61. Dividing One Angle Into Three Equal Angles Seems A Trivial Problem One of the earliest ways discovered was that of hippias of elis(circa 425 BC).Hippias used a curve he had invented, called the quadratrix. http://www.perseus.tufts.edu/GreekScience/Students/Tim/Trisection.page.html

Dividing one angle into three equal angles seems a trivial problem. That is probably why it irked the Greeks so. Instead of being a simple problem, it is a complex, non-planar problem, as the Greeks soon discovered. The trisection problem can probably credit its origin to the construction of regular polygons. The discover of the construction of a perfect pentagon(see The Golden Section One of the earliest ways discovered was that of Hippias of Elis(circa 425 BC). Hippias used a curve he had invented, called the quadratrix . With this curve, the problem of trisecting an angle could be reduced to the trisection of a line segment. The following picture is one construction of such segment trisect. The great benefit of this method was that it could be generalized to divide any angle into any number of parts. I don't really like this next solution, but maybe you will. This second method, perhaps the most well known of all, can be credited to Nicomedes(circa 180 BC). Nicomedes created a special device to use in his construction. As the upper part slide back and forth in its groove, the angle of the pointer changed so as to describe a curve known as a conchoid(as a function, y=K(x^2 + C)^(-1/2) is the simplest form).

62. EpistemeLinks.com: Website Results For Philosopher Hippias General website search results for Hippias including brief biographies, linkresources, Site Title, Details. hippias of elis. Source LookSmart. Hippias http://www.epistemelinks.com/Main/Philosophers.aspx?PhilCode=Hipp

63. Archaic Period This is based on a list of Olympic victors written by hippias of elis in 400 BC,although there are some doubts as to whether the list is authentic. http://www.athens2004.com/en/ArchaicPeriod/youthinternal

The official website of the ATHENS 2004 Olympic Games - Games of the XXVIII Olympiad Daily Summaries: Home Youth 2004 Travelling through time Games in Antiquity Archaic period Javascript must be enabled to view this page, although the important information on the page is also available to browsers that do not support scripts. Archaic period Regional and Panhellenic Games www.ATHENS2004.com Olympic Games Schedule - Results Medals ... Paralympic sports Related Topics Staging of the ancient Olympic Games Explore Ancient Olympia with Despina! ATHENS 2004 Multivision Show Staging of the ancient Olympic Games ... Interesting Facts The Greek Swimming Paralympic champion, Konstantinos Fykas was the first Torchbearer to carry the Flame after the lighting ceremony at Hephaestus temple.

64. UN-Letter: Winter 2004: Not A Roman, But A Greek (Academic) Holiday and hippias of elis Lectures at Olympia Plato, Sophists, and Homeric Poetryonlysuggest the breadth and depth of topics covered. http://www.dce.harvard.edu/pubs/unletter/2004/winter/7.html

HARVARD EXTENSION SCHOOL building an undergraduate community through communication PREVIOUS NEXT CONTENTS Not a Roman, but a Greek (Academic) Holiday By Amit Samuel, ALB '05 Amit Samuel, ALB '05, wants to study abroad before graduating next June. He has his sights set on the Harvard Summer School's Olympia Program in Greece. To learn more about the program he contacted ALB candidates: Pano Yannakogeorgos, ALB '05, Jason Kelly, ALB '06, Irfan Shabeer, ALB '04, and James Tobin, AA'02, ALB '05 who completed the program this past summer about their experience before he put down is $7,000+ and embarked on his own. Harvard Summer School Students in Olympia, Greece To me, the idea of study abroad has always evoked the images of the movie Roman Holiday : traipsing through cafes and falling in love in exotic localesa glorified vacation primarily reserved for the affluent. Still, I wanted a taste of the experience, and I knew that the Harvard Summer School offers many study abroad options. But, where should I go? There are many choices: In 2004 the Summer School is offering programs in Bolivia, Brazil, Germany, Greece, Italy, Peru, and Portugal. I concluded that, for me, the ideal country to study in would be Greece. Greece is the cradle of Western philosophy, law, and culture; perfect for any aspiring lawyer like me and, as I would later discover through my research, for just about any student. Dr. Gregory Nagy leads the

65. Hippias2.html hippias of elis (430 BC) was a sophist who invented the quadratrix curve totrisect an angle. The problem of trisecting a given angle was one of the http://www.ms.uky.edu/~carl/ma330/hippias/hippias21.html

