Life and work

Little is known about the life of Zenodorus, although he may have befriended Philonides

Philonides of Laodicea

Philonides of Laodicea in Syria, was an Epicurean philosopher and mathematician who lived in the Seleucid court during the reigns of Antiochus IV Epiphanes and Demetrius I Soter....

 and made two trips to Athens

Athens

Athens , is the capital and largest city of Greece. Athens dominates the Attica region and is one of the world's oldest cities, as its recorded history spans around 3,400 years. Classical Athens was a powerful city-state...

, as described in Philonides' biography. From the style of his writing, it is known that he lived not much later than Archimedes

Archimedes

Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and an...

.

He is mentioned in Diocles

Diocles

Diocles may refer to:*Diocles, a person in Greek mythology*Roman emperor Diocletian, formerly named Diocles*Diocles of Carystus, Greek physician who lived 4th century BC*Diocles , 2nd century BC and the beginning of the 1st century BC...

' On Burning Mirrors,

And when Zenodorus the astronomer came down to Arcadia

Arcadia

Arcadia is one of the regional units of Greece. It is part of the administrative region of Peloponnese. It is situated in the central and eastern part of the Peloponnese peninsula. It takes its name from the mythological character Arcas. In Greek mythology, it was the home of the god Pan...

 and was introduced to us, he asked us how to find a mirror surface such that when it is placed facing the sun the rays reflected from it meet a point and thus cause burning.

Zenodorus is known for authoring the treatise On isometric figures, now lost. Fortunately, we know many of its propositions from Theon of Alexandria

Theon of Alexandria

Theon was a Greek scholar and mathematician who lived in Alexandria, Egypt. He edited and arranged Euclid's Elements and Ptolemy's Handy Tables, as well as writing various commentaries...

's commentary on Ptolemy

Ptolemy

Claudius Ptolemy , was a Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology. He lived in Egypt under Roman rule, and is believed to have been born in the town of Ptolemais Hermiou in the...

's Syntaxis. In his On isometric figures, Zenodorus studies the areas and perimeters of different geometric figures. The most important propositions proved by him are that,

1. Of all regular polygons of equal perimeter, that is the greatest in area which has the most angles.
2. A circle is greater than any regular polygon of equal contour.
3. Of all polygons of the same number of sides and equal perimeter the equilateral and equiangular polygon is the greatest in area.
4. Of all solid figures the surfaces of which are equal, the sphere is the greatest in solid content.

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