Greek mathematician and geometer said to have been the tutor of Alexander the Great. When his pupil asked him for a shortcut to geometry, he replied "O King, for traveling over the country, there are royal road to geometry and roads for common citizens, but in geometry there is one road for all" (Beckmann 1989, p. 34). However, this quote has also been attributed to the tutor of Napoleon Bonaparte.
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.
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.
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.
Some have inferred from this (see for example [4]) that Menaechmus acted as a tutor to Alexander the Great, and indeed this is not impossible to imagine since as Allman suggests Aristotle may have provided the link between the two.
Proclus that Menaechmus was the head of a School and this is argued convincingly by Allman in [4].
Allman [4] suggests that Menaechmus might have drawn the curves by finding many points on them and that this might be considered as a mechanical device.
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