The Solution of Menaechmus

Auteur:Ku, Yin Bon (Albert)

Menaechmus (380 - 320 BC) was a Greek mathematician. In fact, he was the mathematics tutor of Alexander the Great. His most famous discovery was on conic sections - He was the first to show that the three special curves - parabola, hyperbola and ellipse - are obtained by cutting a cone in a plane not parallel to the base. He gave two solutions to double mean proportionals problem. Both involve the intersection of special curves. Given any two positive real numbers

and

, we want to find

and

such that

First solution: We construct a parabola and a hyperbola (the blue and black curves in the diagram below) that satisfy the following equations respectively:

The intersection point of these two curves is

. Its coordinates are the required values of

and

. Second solution:We construct two parabolas (the blue and red ones in the diagram below) that satisfy the following equations respectively:

The intersection of these two curves is

. Its coordinates are the required values of

and

The Solution of Menaechmus

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