Dinostratus (Greek: Δεινόστρατος, ca. Greek (el ελληνική γλώσσα or simply el ελληνικά — "Hellenic" is an Indo-European language, spoken today by 15-22 million people mainly 390 BCE - ca. 320 BCE) was a Greek mathematician and geometer, and the brother of Menaechmus. Greece (Ελλάδα transliterated: Elláda, historically, Ellás,) officially the Hellenic Republic (Ελληνική Δημοκρατία A mathematician is a person whose primary area of study and research is the field of Mathematics. A geometer is a Mathematician whose area of study is Geometry. There is also a Menaechmus in Plautus ' play The Menaechmi. Menaechmus (Μέναιχμος 380 – 320 BC was a Greek He is known for using the quadratrix to solve the problem of squaring the circle. In Mathematics, a quadratrix (from the Latin word quadrator squarer is a curve having Ordinates which are a measure of the area (or quadrature Squaring the circle is a problem proposed by ancient Geometers.
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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, which later became known as the quadratrix after Dinostratus' solution. In Geometry, a trisectrix is a curve which can be used to trisect an arbitrary angle Hippias can also refer to the tyrant of Athens son of Peisistratus In Mathematics, a quadratrix (from the Latin word quadrator squarer is a curve having Ordinates which are a measure of the area (or quadrature [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. Pentagon constructgif|thumb|right|Construction of a regular pentagon]] Compass-and-straightedge or ruler-and-compass construction is the construction of lengths or Angles [1] Over two thousand years later it would be proved impossible to square a circle using straight edge and compass alone.
Citations and footnotes
- ^ a b Boyer (1991). Carl Benjamin Boyer ( November 3, 1906 – April 26, 1976) has been called the " Gibbon of math history"he "The age of Plato and Aristotle", , 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). Carl Benjamin Boyer ( November 3, 1906 – April 26, 1976) has been called the " Gibbon of math history"he A History of Mathematics, Second Edition, John Wiley & Sons, Inc. . ISBN 0471543977.
External links
- O'Connor, John J. & Robertson, Edmund F. , “Dinostratus”, MacTutor History of Mathematics archive
| 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 |
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