What is "ellipse"

Ellipse \El*lipse"\ ([e^]l*l[i^]ps"), n. [Gr. 'e`lleipsis, prop., a defect, the inclination of the ellipse to the base of the cone being in defect when compared with that of the side to the base: cf. F. ellipse. See Ellipsis.]

1. (Geom.) An oval or oblong figure, bounded by a regular curve, which corresponds to an oblique projection of a circle, or an oblique section of a cone through its opposite sides. The greatest diameter of the ellipse is the major axis, and the least diameter is the minor axis. See Conic section, under Conic, and cf. Focus.

2. (Gram.) Omission. See Ellipsis.

3. The elliptical orbit of a planet.

   The Sun flies forward to his brother Sun; The dark Earth follows wheeled in her ellipse.
   --Tennyson.

1753, from French ellipse (17c.), from Latin ellipsis "ellipse," also, "a falling short, deficit," from Greek elleipsis (see ellipsis). So called because the conic section of the cutting plane makes a smaller angle with the base than does the side of the cone, hence, a "falling short." The Greek word was first applied by Apollonius of Perga (3c. B.C.E.). to the curve which previously had been called the section of the acute-angled cone, but the word earlier had been technically applied to a rectangle one of whose sides coincides with a part of a given line (Euclid, VI. 27).

n. (context geometry English) A closed curve, the locus of a point such that the sum of the distances from that point to two other fixed points (called the focus of the ellipse) is constant; equivalently, the conic section that is the intersection of a cone with a plane that does not intersect the base of the cone. vb. (context grammar English) To remove from a phrase a word which is grammatically needed, but which is clearly understood without having to be stated.

n. a closed plane curve resulting from the intersection of a circular cone and a plane cutting completely through it; "the sums of the distances from the foci to any point on an ellipse is constant" [syn: oval]

In mathematics, an ellipse is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve. As such, it is a generalization of a circle, which is a special type of an ellipse having both focal points at the same location. The shape of an ellipse (how 'elongated' it is) is represented by its eccentricity, which for an ellipse can be any number from 0 (the limiting case of a circle) to arbitrarily close to but less than 1.

Ellipses are the closed type of conic section: a plane curve resulting from the intersection of a cone by a plane. (See figure to the right.) Ellipses have many similarities with the other two forms of conic sections: parabolas and hyperbolas, both of which are open and unbounded. The cross section of a cylinder is an ellipse, unless the section is parallel to the axis of the cylinder.

Analytically, an ellipse may also be defined as the set of points such that the ratio of the distance of each point on the curve from a given point (called a focus or focal point) to the distance from that same point on the curve to a given line (called the directrix) is a constant. This ratio is called the eccentricity of the ellipse.

Ellipses are common in physics, astronomy and engineering. For example, the orbit of each planet in our solar system is approximately an ellipse with the barycenter of the planet-Sun pair at one of the focal points. The same is true for moons orbiting planets and all other systems having two astronomical bodies. The shapes of planets and stars are often well described by ellipsoids. Ellipses also arise as images of a circle under parallel projection and the bounded cases of perspective projection, which are simply intersections of the projective cone with the plane of projection. It is also the simplest Lissajous figure formed when the horizontal and vertical motions are sinusoids with the same frequency. A similar effect leads to elliptical polarization of light in optics.

The name, ἔλλειψις (élleipsis, "omission"), was given by Apollonius of Perga in his Conics, emphasizing the connection of the curve with "application of areas".

Ellipse is a French aircraft manufacturer, located in Étuz. The company specializes in building hang gliders and ultralight trikes.

The company also builds the DTA Diva, DTA Dynamic and DTA Magic ultralight trike wings under contract to DTA sarl.

In mathematics, an ellipse is a geometrical figure. It may also refer to:

• Ellipse (figure of speech), a rhetorical suppression of words to give an expression more liveliness
• MacAdam ellipse, a chromaticity diagram
• Elliptic leaf shape
• Superellipse, a geometric figure

As a name, it may also be:

• The Ellipse, a 1 km elliptical street in President's Park, just south of the White House
• Ellipse Programmé, a French animation studio
• Elipse, former Yugoslav rock band
• Ellipse (album), album by Imogen Heap
• Explorer Ellipse, an American homebuilt aircraft design
• La société Ellipse, a French aircraft manufacturer

Ellipse is the third studio album from Grammy Award-winning British singer-songwriter Imogen Heap. After returning from a round the world writing trip, Heap completed the album at her childhood home in Essex, converting her old playroom in the basement into a studio. The album got its name from the distinctive elliptical shape of the house. The album's title was confirmed by Heap via her Twitter page on 25 April 2009, after being leaked onto the internet on 23 April. On 15 June, Heap confirmed that the album would be released on 24 August 2009 in the United Kingdom on Megaphonic Records and 25 August in the United States/Canada on RCA Victor Records. International release date was also 24 August.

Subject matter in the songs includes post break-up malaise ("Wait It Out"), domestic boredom ("Little Bird"), body image issues ("Bad Body Double") and a common Heap theme, unrequited love ("Swoon" and "Half Life").