Applications
Even in Classical times the dubious story was annexed to a philosophical problem by Zeno of Elea in one of many demonstrations that movement is impossible to define satisfactorily. The second of Zeno's paradoxes is that of Achilles and the Tortoise, in which the hero gives the Tortoise a head start in a race. The argument attempts to show that even though Achilles runs faster than the Tortoise, he will never catch up with her because, when Achilles reaches the point at which the Tortoise started, the Tortoise has advanced some distance beyond; when Achilles arrives at the point where the Tortoise was when Achilles arrived at the point where the Tortoise started, the Tortoise has again moved forward. Hence Achilles can never catch the Tortoise, no matter how fast he runs, since the Tortoise will always be moving ahead.
The only satisfactory refutation has been mathematical and since then the name of the fable has been applied to the function described in Zeno's paradox. In mathematics and computer science, the tortoise and the hare algorithm is an alternate name for Floyd's cycle-finding algorithm.
Read more about this topic: The Tortoise And The Hare