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Topic: Super ellipse

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	super ellipse
		It was Gabriel (1795-1870) who was the first to study this class of curves (in 1818), leading to the name of Lamé curve.
		The curve can be seen as a generalisation of an ellipse, a super ellipse (or superellipse).
		Sometimes the name of super ellipse is only used when the curve is equal in both x- and y-directions.
	www.2dcurves.com /power/powerse.html (260 words)

	Ellipse - Wikipedia, the free encyclopedia
		In mathematics, an ellipse (from the Greek for absence) is the locus of points on a plane where the sum of the distances from any point on the curve to two fixed points is constant.
		An ellipse is a type of conic section: if a conical surface is cut with a plane which does not intersect the cone's base, the intersection of the cone and plane is an ellipse.
		The shape of an ellipse is usually expressed by a number called the eccentricity of the ellipse, conventionally denoted e (not to be confused with the mathematical constant e).
	en.wikipedia.org /wiki/Ellipse (1413 words)

	[No title] (Site not responding. Last check: 2007-10-11)
		In mathematics, an ellipse is a figure resembling a circle which has been stretched in one direction.
		The semi-latus rectum of an ellipse, usually denoted l (a lowercase L), is the distance from a focus of the ellipse to the ellipse itself, measured along a line perpendicular to the major axis.
		An ellipse can also be thought of as a projection of a circle: a circle on a plane at angle φ to the horizontal projected vertically onto a horizontal plane gives an ellipse of eccentricity sin φ, provided φ is not 90°.
	www.wikiwhat.com /encyclopedia/e/el/ellipse.html (554 words)

	Ellipse - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-11)
		In mathematics, an ellipse (from the Greek for absence) is a curve where the sum of the distances from any point on the curve to two fixed points is constant.
		An ellipse is a type of conic section: if a cone is cut with a plane which does not intersect the cone's base, the intersection of the cone and plane is an ellipse.
		The area enclosed by an ellipse is $\pi ab\,\!, where \pi is Archimedes' constant.$
	www.gogog.com /project/wikipedia/index.php/Ellipse (1040 words)

	Super ellipse: Definition and Links by Encyclopedian.com
		...Super ellipse Super ellipse A super ellipse is a geometrical figure which in a...a cross.
		The super ellipse can be described parametrically as: x (θ) = ± a cos...2/ n (θ) y (θ) = ± b sin 2/ n (θ) (0 ≤ θ < π/2).
		A super ellipse is a geometrical figure which in a cartesian coordinate system can be described as the set of all points (x, y) with
	www.encyclopedian.com /su/Super-ellipse.html (585 words)

	Superellipse - Wikipedia, the free encyclopedia
		The case n = 2 yields an ordinary ellipse; increasing n beyond 2 yields the hyperellipses, which increasingly resemble rectangles; decreasing n below 2 yields hypoellipses which develop pointy corners in the x and y directions and increasingly resemble crosses.
		Though he is often credited with its invention, the Danish poet and scientist Piet Hein (1905-1996) did not discover the super-ellipse.
		The general Cartesian notation of the form comes from the French mathematician Gabriel Lamé (1795–1870) who generalized the equation for the ellipse.
	en.wikipedia.org /wiki/Super_ellipse (683 words)

	Kids.Net.Au - Encyclopedia > Semimajor axis
		In mathematics, an ellipse is a figure resembling a circle that has been stretched in one direction.
		It is an example of a conic section and can be defined as the locus of all points in a plane that have the same sum of distances from two given fixed points (called foci, plural of focus).
		The shape of an ellipse is usually expressed by a number called the eccentricity of the ellipse, conventionally denoted e, which is related to a and b by the formula
	www.kids.net.au /encyclopedia-wiki/se/Semimajor_axis (571 words)

	Ellipse
		An ellipse centered at the origin of an x-y coordinate system with its major axis along the x-axis is defined by the equation of the elliptical object.
		The area enclosed by an ellipse is πab, where 'a' and 'b' are the semimajor and semiminor axes and π is Archimedes' constant.
		The circumference of an ellipse is [4 a E(e)], where the function E is the complete elliptic integral of the second kind.
	encycl.opentopia.com /term/Ellipse (1485 words)

