- Bryson of Heraclea
Bryson of Heraclea (ca. 450 BCE - ca. 390 BCE) was an
ancient Greek mathematicianand sophistwho contributed to solving the problem of squaring the circleand calculating pi.
Life and work
Although little is known about the life of Bryson, it is believed that he was probably a pupil of
Socrates. He is said to have upset Aristotle by asserting that obscene languagedoes not exist.
Pi and squaring the circle
Bryson, along with his contemporary Antiphon, was the first to
inscribea polygon inside a circle, find the polygon's area, double the number of sides of the polygon, and repeat the process, resulting in a lower boundapproximation of the area of a circle. "Sooner or later (they figured), ... [there would be] so many sides that the polygon ... [would] be a circle" (Blatner, 16). Bryson later followed the same procedure for polygons circumscribing a circle, resulting in an upper boundapproximation of the area of a circle. With these calculations Bryson was able to approximate π and further place lower and upper bounds on π's true value. But due to the complexity of the method, he only calculated π to a few digits. Aristotlecriticized this method, but Archimedeswould later use a method similar to that of Bryson and Antiphon to calculate π; however, Archimedes calculated the perimeter of a polygon instead of the area.
*Blatner, David. The Joy of Pi. Walker Publishing Company, Inc. New York, 1997.
*Philosophy Dictionary definition of Bryson of Heraclea. The Oxford Dictionary of Philosophy. Copyright © 1994, 1996, 2005 by Oxford University Press.
title=A History of Greek Mathematics, Volume I: From Thales to Euclid
publisher=Dover Publications, Inc
* [http://www.math.rutgers.edu/~cherlin/History/Papers2000/wilson.html The History of Pi]
*MacTutor Biography|id = Bryson
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