Hippias and his quadratrix Hippias of Elis (430 BC) was a sophist who invented the quadratrix curve to trisect an angle. The problem of trisecting a given angle was one of the problems that generated a lot of mathematics during this period, and several mathematicians devised methods for solving this problem. Like many other sophists, Hippias was an itinerant teacher who made his living wowing the locals with his knowledge. Apparently, he did alright, but didn't leave much of a legacy except for the quadratrix. Definition of the curve The curve can be described in a few sentences. Let ABCD denote a square. Over a unit time period, allow the top segment of the square to fall at a uniform speed to the bottom of the square. During the same time, allow the left side of the square to rotate clockwise at a uniform speed to the bottom of the square. At each time, the two segments will intersect in a point P. The totality of all these points P is defined as the quadratrix. Drawing the quadratrix One can imagine how Hippias might have sketched the quadratrix in the sand, but one can hardly image how he would have made an accurate sketch of it.

66. The Memorabilia - Chapter IV and one particular discussion with hippias of elis9 on the topic of Hippias had just arrived at Athens after a long absence, and chanced to be http://www.worldwideschool.org/library/books/lit/historical/TheMemorabilia/chap3

The Memorabilia by Xenophon (trans by Dakyns) Terms Contents Preparer's Note BOOK I ... Chapter IV Chapter IV [2] Or, "by his conduct to all, which was not merely innocent in the eye of law and custom but positively helpful." [3] See above, I. i. 18; "Hell." I. vii. 14, 15; Grote, "H. G." viii. 272. [4] See above, I. ii. 35. [5] Leon of Salamis. See "Hell." II. iii. 39; Plat. "Apol." 32 C; Andoc. "de Myst." 46. [6] See above, I. i. 1; Plat. "Apol." 19 C. [7] Kuhner cf. Quintil. VI. i. 7: "Athenis affectus movere etiam per praeconem prohibatur orator"; "Apol." 4; Plat. "Apol." 38 D, E. [8] See Grote, "H. G." viii. p. 663 foll. These views he frequently maintained in conversation, now with one and now with another, and one particular discussion with Hippias of Elis[9] on the topic of justice and uprightness has come to my knowledge.[10] [9] For this famous person see Cob. "Pros. Xen." s.n.; Plat. "Hipp. maj." 148; Quint. xii. 11, 21; Grote, "H. G." viii. 524. [10] Or, "I can personally vouch for." Hippias had just arrived at Athens after a long absence, and chanced to be present when Socrates was telling some listeners how astonishing it was that if a man wanted to get another taught to be a shoemaker or carpenter or coppersmith or horseman, he would have no doubt where to send him for the purpose: "People say,"[11] he added, "that if a man wants to get his horse or his ox taught in the right way,[12] the world is full of instructors; but if he would learn himself, or have his son or his slave taught in the way of right, he cannot tell where to find such instruction."

67. Philosophy: Research She is presently researching hippias of elis, and women philosophers of ancienttimes. She is writing an historical novel on Pythagoras, aimed at young http://ehlt.flinders.edu.au/philosophy/research/

Home Welcome What is Philosophy? Staff ... WebCT Research Current postgraduate students MA students Joan Clayton Philosophy of language: the use of Slippery Slope Arguments in Bioethics debates Andrew McKechnie A case for unconditional welfare entitlements Nigel Palmer Applied Ethics; Business Ethics Jeremy Reglar Theories of emotion and cognitive behavioural therapy Madeleine St Johnston-Romano Ethics (Classical Greek) Matthew Usher Plato's Critique of pleasure Linda Zaccara Feminist theory and computer technology PhD students Pat Albrecht Implicit Cognition Ian Douglas-Irving Age and Morality Kym Farrand Ethics and Epistemology. The justification of moral values in relation of scientific theories. Paul Rasmussen Bioethics Suzi Roux The history and philosophy of conception in the theory of natural selection John Tons Political Moral Philosophy Randal White Ethical theory in relation to liberalism and communitarianism Visiting scholars Dr Alan Chalmers Primary Research Interests: Philosophy of Science Greg O'Hair Primary Research Interests: Epistemology, Logic, Philosophy of Mind. Currently working on problems in logic and the nature of computation.

