- Bryson of Heraclea
**Bryson of Heraclea**(ca. 450 BCE - ca. 390 BCE) was anancient Greek mathematician andsophist who contributed to solving the problem ofsquaring the circle and calculatingpi .**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 thatobscene 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 alower bound approximation of thearea 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 anupper bound approximation 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.Aristotle criticized this method, butArchimedes would 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.**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

authorlink=Thomas Heath

title=A History of Greek Mathematics, Volume I: From Thales to Euclid

publisher=Dover Publications, Inc

year=1981

isbn=0486240738**External links*** [

*http://www.math.rutgers.edu/~cherlin/History/Papers2000/wilson.html The History of Pi*]

*MacTutor Biography|id = Bryson

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