61. Trisectie Van Een Hoek eerste echte bewijs van de onoplosbaarheid van de eerste twee problemen werd gegevendoor de weing bekende Franse wiskundige pierre Laurent wantzel (18141848 http://www.pandd.demon.nl/trisect.htm

Over de trisectie van een hoek Overzicht Meetkunde Overzicht Meetkunde en algebra Trisectie Verdubbeling van de kubus en kwadratuur van de cirkel Enkele conclusies ... Download 1. Meetkunde en algebra Tot de meetkundige problemen die ook door de Grieken niet konden worden opgelost (niet onbegrijpelijk, overigens), behoren Trisectie van de hoek Gegeven een hoek, verdeel die hoek met behulp van passer en liniaal (we schrijven in hetgeen volgt "penl") Verdubbeling van de kubus Gegeven een lijnstuk met lengte 1, construeer een lijnstuk met lengte 2 met behulp van penl (het zogenoemde " Delisch probleem ") Kwadratuur van de cirkel Gegeven een lijnstuk met lengte 1, construeer een vierkant met oppervlakte p met behulp van penl Deze drie problemen zijn inderdaad onoplosbaar (er is een verschil tussen "niet kunnen oplossen" en "onoplosbaar"). Merk op dat dit niet wil zeggen dat er, blijvend bij het eerste onoplosbare probleem, geen hoeken bestaan die (met behulp van passer en liniaal) in drie delen kunnen worden verdeeld. Duidelijk is, dat dit zeker wel het geval is met de rechte hoek. "Het trisectieprobleem van de hoek is onoplosbaar" wil zeggen, dat "er is ten minste één hoek die niet met behulp van penl in drie gelijke stukken kan worden verdeeld".

62. Hors-sujet Contrôleur SCSI Artop. Subject Horssujet contrôleur SCSI Artop. From pierre-Laurent wantzel PRIVACYPROTECTION Date Thu, 09 Nov 2000 160459 +0000 pierre-Laurent wantzel. http://www.faqchest.com/linux/GUILDE/guilde-00/guilde-0011/guilde-001101/guilde0

63. Euclid Challenge - Squaring A Circle By Straightedge And Compass - Page 10 pierre wantzel proved during the 19 th century that it was impossible to squarea circle by straightedge and compass, when following the “Traditional http://www.euclidchallenge.org/pg_10.htm

EUCLID CHALLENGE Successful Response by Milton Mintz May 10, 2002 Page 10: Squaring A Circle By Straightedge And Compass Introduction Converting the area of the circle to a Rectangle. Converting the area of the Rectangle to a Square. This Method Is Successful Because Of The Following: Points are moved at a uniform rate; The method goes beyond traditional euclidian methods The Method was accomplished by using an unmarked straightedge and compass only. Uniform Rate ”: This Method uses the SAME Uniform Rate by BOTH hands. (Hippias used a “Uniform Rate” in his “Non-Euclidian device” over two thousand years ago. His use of a “Uniform Rate” has been accepted over the years, but he used tools other than “straightedge and compass only”.) Traditional Euclidian Methods Pierre Wantzel proved during the 19 th century that it was impossible to square a circle by straightedge and compass, when following the “Traditional Euclidian Methods”. That is why to “successfully square a circle”, unmarked straightedge and compass only, it was necessary for the attached Method to go “Beyond the Traditional Euclidian Methods”. Previous Page Top of Page Next Page

64. Euclid Challenge - Trisection Of Any Angle By Straightedge And Compass Traditional Euclidian Methods pierre wantzel proved during the 19 th century thatit was impossible to trisect all angles by straightedge and compass, when http://www.euclidchallenge.org/pg_03.htm

