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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 Ant on a rubber rope ： ウィキペディア英語版 Ant on a rubber rope The ant on a rubber rope is a mathematical puzzle with a solution that appears counterintuitive or paradoxical. It is sometimes given as a worm, or inchworm, on a rubber or elastic band, but the principles of the puzzle remain the same. The details of the puzzle can vary, but a typical form is as follows: : An ant starts to crawl along a taut rubber rope 1 km long at a speed of 1 cm per second (relative to the rubber it is crawling on). At the same time, the rope starts to stretch uniformly by 1 km per second, so that after 1 second it is 2 km long, after 2 seconds it is 3 km long, etc. Will the ant ever reach the end of the rope? At first consideration it seems that the ant will never reach the end of the rope, but in fact it does (although in the form stated above the time taken is colossal). Whatever the length of the rope and the relative speeds of the ant and the stretching, providing the ant's speed and the stretching remain steady the ant will always be able to reach the end given sufficient time. Once the ant has begun moving, the rubber rope is stretching both in front of and behind the ant, conserving the proportion of the rope already walked by the ant and enabling the ant to make continual progress. This is similar to the Achilles and the Tortoise Paradox (see Zeno's Paradoxes) == A formal statement of the problem == The problem as stated above requires some assumptions to be made. The following fuller statement of the problem attempts to make most of those assumptions explicit. : Consider a thin and infinitely stretchable rubber rope held taut along an $x$-axis with a starting point marked at $x=0$ and a target point marked at $x=c$, $c>0$. : At time $t=0$ the rope starts to stretch uniformly and smoothly in such a way that the starting point remains stationary at $x=0$ while the target point moves away from the starting point with constant speed $v>0$. : A small ant leaves the starting point at time $t=0$ and walks steadily and smoothly along the rope towards the target point at a constant speed $\backslash alpha>0$ relative to the point on the rope where the ant is at each moment. : Will the ant reach the target point? 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「Ant on a rubber rope」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.