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	Spiral - Wikipedia, the free encyclopedia
		In mathematics, a spiral is a curve which turns around some central point or axis, getting progressively closer to or farther from it, depending on which way one follows the curve.
		For example, a conic helix may be defined as a spiral on a conic surface, with the distance to the apex an exponential function of θ.
		A spherical spiral (rhumb line) is the curve on a sphere traced by a ship traveling from one pole to the other while keeping a fixed angle (but not a right angle) with respect to the meridians of longitude, i.e.
	en.wikipedia.org /wiki/Spiral (319 words)

	Marie Alfred Cornu -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		Marie Alfred Cornu (March 6, 1841—April 12, 1902) was a (The Romance language spoken in France and in countries colonized by France) French (A scientist trained in physics) physicist.
		In particular he carried out a classical redetermination of the (The speed at which light travels in a vacuum; the constancy and universality of the speed of light is recognized by defining it to be exactly 299,792,458 meters per second) speed of light by (additional info and facts about A. Fizeau) A.
		The (additional info and facts about Cornu spiral) Cornu spiral, a graphical device for the computation of light intensities in Fresnel's model of near-field (When light passes sharp edges or goes through narrow slits the rays are deflected and produce fringes of light and dark bands) diffraction, is named after him.
	www.absoluteastronomy.com /encyclopedia/m/ma/marie_alfred_cornu.htm (209 words)

	Spirals
		A spiral is a curve in the plane or in the space, which runs around a centre.
		You use the Cornu spiral to describe the energy distribution of Fresnel's diffraction at a single slit in the wave theory.
		Spirals in their diverse art forms were intended as objects of expressing spirituality for contemplation and meditation.
	www.mathematische-basteleien.de /spiral.htm (1708 words)

	6moons audioreviews: Cornu Compact Spiral
		In simply quantitative terms, the Cornu surely fits the platitude often heard in the context of small two-way speakers: "Where's the sub?" In fact, this is one of the reasons why the Cornu CS puts a smile on people's face.
		I'm not saying that the Cornu CS and listener couldn't be positioned such as to minimize this midbass potential to imbalance the sound towards being a bit bass-shy.
		The front panel of the Cornu CS is fairly wide with respect the size of the driver and the speakers are almost always listened to off-axis where diffractions are known to be less detrimental.
	www.6moons.com /audioreviews/cornu/cornu_2.html (5796 words)

	ipedia.com: Marie Alfred Cornu Article (Site not responding. Last check: 2007-10-08)
		Cornu was born at Orléans, and after being educated at the Ecole Polytechnique and the Ecole des Mines, in 1867 he became professor of experimental physics i...
		Marie Alfred Cornu (March 6, 1841—April 12, 1902) was a French physicist.
		Cornu was born at Orléans, and after being educated at the Ecole Polytechnique and the Ecole des Mines, in 1867 he became professor of experimental physics in the former institution, where he remained throughout his life.
	www.ipedia.com /marie_alfred_cornu.html (295 words)

	Euler's spiral (Site not responding. Last check: 2007-10-08)
		The curvature of Euler´s spiral is linearly related to its arc length
		The spiral, the x and y component are both a Fresnel integral of a square root.
		For the same reason the spiral is used in ship design, specifying the curvature distribution of an arc of a plane curve while drawing a ship.
	www.2dcurves.com /spiral/spirale.html (251 words)

	Upto11.net - Wikipedia Article for Spiral (Site not responding. Last check: 2007-10-08)
		A two-dimensional spiral may be described using polar coordinates by saying that the radius r is a continuous monotonic function of andtheta;.
		For simple 3-d spirals, the third variable, h (height), is also a continuous, monotonic function of andtheta;.
		For compound 3-d spirals, such as the spherical spiral described below, h increases with andtheta; on one side of a point, and decreases with andtheta; on the other side.
	www.upto11.net /generic_wiki.php?q=spiral (241 words)