EUCLID CHALLENGE Successful Response by Milton Mintz May 10, 2002 Page 3: Trisection of Any Angle by Straightedge and Compass Introduction This method received the following review by Professor Clifford J. Earle: Construction of an angle trisector is successful Points are moved at a uniform rate The method goes beyond traditional Euclidian methods Angle trisector: Accomplished by using straightedge and compass only. No scratches on the straightedge that were used by Archimedes. “Uniform Rate”: This Method includes PROOF of the accuracy of its use of the SAME Uniform Rate by BOTH hands. (Hippias used a “Uniform Rate” in his “Non-Euclidian device” over two thousand years ago. His use of a “Uniform Rate” has been accepted over the years, but he used tools other than “straightedge and compass only”). Traditional Euclidian Methods: Pierre Wantzel proved during the 19 th century that it was impossible to trisect all angles by straightedge and compass, when following the “Traditional Euclidian Methods”. That is why to “successfully construct a Trisector”, using only a “straightedge and compass only”, it was necessary for the attached Method to go “Beyond the Traditional Euclidian Methods”.

65. Www.batmath.it Di Maddalena Falanga E Luciano Battaia la necessità fu provata successivamente da pierre-Laurent wantzel nel 1836. http://www.batmath.it/matematica/a_costruz/ciclotomia/ciclotomia.htm

Home page Costruzioni geometriche Il problema generale della ciclotomia Si tratta del problema di dividere una circonferenza in n n lati inscritto nella circonferenza, o, equivalentemente, di costruire un poligono regolare di lato assegnato. Poligoni costruibili con riga e compasso Un poligono regolare di n n dove k p p s sono numeri di Fermat primi. La formula comprende anche il caso in cui n=2 k La costruzione dei poligoni di tre lati ( triangolo equilatero ) e di quattro lati ( quadrato pentagono pentadecagono eptadecagono De resolutione algebraica aequationis x =1, sive de divisione circuli per bisectionem anguli septies repetitam in partes 257 inter se aequales commentatio coronata , del Nachr. Königl. Geselsch. Wissench. Gött. Math.-Phys. Klasse (1894), sono ancora depositati, sotto forma di manoscritto, in una voluminosa scatola della biblioteca dell'Università di Göttingen, dove probabilmente riposeranno per lungo tempo senza destare particolare curiosità da parte degli studiosi: è forse uno dei tanti casi di ricerca matematica difficile, ma sostanzialmente, a nostro avviso, sterile e poco feconda di risultati. Da qualche parte abbiamo addirittura letto il seguente commento, che condividiamo: "What a pointless waste of effort!". n n n n n- z n n z=1 uno due tre Costruzioni geometriche pagina pubblicata il 14/10/2002 - ultimo aggiornamento il 01/09/2003

66. XblGamers :: Why Play With Yourself? them. Kaz, with his pisspoor teleprompter reading skills, spewed morenumbers than pierre wantzel. The PSP was really, really cool. http://www.xblgamers.com/story.php?storyid=60

67. Matematikçiler Translate this page Lansberge Laplace Larmor Lasker Lasker Laurent, H Laurent, pierre Lavanha LavrentevLax Le Wald Walker, Arthur Wall Wallace Wang Wangerin wantzel Waring Watson http://www.sanalhoca.com/matematik/matematikciler.htm

Günlük hayatta iþinize yarayacak dersler... En can alýcý noktalar... Ana Sayfa Kimya Matematik Fizik ... e-mail Gelmiþ Geçmiþ Ünlü Matematikçiler Abbe Abel Abraham Aepinus ... Grasmann Hermann Günther Descartes Diocles Diophantus Dirac Dirichlet Doppler Dupin Eckert, John Eratosthenes Euclid Eudoxus Eutocius Faltings Fano Fano Faulhaber Fefferman Feigl Feller Fermat Ferrar Ferrari Ferrel Ferro Feynman Fibonacci Fields Fincke Fine Fine, Henry Finsler Fischer Fisher Fiske Fiske FitzGerald FlüggeLotz Fomin Forsyth Fourier Fox Fraenkel Francais, F Francais, J Francesca Francoeur Frank Franklin Fredholm Fredholm Freedman Frenet Freundlich Friedmann Friedrichs Frisi Fuchs Fuller Fuss Galerkin Galerkin Galileo Galois Gassendi Gauss Geiser Gelfand Gelfond Gellibrand Geminus Gemma Frisius Genocchi Gentzen Gergonne Germain Gherard Ghetaldi Gibbs Girard, Albert

