**Dionysodorus** was a Greek mathematician who solved a cubic equation using the intersection of a parabola and a hyperbola.

- Strabo, the Greek geographer and historian (about 64 BC - about 24 AD), describes a mathematician named Dionysodorus who was born in Amisene, Pontus in northeastern Anatolia on the Black Sea.
- The Dionysodorus we are interested in here is the mathematician Dionysodorus whom Eutocius states solved the problem of the cubic equation using the intersection of a parabola and a hyperbola.
- It was thought until early this century that the Dionysodorus to whom Eutocius refers, was Dionysodorus of Amisene described by Strabo.
- There is a second Dionysodorus who appears in the writings of Pliny.
- In Natural history Pliny mentions a certain Dionysodorus who measured the earth's radius and gave the value 42000 stades.
- Strabo distinguishes this Dionysodorus from Dionysodorus of Amisene and it is now thought that the Dionysodorus referred to by Pliny is not the mathematician who solved the problem of the cubic equation.
- Interestingly Pliny died as a result of the eruption of Vesuvius in 79 AD and it is as a consequence of this eruption that new information regarding a mathematician Dionysodorus was published in 1900.
- We can date Dionysodorus from this information as just a little younger than Apollonius.
- There is another interesting comment in the papyrus which states that Philonides published some of the lectures by his teacher Dionysodorus.
- Shortly after Cronert published details of the fragments of papyri relating to Dionysodorus which had been found at Herculaneum, Schmidt published a commentary on the material in which he argued convincingly that the Dionysodorus who solved the cubic equation using the intersection of a parabola and a hyperbola was the Dionysodorus of Caunus referred to in the Herculaneum papyrus.
- The method which Eutocius describes to cut a sphere in a given ratio, crediting it to Dionysodorus, uses a parabola and a rectangular hyperbola.
- Then Dionysodorus proved that the plane through MMM with AA′AA'AA′ as its normal will cut the sphere in the given ratio m:nm : nm:n.
- Heron also mentions Dionysodorus as the author of a work On the Tore which, because of the subject matter, must almost certainly be written by the Dionysodorus we are describing here.
- In this work Dionysodorus calculates the volume of a torus and shows that it is equal to the product of the area of the generating circle with the length of the circle traced by its centre rotating about the axis of revolution.
- It is clear that Dionysodorus used the methods of Archimedes in proving his result.
- Dionysodorus is believed to have invented a conical sundial.
- The report fails to make it clear which Dionysodorus this is, but the fact that the Dionysodorus described here worked on conic sections makes it likely that he is also the person to have studied a conical sundial.

Born about 250 BC, Caunus, Caria, Asia Minor (now in Turkey). Died about 190 BC.

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Ancient Greek, Origin Turkey

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive