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Topic: Jules Antoine Lissajous

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Lissajous curve

Harmonograph

List of mathematicians

	Jules Lissajous
		In 1874 Lissajous became rector of the Academy at Chambéry, then in 1875 he was appointed rector of the Academy at Besançon.
		Lissajous was interested in waves and developed an optical method for studying vibrations.
		Lissajous was awarded the Lacaze Prize in 1873 for his work on the optical observation of vibration.
	fys.kuleuven.be /pradem/fysici/Lissajous.htm (226 words)

	Lissajous curve - Biocrawler (Site not responding. Last check: 2007-10-14)
		This family of curves was investigated by Nathaniel Bowditch in 1815, and later in more detail by Jules Antoine Lissajous.
		The visual form of these curves is often suggestive of a three-dimensional knot, and indeed the many kinds of knots, including those known as Lissajous knots, project to the plane as Lissajous figures.
		Lissajous figures are sometimes used in graphic design as logos.
	www.biocrawler.com /encyclopedia/Lissajous (318 words)

	Lissajous, Jules Antoine (Site not responding. Last check: 2007-10-14)
		Lissajous was born in Versailles and educated at the Ecole Normale Supérieure.
		Lissajous first reflected a light beam from a mirror attached to a vibrating object such as a tuning fork to another mirror that rotated.
		Lissajous figures can now be demonstrated on the screen of an oscilloscope by applying alternating currents of different frequencies to the deflection plates.
	www.cartage.org.lb /en/themes/Biographies/MainBiographies/L/Lissajous/1.html (194 words)

	Lissajous Lab (Site not responding. Last check: 2007-10-14)
		Lissajous' setup was similar to the apparatus which is used today to project laser light shows.
		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.
		Lissajous figures often appeared as props in science fiction movies made during the 1950's.
	www.math.com /students/wonders/lissajous/lissajous.html (347 words)

	An Introduction to Lissajous Patterns
		A Lissajous pattern is a graph of one frequency plotted on the y axis combined with a second frequency plotted on the x axis.
		The Lissajous pattern changes to a line when the X and Y frequencies are in phase by either 180 or 0 degrees.
		It is possible to create lissajous patterns by using one wave form function generator, an oscilloscope, a tuning fork and a microphone.
	www.egr.msu.edu /classes/ece482/Teams/99spr/design2/web/resources/lissajous/lissajous.htm (792 words)

	Xah: Special Plane Curves: Lissajous (Site not responding. Last check: 2007-10-14)
		Varieties of Lissajous {aSin[bt2π+c],Sin[t2π]}, where a is the inverse of golder ratio 1/ϕ≈0.618, and b, c are indicated in the corner.
		Lissajous is a family of curves, given by
		Studied by Nathaniel Bowditch in 1815 and Jules Antoine Lissajous (1822-1880).
	xahlee.org /SpecialPlaneCurves_dir/Lissajous_dir/lissajous.html (102 words)

	lissajous
		Enables visualization and interaction with Lissajous figures, a scattered composition of two waves, they represent a link between vibration and matter as composed grids are those found in crystalline substances.
		Jules Antoine Lissajous (1822-1880) was a French physicist who was interested in waves, and around 1855 developed a method for displaying them optically by reflecting a light beam from a mirror attached to a vibrating object such as a tuning fork.
		Lissajous figures are also used in Cymatic research.
	www.voicesync.org /lissajous.htm (121 words)

	Lissajous
		Lissajous figures were actually discovered by the American astronomer and mathematician Nathaniel Bowditch in 1815 when he was studying the movement of a compound pendulum.
		Bowditch (1773-1838) was a self-taught scientist, a captain of a merchant ship, president of an insurance company, actuary for the Massachusetts Hospital Insurance Company of Boston, and president of the American Academy of Arts and Sciences.
		Jules Antoine Lissajous (1822-1880) was a French physicist who extensively studied the curves that bear his name independently of Bowditch during his research on optics [2].
	boj.pntic.mec.es /~jcastine/Lissajous.htm (370 words)

	Lissajous (Site not responding. Last check: 2007-10-14)
		Jules Lissajous entered the École Normale Supérieure in 1841.
		Duhamel had tried to demonstrate these vibrations with a mechanical linkage but Lissajous wanted to avoid the problems caused by the linkage.
		Lissajous studied beats seen when his tuning forks had slightly different frequencies, in this case a rotating
	www.educ.fc.ul.pt /icm/icm2003/icm14/Lissajous.htm (214 words)