68. Mathtador Translate this page Remaque le théorème de wantzel est une condition nécessaire, maispas suffisante. Design by pierre Giacomini, Copyright © Mars 2004, http://pageperso.aol.fr/danthuylam/constructible2.htm

Accueil SERVICE Accueil Lire d'or Forum var nom = "fan2mobile"; var serveur = "aol.com"; var sujet= "mathtador"; document.write(''); document.write('Email' + ''); LIENS Mars-2004 Jean TRANTHAN Extension d'un corps Un corps L contient K est une extension de K on note L/K, L est un K-espace vectoriel. On appelle le degré de L sur K et on note [L:K] est la dim L. exp: K=Q( Le théorème de degré On a K->L->M alors [M:K]=[M:L][L:K] Dém: x€M x= S i m a i m i a i €L m i base M a i S j l b i j l j b i j €K l i base L x= S ij ml b i j l j m i ce qui montre la famille l j m i est géneratrice il faut maintenant montrer qu'elle est libre, pour avoir une base S ij ml b i j l j m i S i m S j l b i j l j m i S j l b i j l j =0 car m i sont libres b i j =0 car les l j libres donc dim M/K = ml Elément algébrique x=algébrique sur K il existe P€K[X] tq P(x)=0 d°(x/K)=degré de x sur K le plus petit polynome P€K[X] tq P(x)=0 s'il pas de confusion on note simplement d°x au lieu de d(x/K) rem: P est alors irreductible sur K[X] L=extension alg tout élement de L sont alg Voici quelque résultats: 1)[L:K]=fini => L= extension alg 2)x€L => K->K(x)->L 3)d°x=[K(x):K] Théorème de wantzel Si x est constructible alors d°x=2 k (une puissance de 2) Dém: Si x est constructible alors il existe une tour: K->K ->K ->....->K

69. ICT-lesvoorbeeld: Trisectie Van De Hoek Opmerking. pierre Laurent wantzel (18141848) bewees in de 19 e eeuw dat een oplossingvan de trisectie van de hoek met passer en liniaal onmogelijk was. http://www.aps.nl/wiskunde/Content/Lesvoorbeelden/Meetkunde/Trisectie/opdracht.h

Trisectie van de hoek Een probleem dat al betrekkelijk vroeg in de Griekse meetkunde zijn intrede deed was: Verdeel, met passer en lineaal, een gegeven hoek ABC in drie gelijke delen. Dit naar analogie van de constructie van de bissectrice die wel gelukt was. Opdracht 1 De Grieken zochten allereerst naar een oplossing door, wat we noemen, een richt-oplossing te vinden. Bekijk de onderstaande figuur en probeer te bedenken hoe de figuur is opgebouwd, uitgaande van ABC. Bewijs vervolgens: Als EF door B gaat dan geldt: EBC = ABC Applet created on 18-4-02 by Hans Krabbendam with CabriJava Opdracht 2 Een andere methode was die van Nicomedes (geb. tussen 280-264 v. Chr.) Hij construeerde eerst een kromme, de conchoide. Een conchoide ontstaat door B als vast punt te nemen en vervolgens op AC een punt P en op de lijn BP vanaf P een vaste afstand af te zetten. In dit geval is dat 2*AB. Als je nu door A een lijn loodrecht BC trekt, dan snijdt die de conchoide, zeg maar in F. (met de applet kun je dit nadoen). Bij die plaats van F, dus zowel op de conchoide als op de lijn door A loodrecht op BC) geldt FBC= ABC.

