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 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). In fact, 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.
Read more about Ant On A Rubber Rope: A Formal Statement of The Problem, Applications of The Problem
Famous quotes containing the words ant, rubber and/or rope:
“As a thinker and planner, the ant is the equal of any savage race of men; as a self-educated specialist in several arts, she is the superior of any savage race of men; and in one or two high mental qualities she is above the reach of any man, savage or civilized.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)
“First, are you our sort of a person?
Do you wear
A glass eye, false teeth or a crutch,
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Stitches to show something’s missing?”
—Sylvia Plath (1932–1963)
“Immortality without eternity is a rope with only one end.”
—Multatuli [Eduard Douwer Dekker] (1820–1887)