
	Where results make sense

Topic: Lemniscate

Related Topics

List of curves

Superellipse

Catenary

Sallie Baliunas

Doctor of the Church

Sagrada Familia

Tetracontakaihexagon

In the News (Thu 26 Nov 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Lemniscate - Wikipedia, the free encyclopedia
		The lemniscate was first described in 1694 by Jakob Bernoulli as a modification of an ellipse, which is the locus of points for which the sum of the distances to each of two fixed focal points is a constant.
		The lemniscate can be obtained as the inverse transform of a hyperbola, with the inversion circle centered at the center of the hyperbola (bisector of its two foci).
		The determination of the arc length of arcs of the lemniscate leads to elliptic integrals, as was discovered in the eighteenth century.
	en.wikipedia.org /wiki/Lemniscate (271 words)

	LEMNISCATE - LoveToKnow Article on LEMNISCATE (Site not responding. Last check: 2007-10-08)
		The lemniscate of Bernoulli may be defined as the locus of a point which moves so that the product of its distances from two fixed points is constant and is equal to the square of half the distance between these points.
		The name lemniscate is sometimes given to any crunodal quartic curve having only one real finite branch which is symmetric about the axis.
		In this case the centre is a crunodc and the curve resembles fig.
	www.1911encyclopedia.org /L/LE/LEMNISCATE.htm (1633 words)

	Cassinian oval
		for the circle: 2 L is the length of the lemniscate's arc.
		The lemniscate is the cissoid of two equal circles, where the distance from the center to the center of the circle is
		Lemniscate is also the name of the longest composition of Western music, made by Simeon ten Holt (30 hours).
	www.2dcurves.com /quartic/quarticca.html (658 words)

	Adam Coffman --- Lemniscates
		It is also called a "hyperbolic lemniscate of Booth," and it is the image of a hyperbola under inversion with respect to its center.
		The elliptic lemniscate can also be described as a projection of the space curve formed by the intersection of a circular paraboloid and an elliptic cone, with the same vertex and axis.
		The hyperbolic lemniscate is equal to a projection of the space curve formed by the intersection of a circular paraboloid and an elliptic cone, with the same vertex and perpendicular axes.
	www.ipfw.edu /math/Coffman/pov/spiric.html (336 words)

	Lemniscate (Site not responding. Last check: 2007-10-08)
		The general properties of the lemniscate were discovered by Giovanni Fagnano in 1750.
		Inverting the lemniscate in a circle centred at the origin and touching the lemniscate where it crosses the x-axis produces a rectangular hyperbola.
		The bipolar equation of the lemniscate is rr' = a
	www-groups.dcs.st-and.ac.uk /~history/Curves/Lemniscate.html (156 words)

	The Lemniscate and Spacetime (Site not responding. Last check: 2007-10-08)
		Of course if we force y to be real but allow x to be imaginary, we rotate the figure 90 degrees, and if both x and y are imaginary we have just the rotated version of the interior region of the green circle.
		It's also worth noting that the lemniscate is the inverse (in the sense of inversive geometry) of the hyperbola relative to the circle of radius k.
		Since the polar equation for the lemniscate is s^2 = k^2 cos(2q) we have sR = k^2.
	www.mathpages.com /home/kmath170.htm (397 words)

	Astronomy Course: Lecture XII
		True as it is then that in the vertebra the one half of the Lemniscate is very much condensed and pressed together, whilst in the pair of ribs the other half is much extended and drawn apart (Figure 2), we must not be put off my this.
		We simply have to imagine that where the ribs are (the drawing indicated those that are joined in front via the sternum) the space is widened, matter being as it were extenuated, while, to make up for this, the matter is compressed and the space lessoned in the vertebra.
		This loop of the Lemniscate is represented by the path's fading away, not being fully maintained; it only indicates the direction but cannot hold it.
	www.awakenings.com /astronomy/l12.html (4087 words)

	Symphonic Eurythmy Tour 2005 - Making Music Visible featuring Antonin Dvorak's New World Symphony
		Lemniscate Arts and Eurythmy Spring Valley are honored to bring the New World Symphonic Eurythmy Tour to 16 cities across the United States and Canada in August, September, and October 2005.
		Lemniscate Arts Inc. is a registered not-for-profit corporation devoted to furthering the human spirit by supporting artistic endeavors.
		Lemniscate Arts seeks to foster the awareness of the Word as an organ of the creative human spirit.
	www.newworldtour.org /levene.html (729 words)