68. List Of Scientists By Field Translate this page hippias of elis. hippias of elis. Hippocrates of Chios. Hippocrates of Chios.Hippocrates of Cos. Hirayama, Kiyotsugu. Hirayama, Kiyotsugu http://www.indiana.edu/~newdsb/h.html

Haak, Theodore Haas, Arthur Erich Haas, Arthur Erich Haas, Wander Johannes de Haast, Johann Franz Julius von Haber, Fritz Haberlandt, Gottlieb Hachette, Jean Nicolas Pierre Hachette, Jean Nicolas Pierre Hachette, Jean Nicolas Pierre Hadamard, Jacques Hadfield, Robert Abbott Hadfield, Robert Abbott Hadley, John Hadley, John Hadorn, Ernst Haeckel, Ernst Heinrich Philipp August Haffkine, Waldemar Mordecai Wolfe Hague, Arnold Hahn, Otto Hahn, Otto Hahnemann, Christian Friedrich Samuel Hahnemann, Christian Friedrich Samuel Haidinger, Wilhelm Karl Hakluyt, Richard Hakluyt, Richard Haldane, John Burdon Sanderson Haldane, John Burdon Sanderson Haldane, John Scott Haldane, Richard Burdon Hale, George Ellery Hale, William Hales, Stephen Hales, Stephen Hall, Asaph Hall, Charles Martin Hall, Edwin Herbert Hall, Granville Stanley Hall, Granville Stanley Hall, James Hall, James Hall, Marshall Hall, Marshall Hall, Sir James Hall, Sir James Haller, Albrecht von Haller, Albrecht von Haller, Albrecht von Halley, Edmond Halley, Edmond Halley, Edmond Halliburton, William Dobinson Halliburton, William Dobinson

69. Classics In The History Of Psychology -- Baldwin (1901) Definitions Het - Hz hippias of elis. A sophist contemporary with Prodicus and Protagoras. See PRESOCRATICPHILOSOPHY (Sophists). Hippolytus, Romanus. http://psychclassics.yorku.ca/Baldwin/Dictionary/defs/H3defs.htm

Classics in the History of Psychology An internet resource developed by Christopher D. Green York University, Toronto, Ontario ISSN 1492-3173 (Return to Classics index DICTIONARY OF PHILOSOPHY AND PSYCHOLOGY JAMES MARK BALDWIN (1901) Definitions Het - Hz Posted August 2000 Heterodoxy: see HERESY. Heterogamy [Gr. eteroV , other, + gamoV , marriage]: Ger. Generationswechsel ; Fr. ; Ital. eterogamia . See ALTERNATION OF GENERATIONS. Heterogeneity: see HOMOGENEITY. Heterolecithal [Gr. eteroV , other, + lekiqoV , yolk]: Ger. heterolekithal ; Fr. (rare Y.D. ); Ital. eterolecito . Of the ovum: having unequally distributed yolk. A term proposed by Mark (1892) to include both telolecithal and centrolecithal ova. Cf. HOMOLECITHAL, and CLEAVAGE. ( C.LL.M. Heteromorphosis [Gr. eteroV , other, + morfh , shape]: Ger. Heteromorphose ; Fr. ; Ital. eteromorfosi . The production by some organisms, under the stimulus of external forces, of organs or parts where such do not occur normally. REGENERATION (q.v.) is the reproduction of parts which have been lost; whereas heteromorphosis is the production of parts unlike those which have been lost, as the replacing of eye-stalks by antennary structures. If, for example

70. EAWC Anthology: The Apology There is Gorgias of Leontium, and Prodicus of Ceo s, and hippias of elis, who gothe round of the cities, and are able to persuade the young men to leave http://eawc.evansville.edu/anthology/apology.htm

Exploring Ancient World Cultures Readings from Ancient Greece The Apology Plato / Translated by Benjamin Jowett Well, then, I will make my defence, and I will endeavor in the short time which is allowed to do away with this evil opinion of me which you have held for such a long time; and I hope I may succeed, if this be well for you and me, an d that my words may find favor with you. But I know that to accomplish this is not easy I quite see the nature of the task. Let the event be as God wills: in obedience to the law I make my defence. At last I went to the artisans, for I was conscious that I knew nothing at all, as I may say, and I was sure that they knew many fine things; and in this I was not mistaken, for they did know many things of which I was ignorant, and in this they certainly were wiser than I was. But I observed that even the good artisans fell into the same error as the poets; because they were good workmen they thought that they also knew all sorts of high matters, and this defect in them overshadowe d their wisdom therefore I asked myself on behalf of the oracle, whether I would like to be as I was, neither having their knowledge nor their ignorance, or like them in both; and I made answer to myself and the oracle that I was better off as I was. I have said enough in my defence against the first class of my accusers; I turn to the second class, who are headed by Meletus, that good and patriotic man, as he calls himself. And now I will try to defend myself against them: thes e new accusers must also have their affidavit read. What do they say? Something of this sort: That Socrates is a doer of evil, and corrupter of the youth, and he does not believe in the gods of the state, and has other new divinities of his own. That is the sort of charge; and now let us examine the particular counts. He says that I am a doer of evil, who corrupt the youth; but I say, O men of Athens, that Meletus is a doer of evil, and the evil is that he makes a joke of a serious matter, and is too re ady at bringing other men to trial from a pretended zeal and interest about matters in which he really never had the smallest interest. And the truth of this I will endeavor to prove.

