Mathematician, Philosopher (c.380 BC – c.320 BC)

Menaechmus was a famous mathematician and Platonic philosopher of the 4^{th} century BC from Alopeconnesus. He is remembered for his contributions in geometry. As Proclus puts it “(he) *and his brother Deinostratus made the whole of geometry still more perfect*”.

Menaechmus was a student of Eudoxus, a polymath who was in turn a student of Plato in the Academy. He served as the tutor of Alexander the Great in geometry. It is believed that he had founded his own school of mathematics. His most important contributions were in the field of conic sections.

The conic sections, one of the most applicable chapters in analytical geometry were discovered by Menaechmus when he was attempting to solve the doubling of the cube, a famous geometrical problem of antiquity known for its high degree of difficulty. Menaechmus managed to solve the problem with two solutions by using the conic sections, thus paving the way for Apollonius of Perga to develop them years later.

He showed that by cutting a cone with a line that is not parallel to the base, one could obtain different shapes, which he named ellipses, parabolas and hyperboles, depending on the angle. It is asserted that the mathematician used mechanical devices to help him in drawing the shapes, something which Plato disapproved in geometry. His works were translated into Arabic and then to Latin during the late Middle Ages. This contributed significantly to the Renaissance and the revival of mathematics.

Menaechmus endorsed Eudoxus’ theory on the heavenly bodies and further developed it based on Theon of Smyrna’s writings. Moreover, he studied the structure of mathematics and was involved with astronomy. His work was continued by Apollonius of Perga, Archimedes and by the mathematicians of the Renaissance.

Bibliography:

- JJ O’Connor, E.F. Robertson.
*Menaechmus*. University of St.Andrews. www-groups.dcs.st-and.ac.uk. Web.
*Ο Μέναιχμος, ο Μεγαλέξανδρος και η Οδός της Γεωμετρίας*. Ιστορίες στο Περιθώριο.. dimitristsolakis.blogspot.bg. Web. August 19, 2012.

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