1. Diocles Biography of diocles (240BC180BC) In this work we are told that dioclesstudied the cissoid as part of an attempt to duplicate the cube. http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Diocles.html

Diocles Born: Died: about 180 BC Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Version for printing Diocles was a contemporary of Apollonius . Practically all that was knew about him until recently was through fragments of his work preserved by Eutocius in his commentary on the famous text by Archimedes On the sphere and the cylinder. In this work we are told that Diocles studied the cissoid as part of an attempt to duplicate the cube . It is also recorded that he studied the problem of Archimedes to cut a sphere by a plane in such a way that the volumes of the segments shall have a given ratio. The extracts quoted by Eutocius from Diocles' On burning mirrors showed that he was the first to prove the focal property of a parabolic mirror. Although Diocles' text was largely ignored by later Greeks, it had considerable influence on the Arab mathematicians, in particular on al-Haytham . Latin translations from about 1200 of the writings of al-Haytham brought the properties of parabolic mirrors discovered by Diocles to European mathematicians.

2. Deportes Espera Terminar La Remodelaci N Del Diocles En Agosto En la ma ana de ayer comenzaron los trabajos de aporte y extendido de arena en el campo del diocles, cuyas obras de mejora comenzaron el pasado 11 http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

3. Cissoid This curve (meaning ivyshaped ) was invented by diocles in about 180 BC inconnection with his attempt to duplicate the cube by geometrical methods. http://www-groups.dcs.st-and.ac.uk/~history/Curves/Cissoid.html

Cissoid of Diocles Cartesian equation: y x a x Polar equation: r a tan( )sin( Click below to see one of the Associated curves. Definitions of the Associated curves Evolute Involute 1 Involute 2 ... Caustic curve wrt another point If your browser can handle JAVA code, click HERE to experiment interactively with this curve and its associated curves. This curve (meaning 'ivy-shaped') was invented by Diocles in about 180 BC in connection with his attempt to duplicate the cube by geometrical methods. The name first appears in the work of Geminus about 100 years later. Fermat and Roberval constructed the tangent in 1634. Huygens and Wallis found, in 1658, that the area between the curve and its asymptote was 3 a . From a given point there are either one or three tangents to the cissoid. The Cissoid of Diocles is the roulette of the vertex of a parabola rolling on an equal parabola. Newton gave a method of drawing the Cissoid of Diocles using two line segments of equal length at right angles. If they are moved so that one line always passes through a fixed point and the end of the other line segment slides along a straight line then the mid-point of the sliding line segment traces out a Cissoid of Diocles Diocles was a contemporary of Nicomedes . He studied the cissoid in his attempt to solve the problem of finding the length of the side of a cube having volume twice that of a given cube. He also studied the problem of Archimedes to cut a sphere by a plane in such a way that the volumes of the segments shall have a given ratio.

4. The Games Gaius Appuleius diocles was perhaps the greatest star of them all. He was a quadriga charioteer who is said to have contested 4257 races. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

5. Cissoid Of Diocles The National Curve Bank project for students of mathematics. http://curvebank.calstatela.edu/diocles/diocles.htm

Click on the thumbnail images below to see experimental solar collectors near Barstow, California focus the sun's rays on a central tower where heat is converted to electricity. The famous Belvedere Apollo at the top of this column is a Roman copy of a much older Greek statue. This marble is now in the Pio Clementino Museum at the Vatican (Rome, Italy). The Burning Mirrows wall painting is from the Stanzino delle Matematiche in the Galleria degli Uffizi (Florence, Italy). Painted by Giulio Parigi (1571-1635) in the years 1599-1600. The Cissoid of Diocles Back to . . . Curve Bank Home This section . . . Another attempt to solve one of the three famous construction problems from Antiquity. Biographical Sketch Diocles is one of many mathematicians who have attempted to construct a cube whose volume is exactly twice that of a given cube. This is often called the "Delian" problem or "duplication of the cube". Legend: A number of legends surround this construction challenge. The good citizens of Athens were being devastated by a plague. History records that in 430 BC they sought advice from the oracle at Delos on how to rid their community of this pestilence. The oracle replied that the altar of Apollo, which was in the form of a cube, should be doubled. Thoughtless builders merely doubled the edges of the cube. Unfortunately the volume of the altar increased by a factor of 8. The oracle insisted the gods had been angered. As if to confirm this reprimand, the plague grew worse. Other delegations consulted Plato. When informed of the oracle's admonition, Plato told the citizens "the god has given this oracle, not because he wanted an altar of double the size, but because he wished in setting this task before them, to reproach the Greeks for their neglect of mathematics and their contempt of geometry."

6. Xah Special Plane Curves Cissoid Of Diocles diocles's construction. By some modern common accounts (Morris Kline, Thomas L. Heath), here's how diocles constructed the curve in his book On http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

7. Diocles - Wikipedia, The Free Encyclopedia In Greek mythology, diocles, or Díoklês was one of the first priests of Demeterand one of the Retrieved from http//en.wikipedia.org/wiki/diocles http://en.wikipedia.org/wiki/Diocles

Wikimedia needs your help in its 21-day fund drive. See our fundraising page Over US$150,000 has been donated since the drive began on 19 August. Thank you for your generosity! Diocles From Wikipedia, the free encyclopedia. In Greek mythology Diocles , or D­oklªs was one of the first priests of Demeter and one of the first to learn the secrets of the Eleusinian Mysteries See also Diocletian , formerly named Diocles This article relating to Greek mythology is a stub . You can help Wikipedia by expanding it Retrieved from " http://en.wikipedia.org/wiki/Diocles Categories Greek mythology stubs Greek mythological people Views Article Discussion Edit this page History Personal tools Create account / log in Navigation Main Page Community portal Current events Recent changes ... Donations Search Toolbox What links here Related changes Upload file Special pages ... Permanent link This page was last modified 02:03, 1 August 2005. All text is available under the terms of the GNU Free Documentation License (see for details). About Wikipedia

8. Circus Maximus diocles, a charioteer from Lusitania who competed during the reign of Hadrian and Antoninus Pius, won prize money totaling 35 863 120 http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

9. Diocles (mathematician) - Wikipedia, The Free Encyclopedia It was used by diocles for doubling the cube. Fragments of a work by dioclestitled On burning mirrors were preserved by Eutocius in his commentary of http://en.wikipedia.org/wiki/Diocles_(mathematician)

Wikimedia needs your help in its 21-day fund drive. See our fundraising page Over US$150,000 has been donated since the drive began on 19 August. Thank you for your generosity! Diocles (mathematician) From Wikipedia, the free encyclopedia. Diocles was a Greek mathematician and geometer , who probably flourished sometime around the end of the second century and the beginning of the first century BC . He was probably the first to prove the focal property of a parabola His name is associated with the geometric curve called the Cissoid of Diocles . It was used by Diocles for doubling the cube. The curve was alluded to by Proclus in his commentary on Euclid and attributed to Diolcles by Geminus as early as the beginning of the first century. Fragments of a work by Diocles titled On burning mirrors were preserved by Eutocius in his commentary of Archimedes On the Sphere and the Cylinder . One of the fragments contains a solution, using conic sections to solve the problem of dividing a sphere by a plane, so that the resulting two volumes are a given ratio. This was equivalent to solving a certain cubic equation . Another fragment uses the cissoid to find two mean porportionals. edit References Heath, Sir Thomas

10. Diocles - Wikipedia, The Free Encyclopedia diocles See also Diocletian, formerly named diocles This mythologyrelated article is a stub. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

11. Xah: Special Plane Curves: Cissoid Of Diocles Cissoid of diocles is a special case of (general) cissoid. It is a cissoid of acircle and The locus of Q (as P1 moves on C) is the cissoid of diocles. http://www.xahlee.org/SpecialPlaneCurves_dir/CissoidOfDiocles_dir/cissoidOfDiocl

If you spend more than 30 minutes on this site, please send $1 to me. Go to http://paypal.com/ and make a payment to xah@xahlee.org. Or send to: P. O. Box 390595, Mountain View, CA 94042-0290, USA. ☠Back to Table of Contents Cissoid of Diocles Parallels of a cissoid of Diocles Mathematica Notebook for This Page History Diocles (~250-~100 BC) invented this curve to solve the doubling of the cube problem. (aka the Delian problem) The name cissoid (ivy-shaped) came from the shape of the curve. Later the method used to generate this curve is generalized, and we call curves generated this way as cissoids From Thomas L. Heath's Euclid's Elements translation (1925) (comments on definition 2, book one): This curve is assumed to be the same as that by means of which, according to Eutocius, Diocles in his book On burning-glasses solved the problem of doubling the cube. From Robert C. Yates' Curves and their properties (1952): As early as 1689, J. C. Sturm, in his Mathesis Enucleata, gave a mechanical device for the constructions of the cissoid of Diocles. From E.H.Lockwood