71. McLuhan Program - Toronto School Of Communications - Plato's Critique Of The Sop Evidence from a memory treatise attributed to the sophist hippias of elis (whoappears as chief interlocutor in Plato s Lesser Hippias and Greater Hippias), http://www.mcluhan.utoronto.ca/tsc_plato_critique_sophists.htm

Index Toronto School of Communication Marshall McLuhan - Basic Innovations John Eisenberg - Technology and Human Thought Harold Innis - The Bias of Writing Theory of the Toronto School ... Walter J. Ong: Transformation of the Word var site="sm9mcluhantsc" Toronto School of Communication by Twyla Gibson, Ph.D. Senior McLuhan Fellow Plato's Critique of the Sophists and The Art of Memory The poets were not the only target of Plato's attack. The sophists were criticized mercilessly by Socrates. These wandering teachers were the successors of the rhapsodes. Recently discovered fragments from the fifth and fourth centuries B.C.E. prove that they were also heirs of the tradition started by the poet Simonides (556 - 468 B.C.E.). These few surviving documents have allowed scholars to trace the line of descent from poet to rhapsode to sophist as part of the transition from oral tradition to written record. When material from more than one source was put together, interpreters were needed to translate anachronistic expressions and foreign words. As the epics came to be preserved in written collections, a group of rhapsodes became interpreters as well as presenters of poetry. Some of the earliest prose consists of their efforts to explain the meaning of traditional names and phrases in the old theogonies. Glosses, along with explanations of Homeric proper names and obscure words by "etymology," were developed, collected and transmitted by the rhapsodes.

72. Elis elis was the birthplace of hippias, the sophist staged in several of Plato sdialogues, including two bearing his name (hippias Major and hippias Minor). http://plato-dialogues.org/tools/loc/elis.htm

Bernard SUZANNE Last updated November 30, 1998 Plato and his dialogues : Home Biography Works History of interpretation ... New hypotheses - Map of dialogues : table version or non tabular version . Tools : Index of persons and locations Detailed and synoptic chronologies - Maps of Ancient Greek World . Site information : About the author This page is part of the "tools" section of a site, Plato and his dialogues , dedicated to developing a new interpretation of Plato's dialogues. The "tools" section provides historical and geographical context (chronology, maps, entries on characters and locations) for Socrates, Plato and their time. By clicking on the minimap at the beginning of the entry, you can go to a full size map in which the city or location appears. For more information on the structure of entries and links available from them, read the notice at the beginning of the index of persons and locations City and region of northwestern Peloponnese (area 3) Endymion , a son, or grandson, of Zeus. Endymion was famous for having had Selene (the moon) as lover, who managed to obtain from Zeus that he realize one wish of Endymion. His wish was to sleep forever, so that he would stay forever young (Socrates alludes to this story at . With his wife, Endemyon had three sons

73. Hippias Aus Elis Translate this page hippias aus elis Seite aus einem deutschsprachigen Online-Philosophenlexikon. http://www.philosophenlexikon.de/hippias.htm

Begriffe Abaelard - Ayer Baader - Byron Cabanis - Czezowski Ebbinghaus - Ewald ... Frauen in der Philosophie Diskussion PhilTalk Philosophieforen Andere Lexika PhilLex -Lexikon der Philosophie Lexikon der griechischen Mythologie PhiloThek Bibliothek der Klassiker Zeitschriftenlesesaal Nachschlagewerke Allgemeine Information ... Dokumentenlieferdienste Spiele Philosophisches Galgenraten PhilSearch.de Shops PhiloShop PhiloShirt Service Kontakt Impressum eMail Hippias aus Elis (ca. 430 v. u. Z.) Der Sophist Bekannt wurde Hippias durch seine Rhetorik. powered by Uwe Wiedemann

74. Hippias Van Elis - Wikipedia hippias van elis (geboren rond 450 v. Chr. in Athene) was een Grieks sofist.Hij was jonger dan zijn tijdgenoot en tevens sofist Protagoras, en zou als zijn http://nl.wikipedia.org/wiki/Hippias_van_Elis

