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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 Poincaré–Miranda theorem ： ウィキペディア英語版 Poincaré–Miranda theorem In mathematics, the Poincaré–Miranda theorem is a generalization of the intermediate value theorem, from a single function in a single dimension, to ''n'' functions in ''n'' dimensions. It says as follows: ::Consider ''n'' continuous functions of ''n'' variables. Assume that for every variable $x\_i$, the function $f\_i$ is constantly negative when $x\_i\; =\; 0$ and constantly positive when $x\_i\; =\; 1$. Then there is a point in the ''n''-dimensional unit cube in which all functions are ''simultaneously'' equal to 0. The theorem is named after Henri Poincaré, who conjectured it in 1883, and Carlo Miranda, who in 1940 showed that it is equivalent to the Brouwer fixed-point theorem. == Intuition == The figure on the right shows an illustration of the Poincaré–Miranda theorem for $n=2$ functions. The function ''f'' is negative on the left boundary and positive on the right boundary. When we go from left to right along ''any'' path, we must go through a point in which ''f'' is 0. Therefore, there must be a "wall" separating the left from the right, along which ''f'' is 0 (green). Similarly, there must be a "wall" separating the top from the bottom, along which ''g'' is 0 (red). These walls must intersect in a point in which both functions are 0 (blue). 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「Poincaré–Miranda theorem」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.