	Diary for raph
		However, I use a Cornu spiral segment where Karow uses a biarc, and I choose the tangents so that the curvature of the final curve is continuous.
		Cornu spiral segments, while resembling biarcs (and having precisely the same control parameters) have smoother variation of curvature.
		That said, the Cornu spiral is remarkably well behaved for being a "special function", and it's probably not anywhere nearly as painful as you might think to work directly in the space of the Cornu parameters.
	www.advogato.org /person/raph/diary.html?start=390 (6110 words)

	Learn more about Marie Cornu in the online encyclopedia. (Site not responding. Last check: 2007-10-08)
		Marie Alfred Cornu, (1841—1902), French physicist, was born at Orleans on March 6, 1841, and after being educated at the Ecole Polytechnique and the Ecole des Mines, became in 1867 professor of experimental physics in the former institution, where he remained throughout his life.
		Although he made various excursions into other branches of physical science, undertaking, for example, with J. Bailie about 1870 a repetition of Cavendish's experiment for determining the gravitational constant G, his original work was mainly concerned with optics and spectroscopy.
		The Cornu spiral, a graphical device for the computation of light intensities in Fresnel's model of near-field diffraction, is named after him.
	www.onlineencyclopedia.org /m/ma/marie_cornu.html (329 words)

	6moons audioreviews: Cornu Compact Spiral
		Speakers with a spiral horn of various types are not unknown to DIY nuts but to the best of my knowledge, there are very few -- if any -- commercial variants based on the spiral horn principle apart from Cornu CS.
		Cornu's website points at the driver and its very efficient motor (a large ferrite magnet with 5.2 Tesla in the gap) to explain why hornloading is required for proper bass reproduction.
		As shown, the Cornu spiral is dissimilar from both the logarithmic and linear spiral.
	www.6moons.com /audioreviews/cornu/cornu.html (2821 words)

	polynomial spiral (Site not responding. Last check: 2007-10-08)
		The curve is a generalization of the Cornu spiral, for which the curvature is linearly related to the arc length s.
		The polynomial form in the arc length s leads to the name of polynomial spiral.
		Another name for the curve is the generalized Cornu spiral.
	www.2dcurves.com /spiral/spiralps.html (46 words)

	Curves
		This spiral is also known as the clothoid, from Clotho, the one of the three fates that spins (th pronounced as t).
		The Cornu spiral is a vibration curve in optics, showing the contributions to the amplitude from elements of a wavefront.
		Therefore, a transition spiral is introduced between the tangent and the circular curve, perhaps 250 to 500 feet in length.
	www.du.edu /~etuttle/math/curves.htm (5870 words)

	The Spiral Family of Curves - National Curve Bank (Site not responding. Last check: 2007-10-08)
		Def: The spiral is the locus of a point P moving uniformly along a ray that, in turn, is uniformly rotating in a plane about its origin.
		The spiral on the tomb of Jakob (James) Bernoulli.
		In nature, the spiraled chambered nautilus is associated with the Golden Ratio, which again is associated with the Fibonacci Sequence.
	curvebank.calstatela.edu /spiral/spiral.htm (440 words)

	Euler Spirals
		The Euler Spiral was considered by Euler in connection to his investigation of a freely coiled up elastic spring held taut horizontally by a weight at its extremity (Euler, 1744).
		Euler spiral segments starting at the origin and tangent to the x-axis of a given length is
		The explicit recovery of a completion curve is useful in a variety of visual tasks, such as the task of disambiguating edge maps in perceptual grouping, the partitioning of visual form for part-based object representation and recognition, and for filling-in tasks in the reconstruction of occluded areas in figure-ground segregation.
	www.lems.brown.edu /vision/researchAreas/EulerSpiral (519 words)

	Fresneloidery
		This shape is called a Fresnel spiral; it is named after Augustin Fresnel, who was one of the first people to perform experiments showing how wavelike light is. The Fresnel Integrals are used to calculate Fresnel Diffraction, and this spiral is a visualisation of these equations.
		This angle shifts along the spiral as each new one is drawn, so that a spiral of spirals starts to be made...
		And then, as you might imagine, the spiral of spirals does the same thing; we can end up with spirals of spirals of spirals, and spirals of spirals of spirals of spirals, and...
	fergusmurray.members.beeb.net /Fresnel.htm (620 words)

