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Dionysodorus of Caunus (Greek: Διονυσόδωρος ὁ Καύνειος, c. 250 BC – c. 190 BC) was an ancient Greek mathematician.

Life and work

Little is known about the life of Dionysodorus. Pliny the Elder writes about a Dionysodorus who measured the earth's circumference, however he is probably the one from Pontus and different from the one from Caunus as Strabo differentiates between the two mathematicians.[1]

Dionysodorus is remembered for solving the cubic equation by means of the intersection of a rectangular hyperbola and a parabola.[2] Eutocius credits Dionysodorus with the method of cutting a sphere into a given ratio, as described by him.[3] Heron mentions a work by Dionysauras entitled On the Tore, in which the volume of a torus is calculated and found to be equal to the area of the generating circle multiplied by the circumference of the circle created by tracing the center of the generating circle as it rotates about the torus's axis of revolution. Dionysodorus used Archimedes' methods to prove this result.[1]

It is also likely that this Dionysodorus was the inventor of a conical sundial.[1] Pliny's mentioning tells of an inscription placed on his tomb, addressed to the world above, stating that he had been to the centre of the earth and found it 42 thousand stadia distant.[4] Pliny calls this a striking instance of Greek vanity; but this figure compares well with the modern measurement.
Citations and footnotes

"Dionysodorus biography". www-groups.dcs.st-and.ac.uk. Retrieved 2016-04-24.
Heath (1921)
Eutocius, Comment on book ii. prop. 5, of the Sphere and Cylinder of Archimedes

Pliny, Hist. Nat. ii. 109


T. L. Heath, A History of Greek Mathematics II (Oxford, 1921).
Netz, Reviel. The Transformations of Mathematics in the Early Mediterranean World. Cambridge University Press, 2004. ISBN 0-521-82996-8. Pags. 29-39.

External links

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


Ancient Greek and Hellenistic mathematics (Euclidean geometry)
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
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
Angle trisection Doubling the cube Squaring the circle Problem of Apollonius
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
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's theorem
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
Cyrene Library of Alexandria Platonic Academy
Ancient Greek astronomy Greek numerals Latin translations of the 12th century Neusis construction

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