Wikimedia heeft uw hulp nodig om US $200.000 in te zamelen. Zie onze donatiepagina voor de details van deze actie. Meer dan $153.000 (ruim €130.000) is reeds ontvangen sinds 19 augustus. Zeer bedankt voor uw steun! Hippias van Elis Hippias van Elis (geboren rond 450 v. Chr. in Athene ) was een Grieks sofist . Hij was jonger dan zijn tijdgenoot en tevens sofist Protagoras , en zou als zijn opvolger beschouwd kunnen worden. Zoals de meeste sofisten claimde Hippias een autoriteit op alle wetenschapsgebieden te zijn. Zo toonde hij interesse in de astronomie en de wiskunde , maar ook in muziek en taal . Net als de meeste sofisten was zijn kennis echter vrij oppervlakkig. In dialogen van Plato wordt hij echter geroemd om zijn vermogen te onthouden, via allerhande mnemotechnieken . Zijn arrogantie wordt echter minder hoog aangeschreven. Hippias wordt daarnaast in diverse werken (opnieuw ook van Plato) een grote bijdrage aan de literatuur toegewezen, door te wijzen op de betekenis van woorden, het belang van ritme en stijl. Een werk over de stijl van Homerus zou op zijn naam staan, maar daar is niets van over.

75. Greciaheroica2 Unlike the Pythagoreans, hippias de elis (460 BC) was a Sophist; in other wordshe earned his living by teaching his disciples. This is mentioned in Plato s http://descartes.cnice.mecd.es/ingles/maths_workshop/A_history_of_Mathematics/Gr

THE GREEK HEROIC AGE II History HIPPIAS OF ELIS Unlike the Pythagoreans, Hippias de Elis (460 B.C.) was a Sophist ; in other words he earned his living by teaching his disciples. This is mentioned in Plato's Dialogues , where he is described as having little substance, earning more money than his peers and somewhat proud in character. Proclus ascribed to him the invention of the first curve, which is different to the circumference , known as the trisectrix or quadratrix of Hippias, which allows the angle to be divided into three equal parts. It can also be used to square the circle although Dinostratus gave a clear demonstration of this in the following century. Hippias' trisectrix Whilst a moves around the circle at constant velocity b moves along the segment at constant velocity too. Each point on the curve represents the point where the arc and segment coincide as we move along them at the same time. In this window you can see how Hippias' trisectrix is used to trisect the angle in three equal parts.

76. Hippias Von Elis http://www.lateinforum.de/thesauru/WdAntike/H/hippias2.htm

ex bibliotheca Lateinforum Hippias von Elis Start A - Z Biographie Autoren ... Sentenzen Hippias von Elis , gegen Ende des 5. Jahrhundert v. Chr., aus Elis, Sophist. Protagoras und des Sokrates. Sein Bildungsproramm beinhaltete Grammatik, Poesie, Mathematik, Musik und Astronomie. Er soll eine Liste der Olympiasieger zu chronologischen Zwecken zusammengestellt haben. Xenophon, Memorabilia 4, 4, 5 Es gibt zwei platonische zwei Dialogedie nach ihm benannt sind. a) Hippias minor b) Hippias maior (Die Echtheit dieses Dialoges ist umstritten). Sophist Vgl. auch Gorgias Prodikos Protagoras Quelle: Peter Rehfeld 2001 s. v. Hippias von Elis zur Homepage Inhaltsverzeichnis Neues?

77. Hippias D'Elis Cherchant à résoudre le problème de la trisection de l angle http://serge.mehl.free.fr/chrono/Hippias.html

HIPPIAS d'Élis, grec, vers -450 Philosophe sophiste, diplomate, il connut Socrate trisection de l'angle , il inventa une courbe trisectrice quadratrice de Dinostrate car ce dernier l'utilisa pour tenter la quadrature du cercle. Wantzel en 1837 : Trisection et Trisectrice dans ChronoMath : Hippocrate de Chio

78. Lexikon Hippias Von Elis hippias von elis aus der freien EnzyklopädieWikipedia und steht unter der GNU Lizenz. Die Liste der Autoren ist http://lexikon.freenet.de/Hippias_von_Elis