	Spiral articles and news from Start Learning Now (Site not responding. Last check: 2007-10-08)
		A two-dimensional spiral may be described using polar coordinates by saying that the radius r is a continuous functioncontinuous monotonic function of θ.
		The helix and vortex can be viewed as a kind of dimensionthree-dimensional spiral.
		A spherical spiral (rhumb line) is the curve on a sphere traced by a ship traveling from one pole to the other while keeping a fixed angle (but not a angle#Types of anglesright angle) with respect to the meridians of longitude, i.e.
	www.startlearningnow.com /spiral.htm (306 words)

	The Curlicue Fractal
		The curlicue fractal is an exceedingly easy-to-make but richly complex pattern composed, at the fundamental level, of Cornu spirals - although that isn't always obvious.
		The Cornu spiral, also known as the clothoid or Fresnel spiral, is a sort of S shape that spirals in on itself at both ends, something like this:
		However, where a clothoid spirals ever-closer to its focus without ever reaching it, our algorithm sooner or later reaches a point where the fixed size of its steps becomes important, and its path diverges from that of the true clothoid because it cannot follow the tight curve.
	fergusmurray.members.beeb.net /curlicue.htm (1197 words)

	Cornu Spiral (Site not responding. Last check: 2007-10-08)
		A Cornu spiral describes diffraction from the edge of a half-plane.
		Gray (1993) defines a generalization of the Cornu spiral given by parametric equations
		These spirals are a further generalization of the Cornu spiral.
	mathserver.sdu.edu.cn /mathency/math/c/c696.htm (77 words)

	Euler's Spiral American Math Monthly Volume 25 (1918) (Site not responding. Last check: 2007-10-08)
		The curve therefore will be in the nature of a spiral so that when the spiral is completed it is rolled up, as it were, in a certain point which may be called the center.
		In 1874 Cornu plotted Euler's spiral accurately 20 by means of Peter's table.
		The Euler integrals, and spiral in connection with the elastic spring, of these notes were also discussed by Laplace in "Sur la reduction des fonctions en tables," Journal de l'Ecole Polytechnique, tome 8, cahier 15, pp.
	xahlee.org /SpecialPlaneCurves_dir/Clothoid_dir/_p/Euler_Spiral/EulerSpiral.html (2555 words)

	Education/Interactive experiments/Optics resources - PhysicsWeb
		The relations between the Fresnel diffraction patterns and the Cornu Spiral construction are demonstrated.
		The Cornu Spiral is the representation of the functions Cu and and Su in the complex plane.
		The Cornu Spiral is used as a tool for the quantitative determination of a diffraction pattern.
	physicsweb.org /resources/Education/Interactive_experiments/Optics (1451 words)

	8.3 Spirals (Site not responding. Last check: 2007-10-08)
		The logarithmic spiral or Bernoulli spiral (Figure 1, left) is self-similar: by rotation the curve can be made to match any scaled copy of itself.
		A curve parametrized by arclength and such that the radius curvature is proportional to the parameter at each point is a Bernoulli spiral.
		In the Archimedean spiral or linear spiral (Figure 1, middle), it is the spacing between intersections along a ray from the origin that is constant.
	www.geom.uiuc.edu /docs/reference/CRC-formulas/node35.html (250 words)

	diyAudio Forums - Cornu spiral horns
		I haven't heard the Cornu spiral horns, but have been following the story about them and listening impressions on a german DIY-forum (Audiotreff).
		So far only versions for smaller drivers are existing, but Daniel (the man behind Cornu) has been trying bigger ones also (as far as I know).
		Supposedly they are sounding very good with a tendency to the "warm" side, peak levels are very limited though but OK with regard to the size of the driver.
	www.diyaudio.com /forums/showthread.php?postid=436134 (272 words)

