| 翻訳と辞書 |
| Mice problem ： ウィキペディア英語版 |
Mice problem
In mathematics, the mice problem is a problem in which a number of mice (or insects, dogs, missiles, etc.) are placed at the corners of a regular polygon. Each mouse begins to move towards its immediate neighbour (clockwise or anticlockwise). It must be determined when the mice meet.
The most common version has the mice starting at the corners of a unit square, moving at unit speed. In this case they meet after a time of one unit, because the distance between two neighboring mice always decreases at a speed of one unit. More generally, for a regular polygon of ''n'' sides, the distance between neighboring mice decreases at a speed of 1 − cos(2π/''n''), so they meet after a time of 1/(1 − cos(2π/''n'')).〔George Gamow, Stern, Marvin (1958), Puzzle math, New York: Viking press, pp. 112–114〕
〔Édouard Lucas, (1877), "Problem of the Three Dogs", Nouv. Corresp. Math. 3: 175–176〕
==Path of the mice==
For all regular polygons, the mice trace out a logarithmic spiral, which meets in the center of the polygon (as shown on the right).〔(【引用サイトリンク】url=http://mathworld.wolfram.com/MiceProblem.html )〕 When additional mice are added and the mice move towards non-immediate neighbours, the paths they trace become more complex.
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「Mice 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.
|
|