	NationMaster - Encyclopedia: Ellipse (Site not responding. Last check: 2007-10-11)
		Algebraically, an ellipse is a curve in the Cartesian plane defined by an equation of the form Analytic geometry, also called coordinate geometry and earlier referred to as Cartesian geometry, is the study of geometry using the principles of algebra.
		Kepler, in 1602, said he believed that the orbit of Mars was oval, then he later discovered that it was an ellipse with the sun at one focus.
		The pedal curve of an ellipse, with its focus as pedal point, is a circle.
	www.nationmaster.com /encyclopedia/Ellipse (1117 words)

	Dianne Peters Clinic (Site not responding. Last check: 2007-10-11)
		The visible light produced by the Ellipse Super Light systems is carefully controlled to produce the correct pulse length and right amount of energy to reduce the acne without damaging the surrounding tissue.
		The Ellipse Super Light flash-lamp emits light that is carefully filtered before it reaches the skin; this ensures that only light of the correct “type” (technically described as “wavelengths”) is allowed to reach the skin – the non-useful wavelengths are removed by filters.
		As the glass prism of the Ellipse Super Light hand piece that is applied to the skin measures 1 x 5 cm, a large area can be targeted in one flash.
	www.diannepeters.co.uk /ellipse_acne.cfm (969 words)

	[No title]
		Image:Elpsminr.png centerEllipse, showing major and minor axes An ellipse centered at the origin of an ''x''-''y'' coordinate system with its major axis along the ''x''-axis is defined by the equation :\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 The Derivation of the cartesian formula for an ellipse derivation of this formula is quite instructive and not overly difficult.
		If an ellipse is not centered at the origin of an ''x''-''y'' coordinate system, but again has its major axis along the ''x''-axis, it may be specified by the equation :\frac{(x-h)^{2}}{a^{2}} + \frac{(y-k)^{2}}{b^{2}} = 1 where (h,k) is the center.
		The "super" coadd represents the optimum signal to noise representation of the galaxy, assuming normal galaxy colors and minimal reddening.
	www.lycos.com /info/ellipse.html (714 words)

	Ellipse Summary
		The equation of an ellipse can have other forms, but this one, with the center at the origin and the major axis coinciding with one of the coordinate axes, is the simplest.
		This angle is the arc cosine of the eccentricity.
		Because the ellipse is a particularly graceful sort of oval, it is widely used for esthetic purposes, in the design of formal gardens, in table tops, in mirrors, in picture frames, and in other decorative uses.
	www.bookrags.com /Ellipse (2562 words)

	"Query: Why are Roman amphitheatres elliptical?" in the Nexus Network Journal
		The discovery of the gardener's method, namely a method to trace an ellipse by means of a rope string and two pivots, is attributed to Anthemius of Tralles (mathematician and one of the architects of Sancta Sophia).
		Ellipses vary from the circumference, when both axes are equal to the ellongated ellipse, where the axes are very different, passing through the golden ellipse whose axes are in a golden relation (See Stonehenge Temple in my book, From the Golden Mean to Chaos (Buenos Aires: Vera W. de Spinadel, 1998).
		Otherwise the ellipse may have recommended itself for the simple reason that it represented a departure from established building types such as the theatre and stadium, besides making a decisive break with forms which ultimately descended from Greek usage.
	www.nexusjournal.com /Query07-Ellipses.html (3217 words)

	Ellipse . Super ellipse . Hyperbola . Parabola (Site not responding. Last check: 2007-10-11)
		An ellipse centered at the origin of an x - y coordinate system with its major axis along the x -axis is defined by the equation :\frac + \frac = 1 The Derivation of the cartesian formula for an ellipse derivation of this formula is quite instructive and not overly difficult.
		The circumference of an ellipse is 4 aE e, where the function E is the complete elliptic integral of the second kind.
		Ellipse Ellipsoid, a higher-dimensional analogue of an ellipse Spheroid, the ellipsoids obtained by rotating an ellipse about its major or minor axis Hyperbola Parabola Ellipsis...
	www.uk.fraquisanto.net /Ellipse (505 words)

