Zenodorus (Greek: Ζηνόδωρος; c. 200 – c. 140 BC) was an ancient Greek mathematician.

Life and work

Little is known about the life of Zenodorus, although he may have befriended Philonides and made two trips to Athens, as described in Philonides' biography. From the style of his writing, it is known that he lived not much later than Archimedes.

He is mentioned in Diocles' On Burning Mirrors:

And when Zenodorus the astronomer came down to Arcadia 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.[1]

Zenodorus is known for authoring the treatise On isoperimetric figures, now lost. Many of its propositions are known from Theon of Alexandria's commentary on Ptolemy's Syntaxis. In his On isoperimetric figures, Zenodorus studies the areas and perimeters of different geometric figures. The most important propositions proved by him are that,

Of all regular polygons of equal perimeter, that is the greatest in area which has the most angles.

A circle is greater than any regular polygon of equal contour.

Of all polygons of the same number of sides and equal perimeter the equilateral and equiangular polygon is the greatest in area.

Of all solid figures the surfaces of which are equal, the sphere is the greatest in solid content..[2][3]

Notes

Toomer (1976)

Heath (1981) p. 207–213

Kline (1972), p. 126

References

Heath, Thomas Little (1981). A History of Greek Mathematics, Volume II. Dover publications. ISBN 0-486-24074-6.

Morris Kline, Mathematical Thought From Ancient to Modern Times, Oxford University Press, 1972.

G. J. Toomer, Diocles On Burning Mirrors, Sources in the History of Mathematics and the Physical Sciences 1 (New York, 1976).

External links

O'Connor, John J.; Robertson, Edmund F., "Zenodorus (mathematician)", MacTutor History of Mathematics archive, University of St Andrews.

History of the Isoperimetric Problem at Convergence

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Ancient Greek and Hellenistic mathematics (Euclidean geometry)

Mathematicians

(timeline)

Anaxagoras Anthemius Archytas Aristaeus the Elder Aristarchus Apollonius Archimedes Autolycus Bion Bryson Callippus Carpus Chrysippus Cleomedes Conon Ctesibius Democritus Dicaearchus Diocles Diophantus Dinostratus Dionysodorus Domninus Eratosthenes Eudemus Euclid Eudoxus Eutocius Geminus Heliodorus Heron Hipparchus Hippasus Hippias Hippocrates Hypatia Hypsicles Isidore of Miletus Leon Marinus Menaechmus Menelaus Metrodorus Nicomachus Nicomedes Nicoteles Oenopides Pappus Perseus Philolaus Philon Philonides Porphyry Posidonius Proclus Ptolemy Pythagoras Serenus Simplicius Sosigenes Sporus Thales Theaetetus Theano Theodorus Theodosius Theon of Alexandria Theon of Smyrna Thymaridas Xenocrates Zeno of Elea Zeno of Sidon Zenodorus

Treatises

Almagest Archimedes Palimpsest Arithmetica Conics (Apollonius) Catoptrics Data (Euclid) Elements (Euclid) Measurement of a Circle On Conoids and Spheroids On the Sizes and Distances (Aristarchus) On Sizes and Distances (Hipparchus) On the Moving Sphere (Autolycus) Euclid's Optics On Spirals On the Sphere and Cylinder Ostomachion Planisphaerium Sphaerics The Quadrature of the Parabola The Sand Reckoner

Problems

Angle trisection Doubling the cube Squaring the circle Problem of Apollonius

Concepts/definitions

Circles of Apollonius

Apollonian circles Apollonian gasket Circumscribed circle Commensurability Diophantine equation Doctrine of proportionality Golden ratio Greek numerals Incircle and excircles of a triangle Method of exhaustion Parallel postulate Platonic solid Lune of Hippocrates Quadratrix of Hippias Regular polygon Straightedge and compass construction Triangle center

Results

In Elements

Angle bisector theorem Exterior angle theorem Euclidean algorithm Euclid's theorem Geometric mean theorem Greek geometric algebra Hinge theorem Inscribed angle theorem Intercept theorem Pons asinorum Pythagorean theorem Thales's theorem Theorem of the gnomon

Apollonius

Apollonius's theorem

Other

Aristarchus's inequality Crossbar theorem Heron's formula Irrational numbers Menelaus's theorem Pappus's area theorem Problem II.8 of Arithmetica Ptolemy's inequality Ptolemy's table of chords Ptolemy's theorem Spiral of Theodorus

Centers

Cyrene Library of Alexandria Platonic Academy

Other

Ancient Greek astronomy Greek numerals Latin translations of the 12th century Neusis construction

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