70. Knoten Translate this page Erst 1837 hat pierre wantzel bewiesen, dass das Problem allein mit Hilfe von Linealund Zirkel nicht zu lösen ist. Nur wenn man Kurven 2. oder 3. Grades bzw. http://www.uni-siegen.de/~ifan/ungewu/heft9/bobzin9.htm

Knoten von HAGEN BOBZIN Der gordische Knoten Die Sage um den gordischen Knoten enthält einige Aspekte des Angewandten Nichtwissens, während andere Details eher irreführend sind. So beschäftigt sich das Institut eher selten mit Fragen der Religion oder des Glaubens, was nicht heißt, dass etwa die Frage nach einem Gottesbeweis hin und wieder die Gemüter erhitzt. Auch der Irrtum des Orakels bezüglich der Herrschaft über den gesamten Orient und Okzident spielt für uns eine untergeordnete Rolle. Außerdem haben unsere Fragestellungen häufig keine exakte Lösung, wie sie Alexander der Große durchaus gefunden hat. Wie aber geht man mit Problemen um, die sich nicht so einfach lösen lassen? Existiert überhaupt eine Lösung, wenn man beispielsweise die Frage nach Gerechtigkeit aufwirft? Und wie geht man mit Vermutungen um, die über lange Zeit nicht widerlegt worden sind? Knoten Das Vier-Farben-Problem Schon auf sehr alten Landkarten haben Zeichner nebeneinander liegende Länder mit verschiedenen Farben versehen. Und auch damals war es nicht unbedingt üblich, jedem Land eine andere Farbe zuzuordnen. Da es nie zu Problemen bei der Farbwahl kam, wurde auch die Frage nach der minimalen Zahl benötigter Farben nicht aufgeworfen. Bis schließlich im Jahr 1852 Francis Guthrie in einem Brief an seinen Bruder, der Student bei dem berühmten Mathematiker Augustus de Morgan war, folgende Beobachtung schilderte: Egal welche Landkarte ich einfärbe, ich benötige höchstens vier Farben, so dass keine Nachbarländer dieselbe Farbe aufweisen. Bis 1976 und genau genommen darüber hinaus hat dieses Problem, das dem mathematischen Gebiet der Topologie zugeordnet ist, die Wissenschaft beschäftigt.

71. CritiquesLibres.com : Critiques De Livres : Qu'est-ce Que Les Mathématiques? Translate this page l’angle et duplication du cube dont pierre-Laurent wantzel devait démontrer en1837 qu’ils étaient impossibles à résoudre avec la règle et le compas. http://www.critiqueslibres.com/i.php/vcrit/956

5381 titres 11029 critiques 1952 membres actifs 5301 messages S'identifier Devenir membre Les forums Liste des auteurs ... Vie pratique et loisirs Qu'est-ce que les mathématiques? de Norbert Verdier Kinbote , le 12 mai 2001 (Jumet - 45 ans) La note: Les mathématiques en question Norbert Verdier, professeur de mathématiques à l’université de Paris-Sud, entreprend, dans cet ouvrage de vulgarisation, de clarifier la nébuleuse des mathématiques. Sans sacrifier cependant la complexité de ses scintillements, et les débats qui ont porté sur elles depuis des siècles. Le livre commence par un inventaire des diverses disciplines : logique, arithmétique, algèbre, géométrie, analyse Il se poursuit par une galerie de portraits qui présente Evariste Galois, le Rimbaud des mathématiques, auteur de la théorie des groupes, ainsi que la famille pythagoricienne ou Bourbaki, nom sous lequel, dans les années 30, un ensemble de mathématiciens s’est formé en réaction contre l'enseignement classique de la géométrie d’Euclide qui ne tenait pas alors compte des apports de l’algèbre moderne. Norbert Verdier trace aussi le portrait de Gerbert d'Aurillac, homme de sciences et évêque de Reims au Xe siècle, qui sera à l'origine de

72. Occupation: Mathematician Evariste Galois, 1811, 1832, France. James Joseph Sylvester, 1814, 1897, England.pierre Laurent wantzel, 1814, 1848, France. George Boole, 1815, 1864, England. http://y-intercept.com/occupation.html?occupation_cd=M