	Xah: Special Plane Curves: Naming and Classification of Curves
		Euler's spiral (aka Clothoid), Euler's curve (x^y==y^x), spiral of Cornu, Durer's conchoid, lissajous (aka Bowditch curve).
		Note that in general, the name attached to a curve or a math theorem is not necessary the person who invented or worked on it.
		Sinusoidal “spiral” is defined to be r^n==a^nCos[nθ], n rational.
	www.xahlee.org /SpecialPlaneCurves_dir/Intro_dir/familyIndex.html (1043 words)

	Advogato diary for raph
		I suppose the Cornu could be seen as a French-curve style extension of circles.
		It also helps that the Cornu spiral representation is so concise - the primitive is fully determined by the endpoints and tangents at the endpoints (six degrees of freedom, as opposed to four for straight lines and eight for cubic Beziers).
		Near the end of that presentation, he raises the possibility of using a >Cornu Spiral, which is mathematically constructed so that curvature is continuous at endpoints, and linearly interpolated in between.
	www.dasbistro.com /~sam/news/cache/advogato.org.person.raph.rss.xml/rawfeed (8040 words)

	[No title]
		From both the treatment plants sine and cosine, the outlet spiral guides the water to the softener [which metaphorizes the = (equal to) sign in the equation] The spiral is the modification and it has a unique use in the entire usability factor of the metaphor.
		The water would enter from one curve of the spiral at low speed and move towards the core of the spiral whereby the speed would increase, as there are two opposite directions to the flow of water from the core.
		Using this concept, I decided to map the integral sign to the spiral as it not only integrates the water to the actual use (visually) but also kind of explores the range of 0 to t (again the same variable) and can be designed for the equation requirement.
	www.cise.ufl.edu /research/acomputing/spring03/Pooja/Proj_2d_pooja.doc (1421 words)

	Diary for raph
		By these criteria, segments of the Cornu spiral are an excellent primitive.
		It also helps that the Cornu spiral representation is so concise - the primitive is fully determined by the endpoints and tangents at the endpoints (six degrees of freedom, as opposed to four for straight lines and eight for cubic Beziers).
		Near the end of that presentation, he raises the possibility of using a Cornu Spiral, which is mathematically constructed so that curvature is continuous at endpoints, and linearly interpolated in between.
	www.advogato.org /person/raph/diary.html?start=385 (7573 words)

	VHF/UHF/Microwave Radio Propagation: A Primer for Digital Experimenters
		Therefore, the received components form only the upper half of the spiral, and the resultant vector is exactly half the length of the free space case, corresponding to a 6 dB reduction in amplitude.
		Further progression up B-B' results in further motion around the spiral, and the amplitude of the resultant oscillates back and forth, with the amplitude of the oscillation steadily decreasing as the resultant converges on the free space value, given by the complete Cornu spiral (vector X-Y).
		This means that we have passed the bottom of the spiral and are on the way back up, and the resultant vector is near the free space magnitude (a line between X and Y in Fig.
	www.tapr.org /ve3jf.dcc97.html (10080 words)

	The world's top fresnel integral websites
		The Cornu spiral is the curve generated by a parametric plot of S(x) against C(x).
		The Cornu spiral was created by Alfred Cornu as a nomogram for diffraction computations in science and engineering.
		(Note that the spiral should actually converge on the centre of the holes in the image as x tends to positive or negative infinity) If πt²/2 was used, instead of t², then the image would be scaled by the factor mentioned above.
	dirs.org /wiki-article-tab.cfm/fresnel_integral (424 words)

	AllRefer.com - Marie Alfred Cornu (Physics, Biography) - Encyclopedia
		AllRefer.com - Marie Alfred Cornu (Physics, Biography) - Encyclopedia
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		More articles from AllRefer Reference on Marie Alfred Cornu
	reference.allrefer.com /encyclopedia/C/Cornu-Ma.html (156 words)

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