	[No title] (Site not responding. Last check: 2007-10-14)
		Lissajous figures are patterns generated by the junction of a pair of sinusoidal waves with axes that are perpendicular to one another.
		Presented in the tutorial is a three-dimensional simulation of a cathode ray oscilloscope producing Lissajous figures as it compares sinusoidal voltages.
		Included in the simplified illustration of the oscilloscope are a cathode ray gun, which produces the Lissajous figures on the oscilloscope screen, and horizontal and vertical deflection plates to which the voltages are applied.
	java.magnet.fsu.edu /electromag1/lissajous (399 words)

	.: LucidQuest :. A Brief History of Cymatics
		Jules Antoine Lissajous (1822-1880) - Jules Lissajous, a French physicist and mathematician, investigated the relationships of sound frequencies, waves, and vibrations.
		Lissajous began his experiments with sound waves and vibrations by using tuning forks in water and noting the ripple patterns from different applied frequencies.
		Before the onset of digital technology, Lissajous Figures were used to represent the frequencies of sound waves in radio signals.
	lucidquest.com /resources/learn/cymatics_2.htm (295 words)

	Lissajous curve - Wikipedia, the free encyclopedia
		Prior to modern computer graphics, Lissajous curves were typically generated using an oscilloscope (as illustrated).
		Two, phase-shifted, sinusoid inputs are applied to the oscilloscope in X-Y mode and the phase relationship between the signals are presented as a Lissajous figure.
		Even though they look similar, Spirographs are different as they are generally enclosed by a circular boundary where a Lissajous curve is bounded by a square (±1, ±1).
	en.wikipedia.org /wiki/Lissajous_curve (330 words)

	Historical sketch: Jules Antoine Lissajous
		Jules Antoine Lissajous was a French mathematician and physicist.
		He obtained figures, now referred to as Lissajous curves, by successively reflecting light from mirrors on two tuning forks vibrating at right angles.
		Lissajous curves or Lissajous figures are sometimes called Bowditch curves after Nathaniel Bowditch who considered them in 1815.
	www.hardycalculus.com /calcindex/IE_lissajous.htm (256 words)

	Lissajous Curve -- from Wolfram MathWorld
		Lissajous curves are the family of curves described by the
		They were studied in more detail (independently) by Jules-Antoine Lissajous in 1857 (MacTutor Archive).
		Lissajous curves are a special case of the harmonograph with damping constants
	mathworld.wolfram.com /LissajousCurve.html (190 words)

	Lissajous or Bowditch Curves - National Curve Bank (Site not responding. Last check: 2007-10-14)
		Moreover, he was the first to investigate a family of curves now usually named for the French physicist, Jules-Antoine Lissajous.
		Lissajous independently published his work much later in 1857.
		Lissajous (1822 - 1880) is thought to have encountered these curves when he collected data for his optical method of studying vibrations.
	curvebank.calstatela.edu /lissajous/lissajous.htm (397 words)

	MIT Lincoln Laboratory - MIT Lincoln Laboratory Logo (Site not responding. Last check: 2007-10-14)
		The Lissajous figures, named for the French mathematician Jules-Antoine Lissajous, are also known as Bowditch curves after their discoverer, Nathaniel Bowditch, the mathematician from Salem, Massachusetts.
		Overhage drew a Lissajous figure based on the superposition of two simple harmonic vibrations and commissioned retired Brigader General Robert Steinle and the firm Advertising Designers of Los Angeles to transform the Lissajous figure into an artistic image.
		The figure is traced along the horizontal axis x and the vertical axis y as the variable t progresses from t = 0 to T. The Lissajous figure, familiar to most physical scientists and engineers, connotes harmony, order and stability.
	www.ll.mit.edu /about/lissajous.html (240 words)

	Lissajous Figures
		I don't know much about Lissajous figures; probably there's some place else on the web that you could learn a whole lot about them from.
		Basically they're sort of failed circles, or rather, a circle is the simplest Lissajous figure.
		Lissajous figures can be thought of as a simple physical system with springs.
	www.physics.emory.edu /~weeks/ideas/lissajou.html (460 words)

	The ABC's of Lissajous figures (Site not responding. Last check: 2007-10-14)
		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.
	abc.net.au /science/holo/liss.htm (364 words)

	Jules Antoine Lissajous (Site not responding. Last check: 2007-10-14)
		He later earned the Lacaze Prize in 1873 for his pioneering of a new method for optical observation of vibration.
		Lissajous did extensive study into specific systems of parametric equations that demonstrate complex harmonic motion.
		Today, the graphs of such systems are called Lissajous cuves, which can be traced by a harmonograph, a device Lissajous invented.
	www.danielcromer.com /resources/mathematicians/Lissajous.htm (100 words)

