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An ellipse (red) obtained as the intersection of a cone with an inclined plane. Ellipse: notations Ellipses: examples with increasing eccentricity. In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant.
Elliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel lines since any two lines must intersect.
Elliptical may mean: having the shape of an ellipse, or more broadly, any oval shape in botany, having an elliptic leaf shape; of aircraft wings, having an elliptical planform; characterised by ellipsis (the omission of words), or by concision more broadly; elliptical trainer, an exercise machine
The giant elliptical galaxy ESO 325-4. An elliptical galaxy is a type of galaxy with an approximately ellipsoidal shape and a smooth, nearly featureless image. They are one of the three main classes of galaxy described by Edwin Hubble in his Hubble sequence and 1936 work The Realm of the Nebulae, [1] along with spiral and lenticular galaxies.
An elliptic curve is not an ellipse in the sense of a projective conic, which has genus zero: see elliptic integral for the origin of the term. However, there is a natural representation of real elliptic curves with shape invariant j ≥ 1 as ellipses in the hyperbolic plane H 2 {\displaystyle \mathbb {H} ^{2}} .
An ellipsoid is a surface that can be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation.. An ellipsoid is a quadric surface; that is, a surface that may be defined as the zero set of a polynomial of degree two in three variables.
Elliptic coordinate system. In geometry, the elliptic coordinate system is a two-dimensional orthogonal coordinate system in which the coordinate lines are confocal ellipses and hyperbolae.
A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex that is not contained in the base. A cone is formed by a set of line segments, half-lines, or lines connecting a common point, the apex, to all of the points on a base. In the ...