Dinostratus

Dinostratus (Greek: Δεινόστρατος, c. 390 BCE – c. 320 BCE) was a Greek mathematician and 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 trisectrix of Hippias, for which he proved a special property (Dinostratus' theorem) that allowed him the squaring of the circle. Due to his work the trisectrix later became known as the quadratrix of Dinostratus as well.^[1] Although Dinostratus solved the problem of squaring the circle, he did not do so using ruler and compass alone, and so it was clear to the Greeks that his solution violated the foundational principles of their mathematics.^[1] Over two thousand years later it would be proved impossible to square a circle using straight edge and compass alone.

Citations and footnotes

1. ^ ^{a b} Boyer (1991). "The age of Plato and Aristotle". pp. 96–97. "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

• Boyer, Carl B. (1991). A History of Mathematics (Second ed.). John Wiley & Sons, Inc.. ISBN 0-471-54397-7. 

External links

• O'Connor, John J.; Robertson, Edmund F., "Dinostratus", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Dinostratus.html .

Persondata
Name	Dinostratus
Alternative names
Short description	Greek mathematician
Date of birth	390 BCE
Place of birth	Greece
Date of death	320 BCE
Place of death	Greece

This article about a European mathematician is a stub. You can help Wikipedia by expanding it.v · Categories: 390 BC births 320 BC deaths Ancient Greek mathematicians Geometers 4th-century BC Greek people Ancient Greek people stubs European mathematician stubs Wikimedia Foundation. 2010. Игры ⚽ Поможем написать реферат Dark retreat Competence (biology) Look at other dictionaries: DINOSTRATUS — Mathematius, Terragoni quandam speciem invenit, et Geometriam insigniter excoluit. Post Pythagoram vixit …   Hofmann J. Lexicon universale Dinostratus' theorem — In geometry, Dinostratus theorem describes a property of Hippias trisectrix, that allows for the squaring the circle if the trisectrix can be used in addition to straightedge and compass. The theorem is named after the Greek mathematician… …   Wikipedia Dinóstrato — Saltar a navegación, búsqueda Dinóstrato (en griego Δεινόστρατος, ca. 390 a.C. ca. 320 a.C) fue un matemático y geómetra griego, hermano de Menecmo. Es conocido por emplear la cuadratriz para resolver el problema de la cuadratura del círculo …   Wikipedia Español Quadratrix — In mathematics, a quadratrix (from the Latin word quadrator, squarer) is a curve having ordinates which are a measure of the area (or quadrature) of another curve. The two most famous curves of this class are those of Dinostratus and E. W.… …   Wikipedia Menaechmus — There is also a Menaechmus in Plautus play, The Menaechmi. Menaechmus (Greek: Μέναιχμος, 380–320 BC) was an ancient Greek mathematician and geometer born in Alopeconnesus in the Thracian Chersonese, who was known for his friendship with the… …   Wikipedia Nicomedes (mathematician) — Conchoids of line with common center. Nicomedes (Νικομήδης; ca. 280 BC – ca. 210 BC) was an ancient Greek mathematician. Contents 1 Life and work …   Wikipedia Динострат — (греч. Δινόστρατος, лат. Dinostratus, ок. 390 до н. э. ок. 320 до н. э.) древнегреческий математик, член Платоновской Академии, ученик Евдокса, брат математика Менехма …   Википедия Quadratrix — Quad*ra trix, n.; pl. { trixes}, or { trices}. [NL.] (Geom.) A curve made use of in the quadrature of other curves; as the quadratrix, of Dinostratus, or of Tschirnhausen. [1913 Webster] …   The Collaborative International Dictionary of English -trices — Quadratrix Quad*ra trix, n.; pl. { trixes}, or { trices}. [NL.] (Geom.) A curve made use of in the quadrature of other curves; as the quadratrix, of Dinostratus, or of Tschirnhausen. [1913 Webster] …   The Collaborative International Dictionary of English -trixes — Quadratrix Quad*ra trix, n.; pl. { trixes}, or { trices}. [NL.] (Geom.) A curve made use of in the quadrature of other curves; as the quadratrix, of Dinostratus, or of Tschirnhausen. [1913 Webster] …   The Collaborative International Dictionary of English 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”