Menaechmus

Menaechmus was an ancient Greek mathematician of the fourth century BC, born at Alopeconnesus on the Thracian coast, in what is now Turkey. Ancient writers describe him as a pupil of Eudoxus who had also studied with Plato, and a later anecdote makes him the tutor to whom Alexander the Great put the question of an easy road to geometry, answered with the line that there is one road for all. He is remembered as the first to show that the ellipse, parabola and hyperbola arise when a cone is cut by a plane not parallel to its base. He reached these curves while trying to duplicate the cube, which he reduced to finding two mean proportionals between two lines, and he solved it by intersecting a parabola with a rectangular hyperbola, or two parabolas, as the commentator Eutocius reports. He also discussed what counts as an element of mathematics and argued that theorems and problems are not fundamentally different.