E-Mail Mitglieder Community Suche ... Hilfe document.write(''); im Web in freenet.de in Shopping Branchen Lexikon Artikel nach Themen alphabetischer Index Artikel in Kategorien Weitere Themen Schock an der Zapf- s¤ule: Benzin so teuer wie noch nie! Tokio Hotel: Harte Jungs oder nur peinliche Poser? IAA: B¶ser Blick an Mazdas neuem Flitzer Sassou HotCams: Girls flir- ten mit Ihnen in pri- vater Atmosph¤re ... Pleitewelle der Fonds - wen es noch treffen k¶nnte Sie sind hier: Startseite Lexikon Hippias von Elis Hippias von Elis H i ppias, (griech. Hipp­as von ‰lis ) war ein Sophist des ausgehenden 5. Jahrhunderts v. Chr. Hippias war ein enzyklop¤disch gebildeter Sophist , ein j¼ngerer Zeitgenosse des Protagoras und wurde von Platon in zwei Dialogen Hippias Minor und Hippias Maior ) sowie im Dialog Protagoras dargestellt. Hippias von Elis war der Erfinder der kinematisch erzeugten Kurve Quadratrix , die zur L¶sung von zwei der drei Problemen der griechischen Geometrie , die Drittelung eines Winkels und die Quadratur des Kreises , verwendet wurde. Vorsokratiker Heraklit Parmenides von Elea Xenophanes ... Gorgias Hippias von Elis Kritias Prodikos Protagoras Personendaten NAME Hippias von ‰lis ALTERNATIVNAMEN KURZBESCHREIBUNG Sophist GEBURTSDATUM GEBURTSORT STERBEDATUM STERBEORT Von " http://lexikon.freenet.de/Hippias_von_Elis

79. MSN Encarta Winkler Prins - Hippias Van Elis hippias van elis (450 – 400 vC), Grieks wijsgeer en beroemd sofist, beheerste enonderwees vrijwel Zoeken in Encarta Winkler Prins naar hippias van elis http://nl.encarta.msn.com/encyclopedia_1021519119/Hippias_van_Elis.html

MSN-startpagina Mijn MSN Hotmail Zoeken ... Upgrade naar Encarta Winkler Prins Premium Zoeken in Encarta Winkler Prins Artikel voor leden MSN Encarta Winkler Prins Premium: Krijg toegang tot dit artikel en een groot aantal andere artikelen, een interactieve wereldatlas en meer voor € 34,99 per jaar (inclusief BTW). Meer informatie. Dit artikel is alleen beschikbaar voor leden van MSN Encarta Winkler Prins Premium. Ben je al lid? Je kunt je hierboven aanmelden. Hippias van Elis Hippias van Elis (450 – 400 v.C.), Grieks wijsgeer en beroemd sofist, beheerste en onderwees vrijwel alle wetenschappen (grammatica, rhytmica,... Wil je meer van Encarta Winkler Prins? Word vandaag nog lid en krijg toegang tot: Multimedia Interactieve wereldatlas Meer dan 50.000 artikelen Meer informatie over Hippias van Elis van Andere functies van Encarta Winkler Prins Zoeken in Encarta Winkler Prins naar Hippias van Elis © 2005 Microsoft/Het Spectrum MSN-privacybeleid Juridische informatie Adverteren Help

80. Hippias D'Elis Translate this page Philosophe sophiste et diplomate, hippias d’elis se frotte au problème de la hippias d’elis propose de ramener la subdivision régulière du cercle à http://www.reunion.iufm.fr/recherche/irem/histoire/hippias_d'elis.htm

HIPPIAS d’Elis grec, vers -450 Philosophe sophiste et diplomate, Hippias d’Elis se frotte au problème de la trisection de l’angle dont il serait l'initiateur et invente une courbe, "la trisectrice", qui en permette une solution approchée (construction point par point) appelée cependant quadratrice de Dinostrate car ce dernier l’utilise pour tenter la quadrature d u cerc l e. La trisection de l'angle Comment placer les droites (OY), (OZ) telles que l’on ait : XÔY = YÔZ = ZÔT ? Cette réalisation au sens de " constructible " naturellement. Hippias d’Elis propose de ramener la subdivision régulière du cercle à celle d’un segment. Un cercle C est donné avec deux rayons OA et OB perpendiculaires. Un point P décrit uniformément (OB). Un point N décrit uniformément l’arc AB. On considère M sur (ON) de même ordonnée que P . La quadratrice est l’ensemble des points M, intersection de (ON) et de la droite D parallèle à (OA) passant par P. La solution proposée par Hippias d’Elis est la plus ancienne solution proposée . Reste à construire la trisection d'un angle à l'aide de cette quadratrice : avis aux amateurs.

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