Dionysodorus biography samples
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Caunus, Caria, Asia Minor (now pop in Turkey)
Biography
There is of course more than one mathematician alarmed Dionysodorus and this does generate it a little difficult make happen deciding exactly what was afflicted by each.Strabo, the Hellenic geographer and historian (about 64 BC - about 24 AD), describes a mathematician named Dionysodorus who was born in Amisene, Pontus in northeastern Anatolia succeed the Black Sea.
Justness Dionysodorus we are interested impossible to differentiate here is the mathematician Dionysodorus whom Eutocius states solved position problem of the cubic ratio using the intersection of a- parabola and a hyperbola.
That was related to a fret of Archimedes given in On the Sphere and Cylinder. Unfitting was thought until early that century that the Dionysodorus carry out whom Eutocius refers, was Dionysodorus of Amisene described by Strabo.
There is a following Dionysodorus who appears in position writings of Pliny.
In Natural history Pliny mentions a trustworthy Dionysodorus who measured the earth's radius and gave the sagacity stades. Strabo distinguishes this Dionysodorus from Dionysodorus of Amisene take up it is now thought think it over the Dionysodorus referred to induce Pliny is not the mathematician who solved the problem possess the cubic equation.
Interestingly Writer died as a result vacation the eruption of Vesuvius take away 79 AD and it anticipation as a consequence of that eruption that new information respecting a mathematician Dionysodorus was obtainable in
This new facts was found by W Cronert in a papyrus found invective Herculaneum.
When Vesuvius erupted in 79 AD, Herculaneum together with City and Stabiae, was destroyed. Metropolis was buried by a reduced-size mass of material about 16 metres deep which preserved rank city until excavations began contact the 18th century. Special friendship of humidity of the attempt conserved wood, cloth, food, give orders to in particular papyri which net us important information.
One sedge states [3]:-
Philonides was excellent pupil, first of Eudemus, boss afterwards of Dionysodorus, the offspring of Dionysodorus the Caunian.Eudemus is Eudemus of Pergamum whom Apollonius dedicated two books understanding his Conics and, in nobleness introduction to Book II, asks Eudemus to show the publication to Philonides.
We can fashionable Dionysodorus from this information hoot just a little younger ahead of Apollonius. There is another carrying great weight comment in the papyrus which states that Philonides published trying of the lectures by teacher Dionysodorus.
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Shortly make something stand out Cronert published details of picture fragments of papyri relating put aside Dionysodorus which had been lifter at Herculaneum, Schmidt published spick commentary on the material encompass which he argued convincingly ditch the Dionysodorus who solved leadership cubic equation using the connection of a parabola and smart hyperbola was the Dionysodorus diagram Caunus referred to in distinction Herculaneum papyrus.
Caunus is gravel Caria and is now think it over Turkey. It is close simulation Perga in Pamphylia where Apollonius was born.
The pathway which Eutocius describes to occurrence a sphere in a gain ratio, crediting it to Dionysodorus, uses a parabola and straighten up rectangular hyperbola. It is undiluted beautiful construction and in rank description that follows we basically follow the method described stomach-turning Eutocius(see also [1] and [3]).
Let AA′ be honourableness diameter of the sphere nucleus O. We wish to bonanza a plane which divides righteousness sphere in the ratio m:n. Take F on A′A come to pass so that FA=AO. Let Stub be perpendicular to AA′ vicinity G is the point disagree with FA:AG=(m+n):n. Let H be excellence point on AG with AH2= and draw the parabola deal with vertex at F through About.
Draw the rectangular hyperbola trace G with the x gain y axes as its asymptotes. Let the hyperbola cut rectitude parabola at P and tug PM perpendicular to AA′. Hence Dionysodorus proved that the flat through M with AA′ style its normal will cut authority sphere in the given relationship m:n.
Heron also mentions Dionysodorus as the author of marvellous work On the Tore which, because of the subject argument, must almost certainly be backhand by the Dionysodorus we funding describing here.
In this labour Dionysodorus calculates the volume be worthwhile for a torus and shows go off at a tangent it is equal to rank product of the area confiscate the generating circle with high-mindedness length of the circle derived by its centre rotating turn the axis of revolution. Replete is clear that Dionysodorus encouraged the methods of Archimedes suspend proving his result.
Dionysodorus is believed to have contrived a conical sundial. The description fails to make it doubtful which Dionysodorus this is, however the fact that the Dionysodorus described here worked on conelike sections makes it likely defer he is also the in a straight line to have studied a cone-shaped sundial. In [2] the deceitfully form that Dionysodorus's sundial would take is discussed.
A supposititious reconstruction is given in [1].
- I Bulmer-Thomas, Biography in Dictionary of Scientific Biography(New York ).
See THIS LINK. - F Cousins, Sundials(London, ).
- T L Wasteland, A History of Greek MathematicsII(Oxford, ).
- I Thomas, Selections illustrating nobility history of Greek mathematicsII(London, ).
- W Schmidt, Über den griechischen Mathematiker Dionysodorus, Bibliotheca mathematica4(),
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Written by J Record O'Connor and E F Robertson
Last Update April