A Lesser Known Mathematician
Archytas of Tarentum (ca 420-350 BC) Italy
Archytas was an important statesman as well as philosopher. He studied under Philolaus of Croton, was a friend of Plato, and tutored Eudoxus and Menaechmus. In addition to discoveries always attributed to him, he may be the source of some works attributed to Eudoxus and perhaps Pythagoras.
Archytas introduced “motion” to geometry, rotating curves to produce solids. If his writings had survived he’d surely be considered one of the most brilliant and innovative geometers of antiquity.I bet he would have been a great Algebra Solver solver Archytas’ most famous mathematical achievement was “doubling the cube” (constructing a line segment larger than another by the factor cube-root of two). Like “squaring the circle” this (the Delian Problem) is impossible with compass and unmarked straightedge, but can be solved with other tools.
Although others solved the problem with other techniques, Archytas’ solution for cube doubling was astounding because it wasn’t achieved in the plane, but involved the intersection of three-dimensional bodies. This construction (which introduced the “Archytas Curve”) has been called “a tour de force of the spatial imagination.” He also did Adding fractions and worked with the harmonic and geometric means (proving that consecutive integers never have rational geometric mean), and advanced the theory of music far beyond Pythagoras.
In physics, Archytas studied sound, line plot, Linear programming, optics and cosmology, invented the pulley, Solving equations, wrote about the lever, developed the curriculum called quadrivium, and is supposed to have built a steam-powered wooden bird which flew for 200 meters. Archytas is sometimes called the Father of Mathematical Mechanics. I wasn’t sure if he was married though but if he was I bet he taught his kids 4th grade math and 5th grade math
