# Bryson of Heraclea: Wikis

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# Encyclopedia

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 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, but Archimedes 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.
• Heath, Thomas (1981). A History of Greek Mathematics, Volume I: From Thales to Euclid. Dover Publications, Inc. ISBN 0486240738.