1. Lissajous Translate this page Jules Antoine lissajous jules Antoine Lissajous est né à Versailles,le 4 mars 1822, et mort à Plombières, le 24 juin 1880. http://bcev.nfrance.com/lissajous/lissajous.htm

2. Lissajous Jules Antoine Lissajous. Jules Lissajous entered the Ecole Normale Supérieure in1841. Afterwards he became professor of mathematics at the Lycée SaintLouis. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Lissajous.html

Jules Antoine Lissajous Born: 4 March 1822 in Versailles, France Died: Click the picture above to see two larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Jules Lissajous Lissajous was interested in waves and developed an optical method for studying vibrations. At first he studied waves produced by a tuning fork in contact with water. In 1855 he described a way of studying acoustic vibrations by reflecting a light beam from a mirror attached to a vibrating object onto a screen. Duhamel had tried to demonstrate these vibrations with a mechanical linkage but Lissajous wanted to avoid the problems caused by the linkage. He obtained Lissajous figures by successively reflecting light from mirrors on two tuning forks vibrating at right angles. The curves are only seen because of persistence of vision in the human eye. Lissajous studied beats seen when his tuning forks had slightly different frequencies, in this case a rotating ellipse is seen.

3. Strona Dla Mioników Programowania Ciekawe krzywe, które mona wykorzysta jako tory dla animacji, oparte na funkcjach trygonometrycznych. Czy wiesz, e lissajous jules Antoine, 18221880, francuski naukowiec, który szczególnie interesowa si falami http://www.pasman.republika.pl/sinusy.htm

4. Famous People Morris Lee Tsung Lebesgue Henri Lederman Leon Leibniz Gottfried Lenard Philipp LeviCivitaTullio Lie Marius Lippmann Gabriel lissajous jules Ljapunov Alexandr http://www.aldebaran.cz/famous/list_ijkl.html

I, J K L Jacobi Carl Jansky Karl Jarník Vojtìch Jeans James ... Odkazy

5. Lissajous Translate this page lissajous jules Antoine français, 1822-1880 Physicien dans le domainede l'optique, ce normalien, docteur ès sciences, fut professeur http://www.sciences-en-ligne.com/momo/chronomath/chrono1/Lissajous.html

LISSAJOUS Jules Antoine x = a.sin mt , y = b.cos nt x = a.sin(mt + a ) , y = b.cos(nt + b à un changement de variable affine près. A droite, la courbe définie par : x = sin(3t) , y = sin(t + p Pour en savoir un peu plus : Hermite Kronecker

6. Einige Der Bedeutenden Mathematiker Translate this page Lie Marius Sophus, 1842-1899. Liouville Joseph, 1809-1882. Lipschitz Rudolf Otto,1832-1903. lissajous jules Antoine, 1822-1880. Littlewood John Edensor, 1885-1977. http://www.zahlenjagd.at/mathematiker.html

Einige der bedeutenden Mathematiker Abel Niels Hendrik Appolonius von Perga ~230 v.Chr. Archimedes von Syrakus 287-212 v.Chr. Babbage Charles Banach Stefan Bayes Thomas Bernoulli Daniel Bernoulli Jakob Bernoulli Johann Bernoulli Nicolaus Bessel Friedrich Wilhelm Bieberbach Ludwig Birkhoff Georg David Bolyai János Bolzano Bernhard Boole George Borel Emile Briggs Henry Brouwer L.E.J. Cantor Georg Ferdinand Carroll Lewis Cassini Giovanni Domenico Cardano Girolamo Cauchy Augustin Louis Cayley Arthur Ceulen, Ludolph van Chomsky Noel Chwarismi Muhammed Ibn Musa Al Church Alonzo Cohen Paul Joseph Conway John Horton Courant Richard D'Alembert Jean Le Rond De Morgan Augustus Dedekind Julius Wilhelm Richard Descartes René Dieudonné Jean Diophantos von Alexandria ~250 v. Chr. Dirac Paul Adrien Maurice Dirichlet Peter Gustav Lejeune Eratosthenes von Kyrene 276-194 v.Chr. Euklid von Alexandria ~300 v.Chr. Euler Leonhard Fatou Pierre Fermat Pierre de Fischer Ronald A Sir Fourier Jean-Baptiste-Joseph Fraenkel Adolf Frege Gottlob Frobenius Ferdinand Georg Galois Evariste Galton Francis Sir Gauß Carl Friedrich Germain Marie-Sophie Gödel Kurt Goldbach Christian Hadamard Jacques Hamilton William Rowan Hausdorff Felix Hermite Charles Heawood Percy Heron von Alexandrien ~60 n.Chr.

