Archytas

Archytas of Tarentum, who lived between roughly 435 or 410 and 360 or 350 BC, was an Ancient Greek mathematician, music theorist, statesman and strategist from the city of Taras, now Taranto in Apulia, southern Italy. He belonged to the Pythagorean school, was a friend of Plato, and is reputed to be the founder of mathematical mechanics. He is said to have taught mathematics to Eudoxus of Cnidus and, through him, to Menaechmus. The Tarentines elected him general seven years running, and the Seventh Letter attributed to Plato says he tried to rescue Plato from trouble with Dionysius II of Syracuse. According to Eutocius he was the first to double the cube with a geometric construction that used lines generated by moving figures, a step Diogenes Laertius called the first entry of mechanical motion into geometry. He named the harmonic mean, proved that superparticular ratios cannot be divided by a mean proportional, and was counted by Ptolemy as the most sophisticated Pythagorean music theorist. Only four fragments of his writings are generally accepted as authentic.