ARCHYTAS OF TARENTUM

flourished 400, 350 BC, Tarentum, Magna Graecia [now Taranto, Italy] Greek scientist, philosopher, and major Pythagorean mathematician, who is sometimes called the founder of mathematical mechanics. Plato, a close friend, made use of his work in mathematics, and there is evidence that Euclid borrowed from him for Book viii of his Elements. Archytas was also an influential figure in public affairs, and he served for seven years as commander in chief of his city. A member of the second generation of followers of Pythagoras, the Greek philosopher who stressed the significance of numbers in explaining all phenomena, Archytas sought to combine empirical observation with Pythagorean theory. In geometry, he solved the problem of doubling the cube by constructing a three-dimensional model. The conclusions that he then drew concerning continued proportions, expressed as a:b = b:c = c:d, he applied to musical harmony. Thus, he was able to discern intervals of pitch in the enharmonic scale in addition to those already known in the chromatic and the diatonic scales. Rejecting earlier views that the pitch of notes sounded on a stringed instrument is related to the length or tension of the strings, he proposed instead that pitch is related to the movement of vibrating air. Incorrectly, however, he asserted that the speed at which the vibrations travel to the ear is a factor in determining pitch. Archytas' reputation as a scientist and mathematician rests on his achievements in geometry, acoustics, and music theory, rather than on his extremely idealistic explanations of human relations and the nature of society according to Pythagorean number theory. Nonmathematical writings usually attributed to him, including a fragment on legal justice, are most likely the work of other authors.