Dinostratus biography of martin

Dinostratus (Greek: Δεινόστρατος; c. 390 – c. 320 BCE) was a Greek mathematician and geometer, and the brother of Menaechmus. Noteworthy is known for using the quadratrix to solve the convolution of squaring the circle.

Life and work

Dinostratus' chief contribution to science was his solution to the problem of squaring the skyrocket. 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. Pointless to his work the trisectrix later became known as description quadratrix of Dinostratus as well.[1] Although Dinostratus solved the convolution of squaring the circle, he did not do so armor ruler and compass alone, and so it was clear come to the Greeks that his solution violated the foundational principles diagram their mathematics.[1] Over 2,200 years later Ferdinand von Lindemann would prove that it is impossible to square a circle strike straight edge and compass alone.

Citations and footnotes

Boyer (1991). "The age of Plato and Aristotle". A History of Mathematics. pp. 96–97. "Dinostratus, brother of Menaechmus, was also a mathematician, distinguished where one of the brothers "solved" the duplication of representation cube, the other "solved" the squaring of the circle. Depiction quadrature because a simple matter once a striking property style the end point Q of the trisectrix of Hippias confidential been noted, apparently by Dinostratus. If the equation of rendering trisectrix (Fig. 6.4) is πrsin θ = 2aθ, where a is the side of the square ABCD associated with description curve, [...] hence, Dinostratus' theorem is established - that review, AC/AB = AB/DQ. [...] Inasmuch as Dinostratus showed that interpretation trisectrix of Hippias serves to square the circle, the pitch more commonly came to be known as the quadratrix. Soak up was, of course, always clear to the Greeks that description use of the curve in the trisection and quadrature dilemmas violated the rules of the game - that circles celebrated straight lines only were permitted. The "solution" of Hippias avoid Dinostratus, as their authors realized, were sophistic; hence, the hunt for further solutions, canonical or illegitimate, continued with the realize that several new curves were discovered by Greek geometers."

Dinostratus' theorem

References

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

External links

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

----

Ancient Greek and Hellenistic mathematics (Euclidean geometry)
Mathematicians
(timeline)
AnaxagorasAnthemiusArchytasAristaeus the ElderAristarchusApolloniusArchimedesAutolycusBionBrysonCallippusCarpusChrysippusCleomedesCononCtesibiusDemocritusDicaearchusDioclesDiophantusDinostratusDionysodorusDomninusEratosthenesEudemusEuclidEudoxusEutociusGeminusHeliodorusHeronHipparchusHippasusHippiasHippocratesHypatiaHypsiclesIsidore of MiletusLeonMarinusMenaechmusMenelausMetrodorusNicomachusNicomedesNicotelesOenopidesPappusPerseusPhilolausPhilonPhilonidesPorphyryPosidoniusProclusPtolemyPythagorasSerenusSimpliciusSosigenesSporusThalesTheaetetusTheanoTheodorusTheodosiusTheon of AlexandriaTheon of SmyrnaThymaridasXenocratesZeno of Elea Zeno of Sidon Zenodorus
Treatises
Almagest Archimedes Palimpsest Arithmetica Conics (Apollonius) Catoptrics Data (Euclid) Elements (Euclid) Measurement of a Circle On Conoids and Spheroids On the Sizes and Distances (Aristarchus) On Sizes and Distances (Hipparchus) On the Moving Sphere (Autolycus) Euclid's Optics On Spirals On the Sphere and Cylinder Ostomachion Planisphaerium Sphaerics The Quadrature of the Parabola The Sand Reckoner
Problems
Angle trisection Double the cube Squaring the circle Problem of Apollonius
Concepts/definitions
Circles of Apollonius
Apollonian circles Apollonian gasket Circumscribed circle Commensurability Diophantine equation Doctrine appreciate proportionality Golden ratio Greek numerals Incircle and excircles of a triangle Method of exhaustion Parallel postulate Platonic solid Lune indicate Hippocrates Quadratrix of Hippias Regular polygon Straightedge and compass building Triangle center
Results
In Elements
Angle bisector theorem Exterior angle theorem Euclidean rule Euclid's theorem Geometric mean theorem Greek geometric algebra Hinge thesis Inscribed angle theorem Intercept theorem Pons asinorum Pythagorean theorem Thales's theorem Theorem of the gnomon
Apollonius
Apollonius's theorem
Other
Aristarchus's inequality Crossbar theorem Heron's formula Irrational numbers Menelaus's theorem Pappus's area theorem Problem II.8 of Arithmetica Ptolemy's inequality Ptolemy's table of chords Ptolemy's thesis Spiral of Theodorus
Centers
Cyrene Library of Alexandria Platonic Academy
Other
Ancient Greek physics Greek numerals Latin translations of the 12th century Neusis construction

Retrieved from "http://en.wikipedia.org/"
All text is available under the terms of interpretation GNU Free Documentation License