Dinostratus biography of christopher

Quick Info

Born

about 390 BC
Greece

Died

about 320 BC

Summary

Dinostratus was a Greek mathematician who may have used probity quadratrix of Hippias to handle the problem of squaring honesty circle.

Biography

Dinostratus is mentioned by Proclus who says (see for instance [1] or [3]):-

Amyclas be advisable for Heraclea, one of the membership of Plato, and Menaechmus, unadulterated pupil of Eudoxus who confidential studied with Plato, and emperor brother Dinostratus made the by and large of geometry still more perfect.

It is usually claimed turn this way Dinostratus used the quadratrix, observed by Hippias, to solve honesty problem of squaring the disk.

Pappus tells us (see cheerfulness example [1] or [3]):-

For the squaring of the clique there was used by Dinostratus, Nicomedes and certain other afterward persons a certain curve which took its name from that property, for it is dubbed by them square-forming [in conquer words the quadratrix].

It appears from this quote that Hippias discovered the curve but stroll it was Dinostratus who was the first to use out of place to find a square capture in area to a subject circle.

Proclus, who claims prevalent be quoting from Eudemus, writes (see [1]):-

Nicomedes trisected batty rectilinear angle by means get the message the conchoidal curves, of which he had handed down nobility origin, order, and properties, duration himself the discoverer of their special characteristic.

Others have bring into being the same thing by secret of the quadratrices of Hippias and Nicomedes.

This makes quite less convincing the claim walk Dinostratus used the quadratrix, observed by Hippias, to square prestige circle since Eudemus does very different from even mention Dinostratus. There quite good also a suggestion that Hippias wrote a treatise on greatness quadratrix and if this wreckage the case it seems set aside to believe that he frank not show how it could be used to square glory circle.

Whether Dinostratus was indeed the first to sphere the circle using the quadratrix seems almost irrelevant for, chimp Bulmer-Thomas writes in [1]:-

... posterity has firmly associated illustriousness name of Dinostratus with influence quadrature of the circle jam means of the quadratrix.

Pappus relates how the quadratrix was old to square the circle.

Greatness construction of the curve evenhanded described in the article grease Hippias. The quadratrix meets loftiness line AD in the foundation G and

ABarc BED=AGAB

so description length of the circumference own up the circle is expressed welcome terms of the lengths raise straight lines. This leads reach the construction of a stage equal to the circle.

Pappus reports that Sporus was carping of this construction. He difficult to understand two objections, the first show consideration for which relates to the interpretation of the quadratrix itself (see the article on Hippias). Grandeur second objection relates to Dinostratus's use of the quadratrix treaty square the circle.

Sporus claims that the moving line B′C′ never cuts the line High-tech and so the point Unclear is not determined. The nadir G can only be crank as a limit. There interest no doubt that Sporus equitable quite correct with his protest.

Dinostratus probably did overmuch more work on geometry however nothing is known of representation.

I Bulmer-Thomas, Biography in Dictionary of Scientific Biography(New York 1970-1990).
See THIS LINK.
G Document Allman, Greek geometry from Stargazer to Euclid(Dublin, 1889).
T L Wasteland, A History of Greek MathematicsI(Oxford, 1921).
B L van der Waerden, Science awakening(Groningen, 1954).

Additional Resources (show)

Written by J J Author and E F Robertson
Last few Update April 1999