Person: Bryson Of Heraclea
Bryson was a Greek mathematician who was probably a pupil of Socrates and contributed to the problem of squaring the circle.
Mathematical Profile (Excerpt):
 Bryson was a Sophist and Aristotle criticises him both for his assertion that there is no such thing as indecent language, and also for his method of squaring the circle.
 Diogenes Laertius gives some other biographical details of Bryson, but these cannot all be correct since Bryson's interaction with a number of philosophers is stated, yet certain of these are impossible due to the dates during which these men lived.
 Perhaps the most likely of the details preserved by Diogenes Laertius is that Bryson was either a pupil of Socrates or of Euclid of Megara.
 It is a little difficult to reconstruct exactly what Bryson's method of squaring the circle was.
 According to Alexander Aphrodisiensis, writing in about 210 AD, Bryson inscribed a square in the circle and circumscribed a second square.
 Bryson then constructed a third square between the inscribed and circumscribed square (but Alexander does not tell us how this third square was constructed).
 Alexander then claims that Bryson's argument was that the circle was intermediate between the inscribed and circumscribed squares, the third square is also intermediate between the inscribed and circumscribed squares and therefore the third square equals the circle.
 If indeed Alexander is right in what he attributes to Bryson then his contribution would not merit inclusion in this archive.
 However, other commentators attribute a much more significant argument to Bryson.
 Themistius, another ancient commentator, writes that Bryson claimed that the circle was greater than all inscribed polygons and less than all circumscribed polygons.
 This would be an improvement on Antiphon's argument and Bryson is getting close to the method of exhaustion as rigorously applied by Archimedes.
 We know little else of Bryson.
 He wrote Diatribes which some accused Plato of stealing and indeed Bryson is claimed to have associated with Polyxenus who put forward philosophical arguments which appear in Plato's Pramenides and could well be the arguments which were claimed stolen from Bryson's Diatribes.
Born about 450 BC, Tarentum, Heraclea (now Taranto, Italy). Died about 390 BC.
View full biography at MacTutor
Tags relevant for this person:
Ancient Greek, Geometry, Origin Italy, Puzzles And Problems
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Epochs: 1
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References
Adapted from other CC BYSA 4.0 Sources:
 Oâ€™Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive