21. Encyclopædia Britannica MORE GENERAL SUBJECTS. line Cissoid of diocles. CURRENT SUBJECT. Cissoid ofdiocles. Index Entry. MORE SPECIFIC SUBJECTS http://www.britannica.com/eb/subject?subjectId=43973

22. No. 837: Diocles diocles parabolic mirror in an old Arabic book. http://www.uh.edu/engines/epi837.htm

No. 837: DIOCLES by John H. Lienhard Click here for audio of Episode 837. Today, we focus the rays of the sun. The University of Houston's College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them. W ho was Diocles? We don't really know. All we have is a text he wrote over 2000 years ago. It's not even in his own tongue. It was written in AD 1462 by a careless scribe who left only spaces where figures should've gone. But it's enough to tell us that it was Diocles who invented the parabolic mirror. Who was Diocles? Historian G.J. Toomer picks through this skimpy legacy this ancient text, titled On Burning Mirrors . Most of what we knew of Diocles came from reference to his work by a noted 6th-century mathematician. Now we finally read this copy of his book, penned 1600 years after the fact. Toomer does his historical detective work. He decides that Diocles flourished in Greece just after 200 BC. He was a mathematician a geometer. Toomer takes us through the text, recreating the figures. We read Diocles' opening:

23. Light A parabolic section of a cone What diocles is describing, of course, is the shapeof a paraboloid, and paraboloids touch our modern world in the technology http://www.uh.edu/engines/astron2.htm

LIGHT for the JSC Astronomical Society at the Lunar and Planetary Institute, 7:30 PM, Friday, September 8, 2000 (An earlier version of this talk was given at the Retinal Research Foundation Luncheon, River Oaks Country Club, Noon, Wednesday, November 3, 1999.) by John H. Lienhard Mechanical Engineering Department University of Houston Houston, TX 77204-4792 jhl@uh.edu I doubt that anything can be as central to your work as astronomers as is light . At the same time, can anything be as ephemeral? So let's play with light as an idea. What is light that activates the retina and imprints the world out there upon our brains? I guess we can agree that it's electromagnetic radiation in a range of wavelengths between 0.4 and 0.5 microns. I suppose we can think of it as a rain of photons. But if we do that, then we have to say what a photon is. And that means falling into the maelstrom of counterintuitive ideas that make up quantum mechanics. So, it appears, we'll have to devote the entire evening to a lecture on quantum physics. Are you up for that? Okay, okay I'll take a different tack. I'll begin instead on a Saturday afternoon back in 1942. The great weekly event was the matinee at the Uptown theater. Forty cents bought a bag of popcorn, a box of Milk Duds, and a movie ticket.

24. Cissoid Of Diocles Cissoid of diocles. © Copyright 2003, Jim Loy. This is the cissoid of diocles.The distance from the red dot on the circle to the dot on the top of the http://www.jimloy.com/cindy/cissoid.htm

Return to my Cinderella pages Return to my Mathematics pages Go to my home page Cissoid of Diocles This is the cissoid of Diocles. The distance from the red dot on the circle to the dot on the top of the circle is the same as the distance from the green dot to the moving dot on the green horizontal line. Please enable Java for an interactive construction (with Cinderella). The above Java animation was created with Cinderella (a geometry program). Return to my Cinderella pages Return to my Mathematics pages Go to my home page

25. Diocles (2nd Century B.C.) -- From Eric Weisstein's World Of Scientific Biograph Greek mathematician who invented the cissoid of diocles. diocles created thefamous curve as an auxiliary tool for cube duplication. http://scienceworld.wolfram.com/biography/Diocles.html

Branch of Science Mathematicians Nationality Greek ... Barile Diocles (2nd century B.C.) This entry contributed by Margherita Barile Greek mathematician who invented the cissoid of Diocles This discovery appears in the collection of his writings that has reached us in an Arabic transcription entitled On Burning Mirrors ; the original has been lost. Diocles created the famous curve as an auxiliary tool for cube duplication For this construction problem, unrealizable with straightedge and compass he also presented a solution based on two intersecting parabolas Almost nothing is known about Diocles' life. His work contains a hint that he could have spent some time in Arcadia. A careful examination of the text, and the comparison with other sources allowed the historians to locate him as a contemporary of Apollonius , although Diocles' treatment of conic sections does not clearly indicate whether he ever had access to Apollonius' comprehensive work on the subject. On the other hand, he certainly knew some results by Archimedes: his construction of the mean proportional is explicitly intended as a completion of some of the latter's geometric proofs. References MacTutor History Topics. "How Do We Know About Greek Mathematicians?"

26. Cissoid Of Diocles Cissoid of diocles. http://astronomy.swin.edu.au/~pbourke/curves/cissoiddiocles/

Cissoid of Diocles

27. Cissoid This construction has been done by the Greek scholar diocles (about 160 BC) 2) . The cissoid of diocles is a special case of the generalized cissoid, http://www.2dcurves.com/cubic/cubicc.html

cissoid cubic last updated: The cissoid can be constructed as follows: Given a circle C with diameter OA and a tangent l through A. Now, draw lines m through O, cutting circle C in point Q, line l in point R. Then the cissoid is the set of points P for which OP = QR. This construction has been done by the Greek scholar Diocles (about 160 BC) . He used the cissoid to solve the Delian problem, dealing with the duplication of the cube. He did not use the name cissoid. The name of the curve, meaning 'ivy-shaped', is found for the first time in the writings of the Greek Geminus (about 50 BC). Because of Diocles' previous work on the curve his name has been added: cissoid of Diocles Roberval and Fermat constructed the tangent of the cissoid (1634): from a given point there are either one ore three tangents. In 1658 Huygens and Wallis showed that the area between the curve and his asymptote is p The cissoid of Diocles is a special case of the generalized cissoid , where line l and circle C have been substituted by arbitrary curves C1 and C2. The curve, having one cusp and one asymptote, has as Cartesian coordinates:

28. I16040: Diocles (King Of Sicambri) (____ - 300 BC) King of Sicambri diocles ( 300 BC) diocles _ _ _ http://www.b17.com/family/lwp/ged2html/d0048/I16040.html

Diocles King of Sicambri - 300 BC TITLE : King of Sicambri DEATH : 300 BC Father: Helenus I Family 1 Basanus _Helenus I Diocles Notes and Sources: Descendants of 'Ha 'adham (Adam) PAGE : ODT9-0051.html Go to Index of Persons Go to Index of Surnames Send E-mail Comments HTML created by GED2HTML v3.6-WIN95 (Jan 18 2000) on 05/26/2004 01:51:05 AM Central Standard Time Connections of Chaos site sponsored by the Art Galore! A Virtual Art Community Art Galore! Browser Book Gallery Art Galore! Poster Gallery Site page visits since Nov 2002 Powered by counter.bloke.com'

29. Diocles Of Carystus. Volume 1, Text And Translation diocles of Carystus (4th century BCE), also known as the younger Hippocrates , The study of diocles ideas has long been hampered by the absence of a http://www.brill.nl/product.asp?ID=870

30. Lecturer: Diocles (Mr.) diocles (Mr.) P 213 KIST III Year 4, SemII Mechanical Eng. IV. T U E,Refrigeration Air conditioning MEE 3422 diocles (Mr.) P 213 KIST III http://www.kist.ac.rw/academics/t_table/full/resource/s20178.html

Lecturer: Diocles (Mr.) Fullscreen Index Help Finder Weeks: 1-15 M O N Diocles (Mr.) P 213 [KIST III] Year 4, Sem-II Mechanical Eng. [IV] T U E Diocles (Mr.) P 213 [KIST III] Year 4, Sem-II Mechanical Eng. [IV] W E D Heat Transfer [MEE 3324] Diocles (Mr.) P 112 [KIST III] Year 3, Sem-II Mechanical Eng. [III] Year 4, Sem II, Progression Diploma to Degree Mech.engg. [IV] T H U F R I Turbo machinery [MEE 3322] Diocles (Mr.) P 112 [KIST III] Year 3, Sem-II Mechanical Eng. [III] Year 4, Sem II, Progression Diploma to Degree Mech.engg. [IV] Heat Transfer [MEE 3324] Diocles (Mr.) P 112 [KIST III] Year 3, Sem-II Mechanical Eng. [III] Year 4, Sem II, Progression Diploma to Degree Mech.engg. [IV] S A T Created by Administrator with CELCAT Web Publisher on 13-Jul-05

31. Ancistroides Nigrita Diocles Ancistroides nigrita diocles ; Pinratana,1985 63, pl.21, fig.125a. (Nhahin). VIETNAM Kerana diocles ; Lemee,1950 25. (Hagiang / Backan) http://yutaka.it-n.jp/hes/91560010.html

Ancistroides nigrita diocles (Moore,[1866]) ON : * Nisoniades nigrita diocles Moore,[1866] OD : Proc. zool. Soc. Lond. 1865(3):787. TL : Bengal, India. Distribution : Sikkim to Myanmar, N.Thailand, Laos, Vietnam, Hainan. Records taken from Literature [ THAILAND ] Kerana diocles evaira ; Godfrey,1916 : 145. Kerana nigrita ; Godfrey,1930 : 371. (Pak Jong / Chonburi: Sriracha / Me Wong, West) Ancistroides nigrita maura ; Reeves,19XXa : 128. (Khao Yai) Ancistroides nigrita diocles ; Pinratana,1985 : 63, pl.21, fig.125a. (Chiang Mai / Nakhon Nayok) [ LAOS ] Ancistroides nigrita maura Ancistroides nigrita maura [ VIETNAM ] Kerana diocles ; Lemee,1950 : 25. (Hagiang / Backan) Specimens Examined Notes This page was last updated on 04. Sep. 1999.

32. High Field Science: Diocles An ultrahigh-intensity laser system, diocles,* is being built at UNL for forthe purpose of studying the interactions of light with matter at the highest http://www.unl.edu/dumstadter/diocles.htm

DIOCLES LASER An ultra-high-intensity laser system, DIOCLES,* is being built at UNL for for the purpose of studying the interactions of light with matter at the highest attainable field strengths. When completed in 2005, it will have the highest peak power-rate of any laser in the U.S., 1 PW-Hz, and be capable of directly increasing an electron's mass relativistically by amplifying medium Ti:sapphire wavelength 0.8 micron pulse duration 30 fs energy per pulse 3 J peak power 100 TW repetition rate 10 Hz peak power rate 1 PW-Hz peak intensity W/cm peak normalized vector potential a_0 peak electron quiver mass 20 x rest mass * In 200 BC, Diocles invented the parabolic reflector, which-to this day-remains the best focusing element by which the intensity of light can be increased. Home Research People Publications ... Related Links

33. Diocles diocles was a contemporary of Apollonius. Practically all that was knew about In this work we are told that diocles studied the cissoid as part of an http://www.palmers.ac.uk/internet/Previous Events/Eric Excellence day/webs2003/J

Diocles 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. Recently, however, some more information about Diocles' life has come to us from the Arabic translation of Diocles' On burning mirrors whose discovery is described below. From this work we learn that

34. Imago Mundi - Dioclès. - Dioclès, poète comique grec d Athènes ou de Phlionte, appartenant à la période http://www.cosmovisions.com/Diocles.htm

Les gens de l' Anthologie Anal. Controverses de Aristote (ci-dessous). Eutocius Proclus e Hippocrate Galien , Caelius Aurelianus, Oribase Dioclis Carystii fragmenta quae supersunt anatomie bisulque ou diocteum graphiscum Dr L. Hn.). A B C D ... Z

35. CissoidOfDiocles Cissoid of diocles (English). Search for Cissoid of diocles in NRICH PLUS maths.org Google. Definition (keystage 4). A special case of a cissoid; http://thesaurus.maths.org/mmkb/entry.html?action=entryByConcept&id=3275&langcod

