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Achilles and the tortoise
In Greek mythology, when Achilles was born, his mother held him by the heel and dipped him into the river Styx to give him invulnerability. Every part of his body touched by the river became invulnerable except the places where she was holding him; thus he could only be killed by a wound to his heel. Paris killed him with a poisoned arrow which hit him in the heel. This myth has given rise both to the expression "Achilles' heel" to mean a weak or vulnerable spot, and the name "Achilles' tendon" for the large tendon which joins the calf muscle to the heel bone.
In Greek mythology, when Achilles was born, his mother held him by the heel and dipped him into the river Styx to give him invulnerability. Every part of his body touched by the river became invulnerable except the places where she was holding him; thus he could only be killed by a wound to his heel. Paris killed him with a poisoned arrow which hit him in the heel. This myth has given rise both to the expression "Achilles' heel" to mean a weak or vulnerable spot, and the name "Achilles' tendon" for the large tendon which joins the calf muscle to the heel bone.
One of Zeno's paradoxes concerns "Achilles and the tortoise." It concerns an imaginary race between Achilles and a slow-moving tortoise which gets a head start. Although Achilles runs much faster than the tortoise, Zeno argued that Achilles can never actually catch the tortoise. In order to catch him, Achilles must reach the place where the tortoise is now. By the time Achilles reaches that place, the tortoise will have moved. Even if Achilles has run a hundred feet while the tortoise has moved only one foot, Achilles has not yet caught the tortoise. To catch him, Achilles must again first reach the place where the tortoise is now. But, again, by the time he reaches that place the tortoise will have moved. Even though the tortoise moves a smaller distance each time, it seemed to Zeno that Achilles could never actually catch him. In mathematics, the paradox is resolved by observing that the times it takes Achilles to perform each iteration form a [[geometric progression|geometric series]], which has an infinite number of terms but a finite sum.