	Lemniscate Product Development Services
		Lemniscate Inc. was founded by Marke Levene in 1995 as an outgrowth of the British wood manufacturing company that Marke had established in 1981.
		Lemniscate is currently working on a wide variety of projects with a diverse group of clients:
		Lemniscate is the name of the symbol representing infinity.
	www.lemniscateinc.com /services.html (632 words)

	Astronomy Course: Lecture XVII
		This is essential: You must imagine the plane in which I am drawing the Lemniscate (Figure 1) to be rotating about the Lemniscate axis, ie.
		Such is the drawing of the Lemniscate which you must have in mind with regard to all that I have been saying, - so for example when you are tracing the bony system or the nervous system in man. Even the blood-circulation can be traced in this way.
		The figure eight - the Lemniscate - is therefore legitimate, but as I said before, you are really dealing with geometrical figures of rotation.
	www.awakenings.com /astronomy/l17.html (4543 words)

	Byzant Symbols - the Lemniscate
		The symbol of an 'eight on its side' is sometimes known as the lemniscate and is a symbol for infinity.
		The term lemniscate refers to the shape itself, and the Swiss mathematician Jacob Bernoulli (1654-1705) first called the shape a lemniscus (Latin for ribbon) in an article in Acta Eruditorum in 1694.
		The use of a figure eight to represent infinity is an interesting choice, as eight is linked to the pre-creational infinity through the Ogdoad and to a cyclical sense of infinity through the eight pagan festivals of the year and the octagram.
	www.byzant.com /symbols/lemniscate.asp (176 words)

	lemniscate - a Whatis.com definition (Site not responding. Last check: 2007-10-08)
		A lemniscate is a plane curve with a characteristic shape, consisting of two loops that meet at a central point as shown below.
		The curve is also known as the lemniscate of Bernoulli.
		The lemniscate, reduced in size to that of typographical characters, is commonly used as the symbol for infinity, or for a value that increases without limit.
	whatis.techtarget.com /definition/0,,sid9_gci810317,00.html (175 words)

	CoLab Document Server - The Arc Length of the Lemniscate { \| p(z) \| = 1 } (Site not responding. Last check: 2007-10-08)
		The Arc Length of the Lemniscate {
		Borwein, Peter (1993) The Arc Length of the Lemniscate {
		This gives the correct rate of growth in a long standing open problem of Erd\"os, Herzog and Piranian and improves the previous bound of $74n^2$ due to Pommerenke.
	eprints.cecm.sfu.ca /archive/00000066 (92 words)

	Lemniscates Folder (Site not responding. Last check: 2007-10-08)
		The geometric definition of the Lemniscate of Bernoulli is the locus of points with the product of the distances from two fixed points (foci) set at a particular constant.
		Compare the Lemniscate of Bernoulli and the Lemniscate of Gerone.
		Is there a geometric construction, as a locus, for the Lemniscate of Gerone?
	jwilson.coe.uga.edu /Texts.Folder/Lem/Lemniscates.html (132 words)

	Lemniscate of Bernoulli (Site not responding. Last check: 2007-10-08)
		There are several methods for drawing a lemniscate.
		The center of the lemniscate O will be
		The pattern of the lemniscate emerges in the first quadrant.
	curvebank.calstatela.edu /lemniscate/lemniscate.htm (529 words)

	Mathcad Library: Constants
		The lemniscate constant L plays a role for the
		lemniscate analogous to what plays for the circle.
		Open this file with Mathcad 11 to work with the calculations.
	www.mathcad.com /library/Constants/gauss.htm (46 words)

	Lemniscates, Mu-Ency at MROB
		In classical mathematics a 'lemniscate' is a curve defined by a parametric relation.
		The boundary of the Mandelbrot Set is the limit of the Nth lemniscate, where each lemniscate L
		[1] The lemniscates were generated and factored in maxima by the following commands:
	www.mrob.com /pub/muency/lemniscates.html (282 words)

	Lemniscate to Langlands (Site not responding. Last check: 2007-10-08)
		After Gauss and before Langlands came, of course, Abel.
		For an excellent account of how Abel followed up Gauss's hint on the lemniscate, see Henrik Kragh S
		"Abel's Theorem on the Lemniscate," by Michael Rosen,
	log24.com /log04/0117.htm (68 words)

	Tarot - Free Encyclopedia of Thelema
		As with its Marseilles-deck ancestor, the card shows a woman holding the jaws of a lion, but this picture is far more elaborate.
		The strangely-shaped hat of the Marseilles card has traditionally been interpreted as a symbolic lemniscate: the sideways-figure-eight representation of infinity.
		In the newer card, this symbol appears explicitly.
	www.egnu.org /thelema/index.php/Tarot (3751 words)

Try your search on: Qwika (all wikis)