Menaechmus (b. 380 BC, d. 320) was a Greek mathematician and geometer born in Alopeconnesus (within modern-day Turkey), 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. There are few direct sources for Menaechmus' work- his work on conic sections is known primarily from a 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. Proclus also mentions that Menaechmus was taught by Eudoxus
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 solely algebraic.
Menaechmus was said to have been the tutor of Alexander the Great; this belief derives from the following anecdote: supposedly, once, when Alexander asked him for a shortcut to understanding geometry, he replied "O King, for traveling over the country, there are royal road and roads for common citizens, but in geometry there is one road for all" (Beckmann 1989, p. 34). However, this quote is first attributed to Stobaeus ~500 AD, and so whether Menaechmus really taught Alexander is uncertain.
Where precisely he died is uncertain as well- though modern scholars believe that he eventually expired in Cyzicus.
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