Menaechmus | Biography

A student of , Menaechmus is said by some sources to have been a mathematics tutor to Alexander the Great. He is most famous for his discovery of .

Menaechmus was born in about 380 B.C. in Alopeconnesus, Asia Minor, in what is now Turkey. Little is known of the ancient mathematician's personal life. However, his alleged response to Alexander's request for a shortcut to learning geometry suggests something of a sense of humor as well as a reverence for his chosen field of study. He is said to have told Alexander, "O king, for traveling through the country there are private roads and royal roads, but in geometry there is one road for all." Some sources suggest that might have introduced the two men to each other.

It seems likely that Menaechmus took over from Eudoxus as head of an illustrious mathematics school in Cyzicus, a Turkish city. Other references indicate that as a teacher Menaechmus would have stringently focused on the technology and philosophy of mathematics. For instance, ancient writings record the development of his theory that all are and that there are two types of theorems: those that seek a concrete answer and those that seek something's properties (e.g., what it is, what group it belongs to, how it has changed, its relationship to another, etc.).

Records also show that Menaechmus was involved in mathematical astronomy. He is said to have introduced the concept of "counteracting" and "deferent" concentric spheres as part of the era's widely held explanation for planetary movement. According to Menaechmus, one sphere would bear a heavenly body and another would correct its motion, thus explaining the planets' seemingly irregular paths.

Although these contributions were important in their day, Menaechmus's discovery of conic sections is mainly why he is still remembered in modern times. The breakthrough while he was looking for a way to duplicate a cube specifically, how to find two mean proportionals between two straight lines. Indeed, Menaechmus proved that one could obtain the two means by intersecting a and a . For his trouble, Menaechmus become the brunt of anger. According to writings of the period, Plato was infuriated that Menaechmus and others used mechanical devices in their efforts to double the cube, saying that resorting to such means debased geometry as the highest human achievement.

It was actually more important in terms of mathematical discovery that Menaechmus was the first to show that hyperbolas, parabolas, and can be obtained by cutting a cone in a plane that is not parallel to the base of the cone. Most sources assert that Menaechmus did not coin the terms "parabola" and "hyperbola," although some disagree.