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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, [1] [2] but a typical form is as follows:
Ant on a rubber rope: An ant crawling on a rubber rope can reach the end even when the rope stretches much faster than the ant can crawl. Cramer's paradox : The number of points of intersection of two higher-order curves can be greater than the number of arbitrary points needed to define one such curve.
Topics about Paradoxes in general should be placed in relevant topic categories. Pages in this category should be moved to subcategories where applicable. This category may require frequent maintenance to avoid becoming too large.
Mathematical puzzles make up an integral part of recreational mathematics.They have specific rules, but they do not usually involve competition between two or more players.
"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 at a constant rate of 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?"
ant on rubber rope graph: Image title: Absolute position x vs time t graph of an ant crawling at 1 cm/s (red) relative to and along an elastic band of 4 cm initial length stretching at 2 cm/s painted in eights (shaded background) by CMG Lee. The asymptote (dashed purple) shows the position of the ant if the band was not stretching.
Puzzles are problems deemed to have value as entertainments. The term "puzzle" typically refers to problems in recreational mathematics, geometry, and language — often as a means for education, cognitive skills enhancement in symbolic reasoning or logic.
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