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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.
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.
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Download as PDF; Printable version; In other projects Wikimedia Commons; ... Ant on a rubber rope; B. Bellman's lost-in-a-forest problem; C. Carpenter's rule problem;
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"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?"
When a dog named Moscow fell about 200 feet down a waterfall at Cascade Falls near Emerald Bay, it set off a dramatic rescue mission. Despite the terrifying fall, Moscow survived, and his owner ...