Laraudogoitia, Jon Perez (2025) How the tortoise can beat Achilles: a paradox on curves of infinite length. [Preprint]

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Abstract

Achilles and the tortoise compete in a race where the beginning (the start) is at point O and end (the finish) is at point P. At all times the tortoise can run at a speed that is a fraction F of Achilles' speed at most (with F being a positive real number lower than 1, 0 < F < 1), and both start the race at t = 0 at O. If the trajectory joining O with P is a straight line, Achilles will obviously win every time. It is easy to prove that there is a trajectory joining O and P along which the tortoise has a strategy to win every time, reaching the finish before Achilles.

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Item Type:	Preprint
Creators:	Creators Email ORCID Laraudogoitia, Jon Perez jon.perez@ehu.es 0000-0002-9003-4946
Keywords:	Zeno's paradoxes; Achilles and the tortoise; infinity; non-rectifiable curves
Subjects:	General Issues > Scientific Metaphysics Specific Sciences > Physics > Classical Physics Specific Sciences > Mathematics
Depositing User:	Dr. Jon Perez Laraudogoitia
Date Deposited:	25 Jun 2025 17:07
Last Modified:	25 Jun 2025 17:07
Item ID:	25736
Subjects:	General Issues > Scientific Metaphysics Specific Sciences > Physics > Classical Physics Specific Sciences > Mathematics
Date:	18 June 2025
URI:	https://philsci-archive.pitt.edu/id/eprint/25736

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