Zenodorus of Paiania was a mathematician, founder of the theory of isoperimetric figures in geometry. He lived during the end of the 3^rd century BC and taught in the Museum of Alexandria, the greatest spiritual center of humanity at the time.

Zenodorus was active a few years after Archimedes’ death, whose work “Measurement of the Circle” he accounts. He came from a wealthy family in Athens. It is believed that he was also an Epicurean philosopher. He was a close friend of Apollonius of Perga and Diocles of Alexandria.

Zenodorus first introduced the concept of the isoperimetric figures in geometry. His work is survived in his treatise On isoperimetric figures, excerpts of which are contained in the works of Pappus of Alexandria, Proclus and Theon. Zenodorus proved that of all the solid figures with equal surfaces, the sphere is the greatest, that the equiangular and equilateral polygon is the greatest in area out of all the polygons with the same number of sides and equal perimeter and that the circle is greater than any regular polygon of equal contour. Moreover, Zenodorus proved that the polygon with the most angles has the greatest area than all regular polygons with the same perimeter.

It is not known if Zenodorus wrote any other treatises, as nothing else has survived of his work. Nevertheless, his influence in geometry is evident from the fact that he is mentioned by numerous mathematicians such as Diocles, Theon, Proclus, Eutocius, Simplicius as well as multiple Arabian mathematicians. Pappus of Alexandria, who basically compares the area or volume of different geometric shapes with the same perimeter in the 5^th book of his treatise “Mathematical Synagogue”, expands Zenodorus’ work on the isometric or isoperimetric figures.

Not surprisingly, Zenodorus’ work had and important impact on the mathematicians of the 18^th, 19^th and 20^th centuries. His work opened the way for the discovery of the area of mathematics known as calculus of variations. It is worth mentioning that great mathematical minds of history acknowledge Zenodorus as an important figure in the advancement of mathematics. In one of his letters to Leonhard Euler, Joseph – Louis Langange characterizes Zenodorus as “the first teacher (τὸν πρῶτον διδάξαντα)” while Constantine Caratheodory considered him as the Father of the Calculus of Variations.

Bibliography

1. Georgakopoulos, Konstantinos. Ancient Greek Scientists. Georgiades: Athens, 1995. Print.
2. Ζηνόδωρος ο Παιανεύς Ένας Μεγάλος Μαθηματικός. Excerpt from the book Ζηνόδωρος ο Παιανεύς ( Ένας Μεγάλος Μαθηματικός). Αίθρα. Αθήνα, 2011. by Evangelos Spandagos. Eisatopon.blogspot.bg. Web.