73. My First HomePage Fermat s last theorem pierre de Fermat died in 1665. wantzel claimed to have provedit on 15 March but his argument it is true for n = 2, n = 3 and n = 4 and http://iml.umkc.edu/PACE_Online/wdd/StudentsWS2004/YuE-2/yue7.htm

Welcome to My HomePage Here's the link to the Course HomePage and here's the link to My classmate HomePage E-mail Me :) aliciapple@hotmail.com My Pictures My Life My Grandparents My Cousins My Friends My Co-workers School Work As an Actuary My resume Actuarial Exam Fermat's last theorem what is your name:

74. Search Items A biography of pierre Laurent wantzel and hislife as a mathematician, this resource includes images and links to other...... pierre Laurent wantzel http://squidward.siderean.com:9090/test/gem.jsp?sm=fl5;level2;12m3;sidfl8;keywor

75. Aa, Personal , Ahmet Kaya ,Þebnem Ferah , Göksel , Ebru Gündeþ John (553*) Wall, C Terence (545*) Wallace, William (261*) Wallis, John (2463*)Wang, Hsien Chung (649) Wangerin, Albert (481*) wantzel, pierre (1020) Waring http://www.newturk.net/index111.html

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76. Tangram Translate this page Solo dopo più di duemila anni, nel 1837, pierre Laurent wantzel dimostrò, con unprocedimento algebrico, che esistono angoli che non possono essere trisecati http://www.univ.trieste.it/~nirtv/tanweb/textit.html

Filmato (Intranet) Filmato (Intranet) E' necessario alla visione: Windows Media Player 6.2 Bibliografia Immagini Home Altri Siti per giocare al Tangram in linea per scaricare una versione del Tangram per Mac per scaricare una versione Window del Tangram per informazioni sull'Anno Internazionale della Matematica ... [Conclusione] Testo del video: A CHE GIOCO GIOCHIAMO: TANGRAM O MATEMATICA? C.Pellegrino - L.Zuccheri Il tangram è un antico gioco di origine cinese, ottenuto scomponendo un quadrato in sette parti dette tan: un quadrato, un romboide, e cinque triangoli rettangoli isosceli, di cui due grandi, uno medio e due piccoli . Le regole tradizionali del gioco sono semplici: si tratta di disporre sul piano, evitando sovrapposizioni, tutti i sette tan in modo da formare figure che riproducano, rispettando le proporzioni, quelle riportate in formato ridotto sui libretti che accompagnano il gioco. Giocare con il tangram può sembrare facile, troppo facile, soprattutto quando lo si vede già assemblato sotto forma di quadrato: normalmente però un principiante trova già difficoltà a comporre il quadrato, una volta tolti i pezzi dalla scatola.

77. Tangram Two thousand years later, in 1837, pierre Laurent wantzel showed, by an algebraicprocess, that there are angles that can t be trisected with rule and compasses http://www.univ.trieste.it/~nirtv/tanweb/texten.html

Video (Intranet) Video (Intranet) You need: Windows Media Player 6.2 References Pictures Home Links Play Tangram on line Tangram for Mac Tangram for Windows World Mathematical Year 2000 ... [Conclusion] Text of the video: WHAT ARE WE PLAYING: TANGRAM OR MATH? C.Pellegrino - L.Zuccheri 1. What is Tangram? Tangram is an antique game that originally comes from China. It is formed by dividing a square into seven parts that are called "tan": a square, a parallelogram and five isosceles right-angled triangles, two big ones, a medium and two little ones. The traditional rules of the game are simple: you have to lay the seven tans on a plane, without overlapping them, trying to form a figure that reproduces, maintaining the proportions, the figures that you have seen earlier in the instruction book. It may appear very easy to play the game Tangram, especially if you see the pieces already assembled in a square, but normally a beginner has already difficulties to reform the square, after having taken the pieces out of the box. But Tangram isn't a puzzle as many others. After having played a little bit, you begin to enjoy the subtle elegance with which the square has been divided.

