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'''Bryson of Heraclea''' (late 5th-century BCE) was an [[ancient Greek]] [[mathematician]] and [[sophist]] who contributed to solving the problem of [[squaring the circle]] and calculating [[pi]].

==Life and work==

Little is known about the life of Bryson; he came from [[Heraclea Pontica]], and he may have been a pupil of [[Socrates]].

He is mentioned in the ''[[Thirteenth Letter (Plato)|13th Platonic Epistle]]'', and [[Theopompus]] even claimed in his ''Attack upon Plato'' that [[Plato]] stole many ideas for his dialogues from Bryson of Heraclea.

He is known principally from [[Aristotle]], who criticizes his method of squaring the circle.

He also upset Aristotle by asserting that [[obscene language]] does not exist.

[[Diogenes Laërtius]] and the [[Suda]] refer several times to a Bryson as a teacher of various philosophers, but since some of the philosophers mentioned lived in the late 4th-century BCE, it is possible that Bryson became confused with [[Bryson of Achaea]], who may have lived around that time.

== Pi and squaring the circle ==

Bryson, along with his contemporary, [[Antiphon (person)|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."

Bryson later followed the same procedure for polygons [[circumscribe|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 of exhaustion|method]] similar to that of Bryson and Antiphon to calculate π; however, Archimedes calculated the [[perimeter]] of a polygon instead of the area.

== See also ==

* [[Mathematician]]
* [[pi]]
* [[Squaring the circle]]

== External links == 

* [https://en.wikipedia.org/wiki/Bryson_of_Heraclea Bryson of Heraclea] @ Wikipedia

[[Category:Mathematicians]]
[[Category:People]]