:''There is also a Menaechmus in Plautus' play, '' The Menaechmi''.'' Menaechmus ( el, Μέναιχμος, 380–320 BC) was an ancient Greek mathematician, geometer and philosopher 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.

Life and work

Menaechmus is remembered by mathematicians for his discovery of the

conic sections In mathematics, a conic section, quadratic curve or conic is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special ...

and his solution to the problem of doubling the cube. Menaechmus likely discovered the conic sections, that is, the

ellipse In mathematics, an ellipse is a plane curve surrounding two focus (geometry), focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special ty ...

, the parabola, and the hyperbola, as a by-product of his search for the solution to the Delian problem. Menaechmus knew that in a parabola y² = ''L''x, 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. He apparently derived these properties of conic sections and others as well. Using this information it was now possible to find a solution to the problem of the duplication of the cube by solving for the points at which two parabolas intersect, a solution equivalent to solving a cubic equation. There are few direct sources for Menaechmus's work; his work on conic sections is known primarily from an

epigram An epigram is a brief, interesting, memorable, and sometimes surprising or satirical statement. The word is derived from the Greek "inscription" from "to write on, to inscribe", and the literary device has been employed for over two mille ...

Eratosthenes Eratosthenes of Cyrene (; grc-gre, Ἐρατοσθένης ; – ) was a Greek polymath: a mathematician, geographer, poet, astronomer, and music theorist. He was a man of learning, becoming the chief librarian at the Library of Alexandria ...

, 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 Lycius (; 8 February 412 – 17 April 485), called Proclus the Successor ( grc-gre, Πρόκλος ὁ Διάδοχος, ''Próklos ho Diádokhos''), was a Greek Neoplatonist philosopher, one of the last major classical philosophers ...

. 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 purely 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, ''A History of Pi'', 1989, p. 34) However, this quote is first attested by Stobaeus, about 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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Life and work

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