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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.
"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?"
AI trust paradox; Algol paradox; Ant on a rubber rope; B. Bentley's paradox; Birthday paradox; Bracketing paradox; ... Stapp's ironical paradox; Status paradox ...
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.
Ant on a rubber rope; B. Bellman's lost-in-a-forest problem; C. Carpenter's rule problem; ... Hooper's paradox; Hundred-dollar, Hundred-digit Challenge problems; J ...
[1] [2] Diogenes Laërtius, citing Favorinus, says that Zeno's teacher Parmenides was the first to introduce the paradox of Achilles and the tortoise. But in a later passage, Laërtius attributes the origin of the paradox to Zeno, explaining that Favorinus disagrees. [3] Modern academics attribute the paradox to Zeno. [1] [2]
A graph that shows the number of balls in and out of the vase for the first ten iterations of the problem. The Ross–Littlewood paradox (also known as the balls and vase problem or the ping pong ball problem) is a hypothetical problem in abstract mathematics and logic designed to illustrate the paradoxical, or at least non-intuitive, nature of infinity.