Deinostratos

from Wikipedia, the free encyclopedia

Deinostratos ( Greek Δεινόστρατος , * approx. 390 BC; † approx. 320 BC) was a Greek mathematician and geometer and brother of Menaichmos . He is known for developing Hippias's quadratrix to solve the problem of squaring the circle ( theorem of Dinostratos ).

A mention of him and Menaichmos in Proclus's Commentary on Euclid shows that he was in the middle of the 4th century BC. BC and was probably associated with the Academy of Plato in Athens.

It is also cited Dinostratos or in Latinized form Dinostratus.

life and work

Deinostratos' main contribution to mathematics was his solution to the square of the circle. To solve this problem, Deinostratos used the Trisektrix from Hippias von Elis , which later - after Deinostratos had solved the problem - became known as the Quadratrix. Hippias used the curve to divide the angle into three , one of the three classic unsolved problems of Greek mathematics, which it became apparent that they could not be solved with the classic compasses and ruler alone. Deinostratos was one of several Greek mathematicians who wanted to solve the problem of circle quadrature, another of the three classical problems, with methods that went beyond the use of compasses and rulers alone. It was also clear to the Greeks, however, that this actually contradicted their principles of treating geometry exclusively with compasses and rulers. More than 2000 years later it was only to be proven that the squaring of the circle is impossible if one only uses a ruler and compass.

Deinostratos' solution was probably the one that Pappos gives in his collection (Book 4, 30). Pappos is also the main source for Deinostratos' solution to the square of the circle. The theorem of Deinostratos is given by Pappos by a proof of contradiction. That would be one of the earliest proofs of the use of contradiction proof by the Greeks, a proof method that Euclid used extensively. Pappos and Sporus von Nikaia criticized this proof among other things with the argument that it presupposes the knowledge of the circle number Pi.

literature

Individual evidence

  1. ^ A b Carl Benjamin Boyer : A History of Mathematics . 1991, p. 96-97 . : "Deinostratos, brother of Menaichmos, was also a mathematician and while one" solved "the doubling of the cube, the other" solved "the square of the circle. Squaring was a simple matter once you noticed the obvious property of the Q endpoints of the Trisectrix of Hippias , like Deinostratos. If the equation of the Trisectrix (Fig. 6.4) is πrsin θ = 2aθ, where a is the side of the square ABCD that is associated with the curve, [...] then Deinostratos' theorem is established - ie AC / AB = AB / DQ . […] In so far as Deinostratos showed that the trisectrix of Hippias helps to square a circle, this curve became better known as the quadratrix. For the Greeks it was of course always clear that the use of the curve in trisection and quadrature problems violated the rules of the game, namely that only circles and straight lines were allowed. The "solution" of Hippias and Deinostratus, as their authors noted, were sophistic; so it came about that the search for further solutions (canonical or illegitimate) continued, with the result that various new curves were discovered by Greek geometers. "
  2. ^ Ivor Bulmer-Thomas, Article Deinostratos, Dict. Scientific Biography, Volume 4, p. 104
personal data
SURNAME Deinostratos
BRIEF DESCRIPTION Greek mathematician
DATE OF BIRTH around 390 BC Chr.
DATE OF DEATH around 320 BC Chr.