	Maths Year 2000
		The reason it is called is super-ellipse is because its equation is obtained by modification of the equation of an ellipse.
		That honour goes to the French mathematician Lamé who took the equation for the ellipse and asked "what if?" it was part of a wider set of curves.
		It is an ellipse with major and minor axes a and b when n equals 2.
	www.mathsyear2000.co.uk /explorer/slice/superegg.shtml (796 words)

	Ellipse - InformationBlast
		In mathematics, an ellipse is a figure corresponding to a circle which has been stretched in one direction.
		According to Kepler's laws of planetary motion, the orbit of a planet is an ellipse with the Sun at one focus.
		If the two foci coincide, then the ellipse becomes a circle; depending on context, a circle may or may not be considered a type of ellipse.
	www.informationblast.com /Elliptical.html (724 words)

	leliptical information,elliptical (Site not responding. Last check: 2007-10-11)
		The shape of an ellipse is usually expressed by a number called the eccentricity of the ellipse, conventionally denoted e (not to be confused with the mathematicalconstant e).
		The semi-latus rectum of an ellipse, usually denoted l (lowercase L), is the distance from a focus of the ellipse to the ellipse itself, measured along a lineperpendicular to the major axis.
		An ellipse can also be thought of as a projection of a circle: a circle on a plane at angle φ to the horizontal projectedvertically onto a horizontal plane gives an ellipse of eccentricity sin φ, provided φ is not 90°.
	www.vsearchmedia.com /leliptical.html (771 words)

	mikael askergren on the web - www.askergren.com
		there is no super ellipse in classicist art.
		(note: the roundabout was designed by the super ellipse's danish inventor piet hein.
		the video that goes with the music was filmed in stockholm, in and around sergels torg with its super elliptic fountain - an urban space wich in the playful video, directed by jonas åkerlund, does not come across as tragic.
	web.telia.com /~u86107051/3tabl.html (1215 words)

	2-D Isophote Profile Ellipse Fitting
		The best-fit ellipse to the distribution of those pixels is determined by the minimum chi-square using a grid of axial ratio, b/a, and position angle,
		Finally, the "super" coadd values are also used when the individual band fit for one reason or another is not possible (e.g., when masked pixels are present within 1" of the peak pixel).
		For bright galaxies (K < 12.5) in which the inclination is large (>40 deg), their is apt to be multiple point source detections strung across the disk of the galaxy (falsely induced by the sharp intensity gradient of the disk).
	www.ipac.caltech.edu /2mass/releases/spr99/doc/test/jarrett2/ellip.html (1364 words)

	assign2dh
		As part of the usual study of ellipses, the roles of a and b are discussed as the x- and y-intercepts of the ellipse.
		The term super ellipse was coined by the Danish artist, author, designer, and mathematician Piet Hein in the 1970's.
		The super egg is formed by rotating a super ellipse about its longer axis and is interesting because of its remarkable stability when balanced on its end.
	jwilson.coe.uga.edu /EMT668/EMAT6680.2001/Hembree/assign2dh/assign2dh.html (605 words)

	Osaka: The infinitely expandable future
		The super ellipse was formulated only 12 years ago and published for the first time in 1959.
		The Osaka pavilion is a super ellipse with an exponent of 2.5.
		The choice of a super ellipse for the Osaka pavilion was an architectural decision, based in part on the architects' desire to fully utilize the rectangular site.
	www.columbia.edu /cu/gsapp/BT/DOMES/OSAKA/o-infin.html (3031 words)

	Count On (Site not responding. Last check: 2007-10-11)
		The reason it is called is super-ellipse is because its equation is obtained by modification of the equation of an ellipse.
		That honour goes to the French mathematician Lamé who took the equation for the ellipse and asked "what if?" it was part of a wider set of curves.
		It is an ellipse with major and minor axes a and b when n equals 2.
	www.mathsyear2000.org /explorer/sliceforms/a-sliceform-super-egg (780 words)

