Menaechmus (Greek: Μέναιχμος, c. 380 – c. 320 BC) was an ancient Greek mathematician, geometer and philosopher[1] born in Alopeconnesus or Prokonnesos in the Thracian Chersonese, who was known for his friendship with the renowned philosopher Plato and for his apparent discovery of conic sections and his solution to the then-long-standing problem of doubling the cube using the parabola and hyperbola.
Menaechmus is remembered by mathematicians for his discovery of the conic sections and his solution to the problem of doubling the cube.
[2] Menaechmus likely discovered the conic sections, that is, the ellipse, the parabola, and the hyperbola, as a by-product of his search for the solution to the Delian problem.
[3] Menaechmus knew that in a parabola y2 = Lx, where L is a constant called the latus rectum, although he was not aware of the fact that any equation in two unknowns determines a curve.
[5] There are few direct sources for Menaechmus's work; his work on conic sections is known primarily from an epigram by Eratosthenes, and the accomplishment of his brother (of devising a method to create a square equal in area to a given circle using the quadratrix), Dinostratus, is known solely from the writings of Proclus.
There is a curious statement by Plutarch to the effect that Plato disapproved of Menaechmus achieving his doubled cube solution with the use of mechanical devices; the proof currently known appears to be purely algebraic.
"[6] However, this quotation is first attested by Stobaeus, about 500 AD, and so whether Menaechmus really taught Alexander is uncertain.