	Main Brief History (Site not responding. Last check: 2007-10-14)
		Jules Lissajous, a French physicist and mathematician, investigated the relationships of sound frequencies, waves, and vibrations.
		These figures were created by reflecting a light beam from mirrors on two tuning forks vibrating at right angles.
		Cymatics, the study of wave phenomena, is a science pioneered by Swiss medical doctor and natural scientist Hans Jenny (1904-1972).
	www.cymatics.org.uk /main-brief-history.html (695 words)

	Where do I find Jules Antoine Lissajous info? (Site not responding. Last check: 2007-10-14)
		Free is Jules Antoine Lissajous a good persuader.
		The devices appeared in the 19th century and are attributed to Jules Antoine Lissajous.
		Biography at St. Andrew's University â¹The stub template is included per a redirect that has oldfangled promised for deletion.
	en.gentlewoman.info /kittery-maine-outlet/Jules_Antoine_Lissajous (258 words)

	Lissajous.htm
		is called a Lissajous curve, named after Jules-Antoine Lissajous, a 19th century mathematician who studied them.
		Type I versus Type II Note that Lissajous curves come in two "Types".
		Type I curves are "smooth", while Type II curves have sharp "ends".
	www.math.neu.edu /~bridger/u170/lissajous/lissajous.htm (648 words)

	Etymologie, Étymologie, Etymology - AU Australien, Australie, Australia - TV, Télévision, Television (Site not responding. Last check: 2007-10-14)
		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.
		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.
	www.etymologie.info /~e/a_/au-tv____.html (395 words)

	Lissajous curve
		Each Lissajous curve can be described with an algebraic equation.
		besace: its parameter a is equal to the tangent of the Lissajous curve's parameter b.
		There is a relation with the Tchebyscheff polynomial: the Lissajous curve (a, b) corresponds with Tchebyscheff function T
	www.2dcurves.com /higher/higherli.html (330 words)

	Lissajous Figures
		A Lissajous figure is produced by taking two sine waves and displaying them at right angles to each other.
		There are two versions of the Lissajous Patterns: one for fast machines and one for slow machines.
		Before there were frequency counters and phase locked loops, Lissajous Figures were used to compare two frequencies (such as a reference signal to an unknown signal) that were within a few integer multiples apart.
	www.jmargolin.com /mtest/LJfigs.htm (1692 words)

	Vibration microscope
		The vibration microscope is an electromagnetically-driven adaptation by Hermann von Helmholtz (1821-1894) of the earlier optical comparator by Jules Antoine Lissajous (1822-1880).
		The device allows one to determine the frequency of a tuning fork or other vibrating object with respect to a fork of known frequency, by way of Lissajous figure analysis.
		Simple Lissajous figures for various frequency ratios, in different stages of their cycles.
	www.phys.cwru.edu /ccpi/Vibration_microscope.html (221 words)

	Lissajous Lab - games, java, script,
		Lissajous (pronounced LEE-suh-zhoo) figures were discovered by the French physicist Jules Antoine Lissajous.
		Lissajous' set-up was similar to the apparatus which is used today to project laser light shows.
		One of the best examples can be found in the opening sequence of The Outer Limits TV series.
	www.p-pp.tv /games/ilssajous (381 words)

	Hexagons and Lissajous Art. Curves and parametric equations
		Lissajous curves are the family of curves described by the parametric equations:
		The path traced is known as Lissajous figures.
		Jules Antoine Lissajous (1822 - 1880) was a French mathematician, after whom Lissajous figures are named.
	agutie.homestead.com /files/geometric_art/lissajous_art_hexagon_1.htm (111 words)

	Mathematical Oddities, Curiosities and Curves (Site not responding. Last check: 2007-10-14)
		Lissajous curves, named after Jules-Antoine Lissajous who studied them in 1857, are also known as Bowditch Curves, who originally studied them as early as 1815.
		Lissajous curves are generally formed by parametric equations, of the general form; x(t) = a sin(nt+c)
		Here is a java applet that draws lissajous curves.
	www.loganbales.com /sweb.uky.edu/math.html (165 words)

	Debian -- qliss3d
		Qliss3d is a tool that generates various Lissajous figures.
		Also changing the frequency and replay of the sinus sounds by the same frequency rate are implemented.
		In mathematics, a Lissajous curve (Lissajous figure or Bowditch curve) is the graph of the system of parametric equations which describes complex harmonic motion.
	packages.debian.org /unstable/graphics/qliss3d (182 words)

	Lissajous
		They were studied in more detail (independently) by Jules-Antoine Lissajous in 1857.
		Lissajous curves have applications in physics, astronomy and other sciences.
		He learnt Latin to study Newton's Principiaand later other languages to study mathematics in these languages.
	www-gap.dcs.st-and.ac.uk /~history/Curves/Lissajous.html (110 words)

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