Archytas

Archytas (435/410–360/350 BC) was an Ancient Greek mathematician, music theorist, statesman, and strategist from the ancient city of Taras (Tarentum) in Southern Italy. He was a scientist and philosopher affiliated with the Pythagorean school and famous for being the reputed founder of mathematical mechanics and a friend of Plato.
As a Pythagorean, Archytas believed that arithmetic (logistic), rather than geometry, provided the basis for satisfactory proofs, and developed the most famous argument for the infinity of the universe in antiquity.
Life
Archytas was born in Tarentum, a Greek city that was part of Magna Graecia, and was the son of Hestiaeus. He was presumably taught by Philolaus, and taught mathematics to Eudoxus of Cnidus and to Eudoxus' student, Menaechmus.
Politically and militarily, Archytas appears to have been the dominant figure in Tarentum in his generation, somewhat comparable to Pericles in Athens a half-century earlier. The Tarentines elected him strategos ("general") seven years in a row, a step that required them to violate their own rule against successive appointments. Archytas was allegedly undefeated as a general in Tarentine campaigns against their southern Italian neighbors.
In his public career, Archytas had a reputation for virtue as well as efficacy. The Seventh Letter, traditionally attributed to Plato, asserts that Archytas attempted to rescue Plato during his difficulties with Dionysius II of Syracuse. Some scholars have argued that Archytas may have served as one model for Plato's philosopher king, and that he influenced Plato's political philosophy as expressed in The Republic and other works.
Works
Archytas is said to be the first ancient Greek to have spoken of the sciences of arithmetic (logistic), geometry, astronomy, and harmonics as kin, which later became the medieval quadrivium. He is thought to have written a number of works in the sciences but only four genuine fragments are extant.
According to Eutocius, Archytas was the first to solve the problem of doubling the cube (the so-called Delian problem) with an ingenious geometric construction. Hippocrates of Chios before had reduced this problem to the finding of two mean proportionals, equivalent to the extraction of cube roots. Archytas' demonstration uses lines generated by moving figures to construct the two proportionals between magnitudes and was, according to Diogenes Laërtius, the first in which mechanical motions entered geometry. The topic of proportions, which Archytas seems to have worked on extensively, is treated in book VIII of Euclid's Elements, where the construction for two proportional means can also be found.
Archytas named the harmonic mean, important much later in projective geometry and number theory, though he did not discover it. He proved that ratios of the form (n + 1): n cannot be divided by a mean proportional, an important result in ancient harmonics. Ptolemy considered Archytas the most sophisticated Pythagorean music theorist, and scholars believe Archytas gave a mathematical account of the musical scales used by practicing musicians of his day.
Later tradition regarded Archytas as the founder of mathematical mechanics. Vitruvius includes him in a list of twelve authors who wrote works on mechanics. Thomas Nelson Winter presents evidence that the pseudo-Aristotelian Mechanical Problems might have been authored by Archytas and later misattributed. As described in the writings of Aulus Gellius five centuries after him, Archytas was reputed to have designed and built some kind of bird-shaped, self-propelled flying device known as the pigeon, said to have flown some 200 meters.
Notes
References
Further reading
on line
Huffman, Carl A. Archytas of Tarentum, Cambridge University Press, 2005,
External links
Pseudo-Aristotle, Mechanica – Greek text and English translation
Complete fragments (Greek–Spanish bilingual edition)
Fragments and Life of Archytas
428 BC births
347 BC deaths
4th-century BC Greek philosophers
Ancient Greek generals
Ancient Greek mathematicians
Ancient Greek music theorists
Ancient Greek physicists
Ancient Greek inventors
Ancient Tarantines
Pythagoreans of Magna Graecia
5th-century BC mathematicians
4th-century BC mathematicians