Dinostratus

Dinostratus
Dinostratus
Born	c. 390 BCE
Died	c. 320 BCE
Nationality	Greek
Known for	Quadratrix of Dinostratus; Dinostratus' theorem
	Scientific career
Fields	Mathematics

Dinostratus (

geometer, and the brother of Menaechmus. He is known for using the quadratrix to solve the problem of squaring the circle

.

Life and work

Dinostratus' chief contribution to mathematics was his solution to the problem of squaring the circle. To solve this problem, Dinostratus made use of the

ruler and compass alone, and so it was clear to the Greeks that his solution violated the foundational principles of their mathematics.^[1] Over 2,200 years later Ferdinand von Lindemann

would prove that it is impossible to square a circle using straight edge and compass alone.

Citations and footnotes

^
ISBN 9780471543978
. Dinostratus, brother of Menaechmus, was also a mathematician, and where one of the brothers "solved" the duplication of the cube, the other "solved" the squaring of the circle. The quadrature because a simple matter once a striking property of the end point Q of the trisectrix of Hippias had been noted, apparently by Dinostratus. If the equation of the trisectrix (Fig. 6.4) is πrsin θ = 2aθ, where a is the side of the square ABCD associated with the curve, [...] hence, Dinostratus' theorem is established - that is, AC/AB = AB/DQ. [...] Inasmuch as Dinostratus showed that the trisectrix of Hippias serves to square the circle, the curve more commonly came to be known as the quadratrix. It was, of course, always clear to the Greeks that the use of the curve in the trisection and quadrature problems violated the rules of the game - that circles and straight lines only were permitted. The "solution" of Hippias and Dinostratus, as their authors realized, were sophistic; hence, the search for further solutions, canonical or illegitimate, continued with the result that several new curves were discovered by Greek geometers.

References

ISBN 0-471-54397-7
.

External links

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

[Dinostratus-1] 
ISBN 9780471543978
. Dinostratus, brother of Menaechmus, was also a mathematician, and where one of the brothers "solved" the duplication of the cube, the other "solved" the squaring of the circle. The quadrature because a simple matter once a striking property of the end point Q of the trisectrix of Hippias had been noted, apparently by Dinostratus. If the equation of the trisectrix (Fig. 6.4) is πrsin θ = 2aθ, where a is the side of the square ABCD associated with the curve, [...] hence, Dinostratus' theorem is established - that is, AC/AB = AB/DQ. [...] Inasmuch as Dinostratus showed that the trisectrix of Hippias serves to square the circle, the curve more commonly came to be known as the quadratrix. It was, of course, always clear to the Greeks that the use of the curve in the trisection and quadrature problems violated the rules of the game - that circles and straight lines only were permitted. The "solution" of Hippias and Dinostratus, as their authors realized, were sophistic; hence, the search for further solutions, canonical or illegitimate, continued with the result that several new curves were discovered by Greek geometers.

[1]

Authority control databases
International	VIAF 2
National	Germany
People	Deutsche Biographie
Other	IdRef