7. Jules Lissajous jules Antoine lissajous (18221880). jules lissajous entered Ecole Normale Supérieure in 1841. http://www.fys.kuleuven.ac.be/pradem/fysici/Lissajous.htm

Pradem Leuven Demo's Applets Laboproeven ... Zoeken Jules Antoine Lissajous (1822-1880) Jules Lissajous entered Ecole Normale Supérieure in 1841. Afterwards he became professor of mathematics at the Lycée Saint-Louis. In 1850 he was awarded a doctorate for a thesis on vibrating bars using Chladni's Article by: J J O'Connor and E F Robertson Pradem Leuven Premonstreitcollege Plan Naamsestraat 61 3000 Leuven Opmaak: Tony Verheyden Laatste wijziging: 22-aug-02

8. Lissajous lissajous, jules Antoine. (18221880) http://www.aldebaran.cz/famous/people/Lissajous_Jules.html

Lissajous, Jules Antoine Francouzský fyzik zabývající se vlnami a kmity. Vyvinul speciální optickou metodu pro jejich sledování. Sledoval i zvukové vlny pomocí odrazu svìtelného paprsku od zrcadla dotýkajícího se zdroje zvuku. Také sledoval záznìje. Na jeho poèest jsou pojmenovány Lissajousovy obrazce vznikající pøi skládání dvou kolmých kmitù, je-li pomìr frekvencí roven malým celým èíslùm. Astrofyzika Galerie Sondy Úkazy ... Odkazy

9. The ABC's Of Lissajous Figures The story of how the ABC logo came to be, plus a Shockwave simulator of lissajous patterns. jules Antoine lissajous was a French physicist who lived from 1822 to 1880. http://www.abc.net.au/science/holo/liss.htm

To view this page, you need a plug-in called Shockwave that you can download free from the web. Jules Antoine Lissajous was a French physicist who lived from 1822 to 1880. Like many physicists of his time, Lissajous was interested in being able to see vibrations. He started off standing tuning forks in water and watching the ripple patterns, but his most famous experiments involved tuning forks and mirrors. For example, by attaching a mirror to a tuning fork and shining a light onto it, Lissajous was able to observe, via another couple of mirrors, the reflected light twisting and turning on the screen in time to the vibrations of the tuning fork. When he set up two tuning forks at right angles, with one vibrating at twice the frequency of the other, Lissajous found that the curved lines on the screen would combine to make a figure of eight pattern. The ABC logo is a 3:1 Lissajous figure if Lissajous wanted to see this pattern he would have to get one of his tuning forks to vibrate three times faster than the other. Why did the ABC choose a Lissajous figure for its logo?

10. Lissajous jules lissajous entered the Ecole Normale Supérieure in 1841. http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Lissajous.html

Jules Antoine Lissajous Born: 4 March 1822 in Versailles, France Died: Click the picture above to see two larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Jules Lissajous Lissajous was interested in waves and developed an optical method for studying vibrations. At first he studied waves produced by a tuning fork in contact with water. In 1855 he described a way of studying acoustic vibrations by reflecting a light beam from a mirror attached to a vibrating object onto a screen. Duhamel had tried to demonstrate these vibrations with a mechanical linkage but Lissajous wanted to avoid the problems caused by the linkage. He obtained Lissajous figures by successively reflecting light from mirrors on two tuning forks vibrating at right angles. The curves are only seen because of persistence of vision in the human eye. Lissajous studied beats seen when his tuning forks had slightly different frequencies, in this case a rotating ellipse is seen.

11. Lissajous Portraits jules lissajous. http://www-gap.dcs.st-and.ac.uk/~history/PictDisplay/Lissajous.html

Jules Lissajous JOC/EFR August 2001 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/PictDisplay/Lissajous.html

12. Lissajous, Jules Antoine lissajous, jules Antoine (18221880). French physicist who from 1855developed lissajous figures as a means of visually demonstrating http://www.cartage.org.lb/en/themes/Biographies/MainBiographies/L/Lissajous/1.ht

Lissajous, Jules Antoine French physicist who from 1855 developed Lissajous figures as a means of visually demonstrating the vibrations that produce sound waves. Lissajous first reflected a light beam from a mirror attached to a vibrating object such as a tuning fork to another mirror that rotated. The light was then reflected onto a screen, where the spot traced out a curve whose shape depended on the amplitude and frequency of the vibration. He then refined this method by using two mirrors mounted on vibrating tuning forks at right angles, and produced a wider variety of figures. By making one of the forks a standard, the acoustic characteristics of the other fork could be determined by the shape of the Lissajous figure produced. Lissajous figures can now be demonstrated on the screen of an oscilloscope by applying alternating currents of different frequencies to the deflection plates. The curves produced depend on the ratio of the frequencies, enabling signals to be compared with each other.