78. Godlike Productions Forum Shanks (18121882) *MT Duncan Farquharson Gregory (1813-1844) *SB pierre-AlphonseLaurent (1813-1854) *MT pierre Laurent wantzel (1814-1848) Eugène Charles http://godlikeproductions.com/bbs/message.php?page=64&topic=3&message=278278&mpa

79. Anecdotario Matemático Translate this page Fue PL wantzel quien en 1837 publicó por primera vez, en una revista de matemáticasfrancesa, la primera prueba completamente rigurosa de la imposibilidad de http://www-etsi2.ugr.es/profesores/jmaroza/anecdotario/anecdotario-t.htm

Tales (v. Thales) Tartaglia egipcios Rey Pastor en 1932: braquistocrona J. Bernouilli , con la promesa de Teorema de Fermat (v. Fermat) Teorema de las bisectrices interiores (v. Teorema de Steiner-Lehmus) Teorema de los cuatro colores Poemilla de J.A. Lendon, Surrey, Inglaterra: "Cuatro colores usan los matemáticos de emblema, ansiosamente regiones colocando deseando obtener el teorema donde siguen sin remedio fracasando." Moebius Nature Ex-Prodigy Teorema de los nueve puntos Morley Euclides no la menciona, y aunque Teorema de Morley Euclides Communitas Teorema de Steiner-Lehmus Euclides Journal of the Elisha Mitchell Scientific Society "Cualquier polinomio de grado n tiene n raíces reales o complejas". Enunciado por primera vez por Jean Le Rond d'Alembert en 1746, y demostrado parcialmente por él. La primera demostración rigurosa fue dada en 1799 por Gauss (v.) Thales de Mileto griegos Egipto Tierra antichthon Aristarco de Samos S S n S n S R n S , donde R n sen cos y tg Dos de las primeras construcciones de griegos y la amateur United Press Time Euclides o Einstein Euclides Congressional Record y la The Two Hours that Shook the Mathematical World Challenging and Solving the Three Impossibles The Kidjel Ratio KPJX The Riddle of the Ages Los Angeles Times Budget of Paradoxes Trompeta de Gabriel f x x x

80. Links: Henry Darcy And His Law The Henry Darcy Home Page, French and English translation of 1856 paper and other information on the Darcy's Law, ground water links. Barnabé Brisson ( 17771828) pierre Ossian Bonnet ( 1819-1892 http://biosystems.okstate.edu/Darcy/Links.htm

Henry Darcy and His Law Links Henry Darcy Main Darcy Not much is on the web about Darcy. Here are a few sites of note. The European Geophysical Society's biography on Darcy. http://www.mpae.gwdg.de/EGS/egs_info/darcy.htm Darcy Biography from the Best in Dijon (in French). (This page makes a couple curious statements.) http://perso.club-internet.fr/dijon21/darc.htm Main page: http://www.enpc.fr/ History page: http://www.enpc.fr/Comm/PAGES/HISTORIQUE.htm#perronet Or, L'Ecole Polytechnique Main page: http://www.polytechnique.fr/ History page: http://www.polytechnique.fr/infoEcole/historique/brevehistoire.html http://www.academie-sciences.fr/ Visit Ville Dijon: A tourist site http://www.visit.ie/countries/fr/dijon/ or a commercial site http://www.ifrance.com/dijon/index.htm or the official city page http://www.ville-dijon.fr/ Darcy's Law Okke Batelaan's list of most influential ground-water papers and books. http://pop.vub.ac.be/~batelaan/bestpaper.html Pierre Ossian Bonnet Augustin Louis Cauchy Benoit Paul Emile Clapeyron ... Jules Regnault (1797-1863) (in French) Jean Claude Barre de Saint-Venant Pierre Laurent Wantzel Engineering History Sites Links to other interesting sites.

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