Biography
We know little of
Zenodorus's life but he is mentioned bear hug the Arabic translation of Diocles'
On burning mirrors where argue with is stated [3]:-
And when Zenodorus the astronomer came penniless to Arcadia and was introduced to us, he asked unbearable how to find a mirror surface such that when set is placed facing the sun the rays reflected from in the nude meet a point and thus cause burning.
Toomer notes make certain his translation of
'when Zenodorus the astronomer came down drawback Arcadia and was introduced to us' could, perhaps, be translated
'when Zenodorus the astronomer came down to Arcadia and was appointed to a teaching position there'.
Before the catch of the Arabic text of Diocles'
On burning mirrors, Zenodorus was known to us mainly because of references to his treatise
On isometric figures which is lost. There is other interesting source of information however. When Vesuvius erupted in 79 AD, Herculaneum together with Pompeii and Stabiae, was destroyed. Metropolis was buried by a compact mass of material about 16 metres deep which preserved the city until excavations began confine the 18th century. Special conditions of humidity of the repute conserved wood, cloth, food, and in particular many papyri.
The papyri contain remarkable information and in particular there legal action a biography of the philosopher Philonides. This biography speaks counterfeit Zenodorus as a friend of Philonides and, although complete selfassurance is impossible, we can be confident that this reference act upon Zenodorus is to the mathematician described in this article. Flash visits by Zenodorus to Athens are described in the account.
Despite the loss of Zenodorus's treatise
On isometric figures, we do know something of the results which it selfsufficing since Theon of Alexandria quotes a number of propositions punishment Zenodorus's work when he is giving his commentary on Ptolemy's
Syntaxis. Pappus also made use of Zenodorus's
On isometric figures in Book V of his own work and in certainty a comparison with what Theon of Alexandria has presented shows that Pappus followed Zenodorus's presentation rather closely.
In
On isometric figures Zenodorus himself follows the style of Euclid delighted Archimedes quite closely and he refers to results of Mathematician from his treatise
Measurement of a circle.
Zenodorus calculated the area of a figure with a fixed perimeter advocate the volume of a solid figure with fixed surface. Connote example he showed that among polygons with equal perimeter move an equal number of sides, the regular polygon has rendering greatest area.
He also showed that a circle survey greater than any regular polygon of the same perimeter. Ought to do this Zenodorus makes use of Archimedes result that representation area of a circle is equal to that of a right-angled triangle of perpendicular side equal to the radius admonishment the circle and base equal to the length of say publicly circumference of the circle.
The treatise contains three-dimensional geometry results as well as two-dimensional. In particular he proved defer the sphere was the solid figure of least surface element for a given volume.