13. Lissajous Lab Setting concert pitch the elusive 440 A Enter now a physics professor named jules Antoine lissajous. lissajous had written a thesis on the mechanics of tuning http://members.aol.com/edhobbs/applets/lissajous

Lissajous Lab To operate: Select the Preset buttons at the left to see sample patterns. To generate your own patterns, use the digital readouts at the right. Adjust the readouts by clicking on the digits: clicking near the top of a digit increases its value; clicking near the bottom decreases its value. Download Center Download the screen saver: Click on the button at the left to download the Lissajous screen saver. This displays the same patterns full-screen as a screen saver. The screen saver is only for PC's running Windows 95/98/NT. Download this Web page: Click on the button at the left to download a WinZip archive of this Web page. You are welcome to put this page on your own site; just unzip the archive and upload all of the files to a single directory. Lissajous Figures Lissajous (pronounced LEE-suh-zhoo ) figures were discovered by the French physicist Jules Antoine Lissajous. He would use sounds of different frequencies to vibrate a mirror. A beam of light reflected from the mirror would trace patterns which depended on the frequencies of the sounds. Lissajous' setup was similar to the apparatus which is used today to project laser light shows. Before the days of digital frequency meters and phase-locked loops, Lissajous figures were used to determine the frequencies of sounds or radio signals. A signal of known frequency was applied to the horizontal axis of an oscilloscope, and the signal to be measured was applied to the vertical axis. The resulting pattern was a function of the ratio of the two frequencies.

14. Physicists Eduard Anton Lenz, Heinrich Friedrich Emil Lighthill, Micheal James Lindemann,Frederick Alexander Lippmann, Gabriel lissajous, jules Antoine Lodge, Oliver http://www.cartage.org.lb/en/themes/Biographies/Categories/Scientists/Physicists

Leonardo da Vinci Lamb, Willis Landau, Lev Davidovich Langevin, Paul Leonardo da Vinci Lamb, Willis Landau, Lev Davidovich Langevin, Paul ... Lyttleton, Raymond Arthur

15. References For Lissajous References for the biography of jules lissajous References for jules lissajous. Biography in Dictionary of Scientific Biography (New York 19701990). http://www-groups.dcs.st-and.ac.uk/~history/References/Lissajous.html

References for Lissajous Biography in Dictionary of Scientific Biography (New York 1970-1990). Articles: Prix Lacaze, physique, Main index Birthplace Maps Biographies Index History Topics ... Anniversaries for the year JOC/EFR November 2002 School of Mathematics and Statistics University of St Andrews, Scotland The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/References/Lissajous.html

16. No. 1305: A=440 Musicians grew alarmed. Enter now a physics professor named jules Antoine lissajous. lissajous,jules Antoine, The Dictionary of Scientific Biography, Vol. http://www.uh.edu/engines/epi1305.htm

No. 1305: A by John H. Lienhard Click here for audio of Episode 1305. Today, we set the pitch of a concert A . 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. T he story is told of a conductor who had problems with an out-of-tune soprano. Finally he turned to her in frustration and hissed, "Madam, would you please give the concertmaster your A Today's A above middle C has been set at 440 cycles per second or 440 Hertz. Before the concert, the concertmaster bids the oboist play an A for the winds. Then he tunes to that A and plays it for the strings. In the end, all ninety players should be agreed on the same 440 A , but the best human ear is hard put to tell a 440 A from, say, a 442 A . The best-tuned orchestra is close to, but never exactly on, the standard A So how did we create that particular pitch before we had electronic measurements? How did we tune a tuning fork? Agreeing on pitch became a serious problem as orchestra sizes increased during the Baroque era. Baroque musicians often used organ pipes as standards even though pitches varied greatly from one organ to another. In 1619 composer Michael Praetorius proposed a particular A -425 organ pipe as a standard. He pointed out that higher pitches led to broken violin strings. That was almost a half-step below today's

17. Lissajous Curves Remember that you have to finish all of the labs by Friday May 3 at 500. lissajousfigures were discovered by the French physicist jules Antoine lissajous. http://jacobi.math.wvu.edu/~mays/WvEB128/Labs/Lab11/Lab11q.htm

Click here to open a WebCT window. Log on to myWebCT. Answer the questions in Lab 11. After you complete the lab you can submit your answers and review the correct answers to make sure you understand. You can redo the lab later and complete the lab more than once. If you do it again, the higher grade will count. Remember that you have to finish all of the labs by Friday May 3 at 5:00. Lissajous figures were discovered by the French physicist Jules Antoine Lissajous. At first he studied waves produced by putting a vibrating tuning fork in contact with water. Then he reflected a beam of light from a mirror and used sounds of different frequencies to make the mirror vibrate. The light traced patterns that varied depending on the frequencies of the sounds. Lissajous figures can be used to compare frequencies of either sounds or of radio signals. A signal of known frequency can be applied to the horizontal axis of an oscilloscope, and a signal to be measured applied to the vertical axis. The resulting pattern depends only on the ratio of the two frequencies. Lissajous figures often appeared as props in science fiction movies and TV shows from the 50's and 60's. Usually one of the screens on the bridge of the starship Enterprise has a lissajous pattern on it. The original technique of Jules Antoine Lissajous is still used today for special effects in laser light shows.

