# Bryson of Heraclea

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Bryson of Heraclea

Bryson of Heraclea (ca. 450 BCE - ca. 390 BCE) was an ancient Greek mathematician and sophist who contributed to solving the problem of squaring the circle and 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 language does not exist.

Pi and squaring the circle

Bryson, along with his contemporary Antiphon, was the first to inscribe a 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 bound approximation 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 bound approximation of the area of a circle. With these calculations Bryson was able to approximate &pi; and further place lower and upper bounds on &pi;'s true value. But due to the complexity of the method, he only calculated &pi; to a few digits. Aristotle criticized this method, but Archimedes would later use a method similar to that of Bryson and Antiphon to calculate &pi;; however, Archimedes calculated the perimeter of a polygon instead of the area.

References

*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.
*cite book
first=Thomas
last=Heath
title=A History of Greek Mathematics, Volume I: From Thales to Euclid
publisher=Dover Publications, Inc
year=1981
isbn=0486240738

* [http://www.math.rutgers.edu/~cherlin/History/Papers2000/wilson.html The History of Pi]
*MacTutor Biography|id = Bryson

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