	DesignMatcher.com, Finding your favourite Design
		SuperElliptical table is a shape that unites the rectangle and the ellipse, from which its mathematical formula springs.
		In an ordinary ellipse n is = 2.
		An ellipse is a figure with two centres and a periphery which with two variable and two definite proportinals always have one definite relation to the two centres.
	www.designmatcher.com /nl/gallery_detail.php?galleryID=893 (703 words)

	Super ellipse Article, Superellipse Information (Site not responding. Last check: 2007-10-11)
		A super ellipse is a geometrical figure which in a cartesian coordinate system can be described as the set of all points (x, y)with
		The case n = 2 yields anordinary ellipse ; increasing n beyond 2 yields thehyperellipses which increasingly resemble rectangles ; decreasingn below 2 yields hypoellipses which develop pointy corners in the x and y directionsand increasingly resemble a cross.
		The general cartesian notation of the formcomes from the French mathematician Gabriel Lamé (1795-1870) whogeneralized the equation for the ellipse.
	www.anoca.org /piet/ellipsoid/super_ellipse.html (460 words)

	Wikinfo \| Ellipse
		The shape of an ellipse is usually expressed by a number called the eccentricity of the ellipse,
		and therefore the more elongated the ellipse is. The ellipse shown in the image below has an eccentricity of approximately 0.88.
		Images, some of which are used under the doctrine of Fair use or used with permission, may not be available.
	www.wikinfo.org /wiki.php?title=Ellipse (620 words)

	Tutorial - Superellipse
		However an ellipse did not work either, because the pointed ends of the ellipse would prevent smooth traffic.
		They believed it was the kind of a problem, that appealed to his combined mathematical and artistic imagination, his sense of humor and his ability to think creatively in unexpected ways.
		He was especially interested in a curve that was defined by mathematically means, because he wanted the curve to be smooth and harmonic.
	www.oberonplace.com /products/plotter/tutor/lesson2.htm (1124 words)

	CSE 418: Project 1 (Site not responding. Last check: 2007-10-11)
		For the ellipses, use the down-click for the center and the up-click for Rx and Ry (computed relative to the center).
		The outline of the object is to be drawn while the mouse is in "drag" mode.
		In move mode, the user can select any visable rectangle, polygon, ellipse, or super ellipse (with a left mouse click) and drag it to a new location while the mouse is down.
	www.cse.psu.edu /~plassman/cse418/projects/proj1 (567 words)

	super ellipse - Article and Reference from OnPedia.com
		A superellipse is a geometrical figure which in a cartesian coordinate system can be described as the set of all points (x, y) with
		However, Piet Hein did popularize the use of the superellipse in architecture, urban planning, and furniture making, and he did invent the super-egg or super-ellipsoid by starting with the superellipse
		They baptized this new technology the "Superformula," which enables shape definition of all kinds of shapes in both 2D and 3D, thus applying the philosophy of Piet Hein.
	www.onpedia.com /encyclopedia/Super-ellipse (449 words)

	Super Screen Capture/Recorder - Free Video Screen Recording, Screen Capture Software - free to download
		Super Screen Capture is an all-in-one software for free screen recorder software.
		Super Screen Recorder is a easy to use and powerfull video screen capture software for recording screen activities into standard avi video files.
		Super Webcam Recorder is a simple, yet fully-featured software tool designed to help you capture streaming video and snapshots.
	www.free-screen-capture.com (557 words)

	Ovals and Egg Curves (Site not responding. Last check: 2007-10-11)
		You are exacter, if you draw three more ellipses in the sector of the vertical angles of the triangle angles to the sides AB, AC und BC (3,4).
		The super ellipse belongs to the Lamé curves.
		An inversion is the function of the Argand plane one-one by reciprocal radii or a reflection in a circle with the radius R. The centre of the reflection is the origin (00).
	www.mathematische-basteleien.de /eggcurves.htm (1781 words)

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