36. Dioclès http://serge.mehl.free.fr/chrono/Diocles.html

DIOCLES, grec, vers -150/-200 duplicatrice duplication du cube On ne le confondra pas avec Aristote OM MK On obtient ainsi une (du grec kissos lierre et eidos forme (OA) y (1-x) = x r = 1/cost - cost au sens d' Euclide ou de Platon Une vision nouvelle des coniques : Pappus d'Alexandrie Apollonius de Perge miroirs ardents (dont le principe est attribué à Archimède foyer (ce terme est de Kepler , bien plus tard) et directrice conique la parabole : MF/MH = 1 Ces travaux sont l'objet du livre VII de Pappus dans ses Coniques : Miroir parabolique : Apollonius Hipparque

37. Matt & Andrej Koymasky - Famous GLTB - Diocles diocles (end 8th cent. BC) Greece Olympic athlete. separator. diocles was anOlympic athlete and was the lover of Philolaus, a Corinthian of the family of http://andrejkoymasky.com/liv/fam/biod2/dioc1.html

BIOGRAPHIES Last update: September 2 nd Diocles (end 8th cent. BC) Greece Olympic athlete Diocles was an Olympic athlete and was the lover of Philolaus, a Corinthian of the family of the Bacchiadae, and the lawgiver of Thebes, lasted until death; and even their graves were turned towards one another in token of their affection. Aristotle relates the story of how they were buried together, and wrote that, at his day, the inhabitants pointed out their tomb. Contrary to many opinions, male homosexual relationships in Ancient Greece were not just an older aristocrat having crushes on boys in the gymnasia, but included lifelong partnerships. The loves of Philolaus and Diocles lasted until death; and even their graves were turned towards one another in token of their affection. For an account of Philolaus and Diocles, you can read Aristotle, Pol . II. 9. Click on the letter D to go back to the list of names

38. Matt & Andrej Koymasky - Famous GLTB - Philolaus & Diocles Philolaus and diocles (8th century BC) Greece For an account of Philolausand diocles, see Aristotle, Politics, ii. 9 http://andrejkoymasky.com/liv/fam/biop2/phil09.html

BIOGRAPHIES Last update: October 28 th Philolaus and Diocles (8th century BC) Greece Lovers Philolaus, born in the Corinthian family of the Bacchiadae, was the lawgiver of Thebes, and his lover Diocles was an Olympic Athlete. Their love lasted until death and even their graves were turned towards one another in token of their affection. Aristotle relates the story of how they were buried, and says that the inhabitants point out the tomb. Contrary to many opinions, male homosexual relationships in Ancient Greece were not just an older aristocrat having crushes on boys in the gymnasia, but included also lifelong partnerships and love. For an account of Philolaus and Diocles, see: Aristotle, Politics , ii. 9 Click on the letter P to go back to the list of names

39. Science, Civilization And Society The Roman author Pliny said that diocles was both in time and diocles studiedanimal anatomy through dissection and wrote his findings down in a http://www.es.flinders.edu.au/~mattom/science society/lectures/illustrations/lec

40. Tree: Diocles (King) Of SICAMBRI The PEDIGREE of diocles (King) of SICAMBRI. Born ? Died abt. 300 BC. HRH William s65Great Grandfather diocles (King) of SICAMBRI. \. \, (missing) http://freepages.genealogy.rootsweb.com/~jamesdow/s064/f004464.htm

OAS_AD('Top'); The PEDIGREE of Diocles (King) of SICAMBRI Born: ? Died: abt. 300 BC HRH William's 65-Great Grandfather. Agnes Harris's 58-Great Grandfather. Wife: (missing) Child: Bassanus Magnus (King) of SICAMBRI Almadius of CIMMERIANS ,,Y Dilulius I (King) of the CIMMERIANS Helenus III (King) of the CIMMERIANS Plaserius III (King) of the CIMMERIANS Dilulius (Diluglio) II (King) of the CIMMERIANS ... (? - 339? BC) Diocles (King) of SICAMBRI (missing) His 3-Great Grandchild: Clodius I (King) of SICAMBRI His 9-Great Grandchild: Francus (King) of the WEST FRANKS Start OAS_AD('Bottom');

A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z

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