484 used the underline version. The vinculum is used as part of the notation of a radical to indicate the radicand whose root is being indicated. In the following, the quantity $ab+2$ is the whole radicand, and thus has a vinculum over it: :$\backslash sqrt().$ In 1637 Descartes was the first to unite the German radical sign √ with the vinculum to create the radical symbol in common use today. The symbol used to indicate a vinculum need not be a line segment (overline or underline), sometimes braces, pointing up or down can be used. ==Other notations== There are several mathematical notations which use an overbar that can easily be mistaken for a vinculum. Among these are: It can be used in signed-digit representation to represent negative digits, such as the following example in balanced ternary: :$\backslash pi\; \backslash approx\; 10.011\backslash overline111\backslash overline000\backslash overline011\backslash overline1101\backslash overline/11111100\backslash overline0000\backslash overline1\backslash overline\backslash overline\backslash overline\backslash overline0\backslash overline$ The overbar is sometimes used in Boolean algebra, where it serves to indicate a group of expressions whose logical result is to be negated, as in: :$\backslash overline.$ It is also used to refer to the conjugate of a complex number: :$\backslash bar\; =\; \backslash overline\; =\; .$ In statistics the overbar can be used to indicate the mean of series of values. In particle physics, the overline is used to indicate antiparticles. For example, p and are the symbols for proton and antiproton, respectively. In electronics, the vinculum is used to notate complementary signals. For example, pronounced "control-not," would be the same signal as CONTROL but with the opposite polarity. The vinculum should also not be confused with a similar-looking vector notation, e.g. $\backslash overrightarrow$ "vector from A to B", or $\backslash vec$ "vector named ''a''", though an overline or underline without the arrowhead is sometimes used instead (e.g., $\backslash overline$ or $\backslash underline$). 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「Vinculum (symbol)」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.