MATHEMATICIAN

Life
Menaechmus was born in Alopeconnisus, in Thrace. He was a disciple of Eudoxus, a friend of Plato, brother of the famous geometer Deinostratus, and an early tutor of Alexander the Great. Menaechmus paved the way for the work of Eratosthenes. He wrote a number of treatises that have not survived, except in small fragments preserved by Eutocius; some information about his work may also be gleaned from other writers. He is cited by Eutocius and Proclus.


Work
Menaechmus was the first to describe and study conic sections (the ellipse, the parabola and the hyperbola): these are the curves that result from plane intersections of a cone (the "triad", or three conic sections, of Menaechmus).

He studied the problem of the duplication of the cube, and proved that the point demanded is a function of the intersection of two parabolas or of a parabola and a hyperbola.

Menaechmus was the first to solve equations in the third degree. He also worked on problems of astronomy, and further developed Eudoxus' theory of concentric circles. His work on conic sections was subsumed into Euclid's "Conics", which is lost.

He defined the meaning of the term 'element' in geometry, and debated with Speusippus on the relative compass of the terms "theorem" and "problem".

"Geometry of the Academy": Compiled in collaboration with Theudius Magnetas.