12. Diocles Of Carystus diocles of Carystus A Collection of the Fragments with Translation and diocles of Carystus (4th century BCE), also known as "the younger http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

13. Cissoid Of Diocles -- From MathWorld then the midpoint of the sliding line segment traces out a cissoid of diocles.The cissoid of diocles is given by the parametric equations http://mathworld.wolfram.com/CissoidofDiocles.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Geometry Curves Plane Curves ... Geometric Construction Cissoid of Diocles A cubic curve invented by Diocles in about 180 BC in connection with his attempt to duplicate the cube by geometrical methods. The name "cissoid" first appears in the work of Geminus about 100 years later. Fermat and Roberval constructed the tangent in 1634. Huygens and Wallis found, in 1658, that the area between the curve and its asymptote was (MacTutor Archive). From a given point there are either one or three tangents to the cissoid. Given an origin and a point on the curve, let be the point where the extension of the line intersects the line and be the intersection of the circle of radius and center with the extension of . Then the cissoid of Diocles is the curve which satisfies The cissoid of Diocles is the roulette of a parabola vertex of a parabola rolling on an equal parabola Newton gave a method of drawing the cissoid of Diocles using two line segments of equal length at right angles . If they are moved so that one line always passes through a fixed point and the end of the other line segment slides along a straight line, then the

14. Cissoid Of Diocles The Cissoid of diocles Back to Toomer, Gerald. diocles on Burning Mirrors, Springer, 1976. The History of Mathematics A Reader. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

15. Cissoid Of Diocles Catacaustic -- From MathWorld Cissoid of diocles Catacaustic SEE ALSO Cardioid, Catacaustic, Cissoid ofdiocles. Pages Linking Here. CITE THIS AS. Eric W. Weisstein. http://mathworld.wolfram.com/CissoidofDioclesCatacaustic.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Geometry Curves Plane Curves ... Caustic Curves Cissoid of Diocles Catacaustic For the parametric representation the catacaustic of this curve from the radiant point is given by Eliminating gives the Cartesian equation Therefore, since is the equation of a cardioid , the catacaustic of the cissoid of Diocles for radiant point at is a cardioid with SEE ALSO: Cardioid Catacaustic Cissoid of Diocles [Pages Linking Here] CITE THIS AS: Eric W. Weisstein. "Cissoid of Diocles Catacaustic." From MathWorld A Wolfram Web Resource. http://mathworld.wolfram.com/CissoidofDioclesCatacaustic.html Wolfram Research, Inc.

16. No. 837 Diocles diocles' parabolic mirror in an old Arabic book http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

17. Cissoid Of Diocles The cissoid of diocles is the cissoid of a circle and a tangent line, To dothat, we note that the cissoid of diocles is a cubic curve with a cusp in http://www.geocities.com/famancin/cissoid_diocles.html

Cissoid of Diocles Here is the definition of cissoid of two curves. Cissoid[ Let O be a fixed point and let L be a line through O intersecting the curves C and C at Q and Q . The locus of points P and P on L such that OP = OQ - OQ = Q Q is the cissoid of C and C with respect to O. The cissoid of Diocles is the cissoid of a circle and a tangent line, with respect to a fixed point O on the circumference opposite the point of tangency A. The screenshot below shows the cissoid drawn using Jeometry Let O be the origin and x = a be the line tangent to the circle. Let Ô be the angle BÔA in the picture above. Considering the right triangles OBA and CAO, we have OP OC OB a secÔ - a cosÔ a sinÔ tanÔ Hence the polar equation of the cissoid is r = a sinÔ tanÔ Then the Cartesian equation follows immediately by substitution, y (a - x) = x This is the same equation we found when considering the pedal of a parabola with respect to its vertex (let a = - We would like to find a parametric rapresentation of the curve. To do that, we note that the cissoid of Diocles is a cubic curve with a cusp in the origin, so we can find a rational parametrization by intersecting the cissoid with the line

18. It's Saturday posted by diocles @ 732 PM 1 comments About Me Namediocles LocationLos Angeles, California, United States View my complete profile http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

19. Diocles --  Encyclopædia Britannica diocles philosopher and pioneer in medicine, among Greek physicians second onlyto Hippocrates in reputation and ability, according to tradition. http://www.britannica.com/eb/article?tocId=9030520

20. Diocles Encyclop Dia Britannica diocles philosopher and pioneer in medicine, among Greek physicians second only to Hippocrates in reputation and ability, according to tradition. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

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