18. Lissajous Curves lissajous figures were discovered by the French physicist jules Antoinelissajous. At first he studied waves produced by putting http://jacobi.math.wvu.edu/~mays/128f02/Labs/Lab11/Lab11q.htm

Click here to open a WebCT window. Log on to myWebCT. Answer the questions in Lab 10. After you complete the lab you can submit your answers and review the correct answers to make sure you understand. You can redo the lab later and complete the lab more than once. If you do it again, the higher grade will count. Remember that you have to finish all of the labs by Friday December 6 at 5:00. Lissajous figures were discovered by the French physicist Jules Antoine Lissajous. At first he studied waves produced by putting a vibrating tuning fork in contact with water. Then he reflected a beam of light from a mirror and used sounds of different frequencies to make the mirror vibrate. The light traced patterns that varied depending on the frequencies of the sounds. Lissajous figures can be used to compare frequencies of either sounds or of radio signals. A signal of known frequency can be applied to the horizontal axis of an oscilloscope, and a signal to be measured applied to the vertical axis. The resulting pattern depends only on the ratio of the two frequencies. Lissajous figures often appeared as props in science fiction movies and TV shows from the 50's and 60's. Usually one of the screens on the bridge of the starship Enterprise has a lissajous pattern on it. The original technique of Jules Antoine Lissajous is still used today for special effects in laser light shows.

19. Experiment 13 jules lissajous entered the École Normale Supérieure in France in 1841. Afterwardshe became professor of mathematics at the Lycée SaintLouis. http://faculty.millikin.edu/~jaskill.nsm.faculty.mu/musicexp13.html

Experiment 13 A Study of Lissajous Patterns Purpose To study Lissajous patterns using an oscilloscope. Apparatus Oscilloscope (Elenco S-1325 or similar), two audio generators (Elenco GF8026 or similar), connecting cables. Theory When two different frequencies that are in phase with each other are applied to the horizontal and vertical inputs of an oscilloscope (or channels 1 and 2 of a dual beam oscilloscope), and the ratio of the frequencies is a ratio of integers, stationary patterns are observed on the screen. These patterns are called Lissajous patterns (named after the Frenchman, Jules Antoine Lissajous (1822-1880) who first investigated them in detail in 1860 while doing sound experiments). Similar patterns had previously been found by Nathaniel Bowditch (1773 - 1838), an American mathematician and astronomer who lived in Boston, Mass. Jules Lissajous entered the École Normale Supérieure in France in 1841. Afterwards he became professor of mathematics at the Lycée Saint-Louis. In 1850 he was awarded a doctorate for a thesis on vibrating bars using Chladni's sand pattern method to determine nodal positions. Lissajous went on to study sound waves produced by a tuning fork in contact with water, and in 1855 he found a way of studying acoustic vibrations by reflecting a light beam from a mirror attached to a vibrating object onto a screen. He set up two tuning forks at right angles, with one vibrating at twice the frequency of the other, and found that the curved lines would combine to make a figure of eight pattern. Some typical Lissajous patterns are shown below.

20. Hollis: Differential Equations Hôpital, Guillaume de Lagrange, JosephLouis Laplace, Pierre-Simon Legendre, Adrien-MarieLiouville, Joseph Lipschitz, Rudolf lissajous, jules Lorenz, Edward N http://www.math.armstrong.edu/faculty/hollis/dewbvp/

Differential Equations with Boundary Value Problems by Selwyn Hollis Contents and Preface Marketing Blurb Book Site @ Prentice Hall ... Solutions Manual Technology Mathematica Maple Java M ... ATLAB Sundry Items Problem graphics and extra graphical problems for Section 3.1. Please send bug reports here Professors: Please send me an email Some Biographical References The following are links to information on most of the mathematicians/scientists whose names appear in the book. Unless otherwise noted, each of these is a link to the MacTutor History of Mathematics Archive at the University of St Andrews, Scotland. Abel, Niels Henrik Airy, George Banach, Stefan Bendixson, Ivar ... Edelstein-Keshet, Leah (U. BC) Euler, Leonhard Fourier, Joseph Frobenius, Georg Gauss, Carl Friedrich ... Hertz, Heinrich Rudolf (Google search) Hodgkin, Alan Nature Hooke, Robert Huxley, Andrew (sfn.org) Jacobi, Carl Jordan, Camille Kirchhoff, Gustav Kutta, Martin Wilhelm ... Lorenz, Edward N. (xrefer.com) Lotka, Alfred (Google search) Lyapunov, Aleksandr Maclaurin, Colin Malthus, Thomas (Google search) Menten, Maud

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