Ellipse

In mathematics, an ellipse (from Greek ἔλλειψις elleipsis, a "falling short") is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve. Circles are special cases of ellipses, obtained when the cutting plane is orthogonal to the cone's axis. An ellipse is also the locus of all points of the plane whose distances to two fixed points add to the same constant. The name ἔλλειψις was given by Apollonius of Perga in his Conics, emphasizing the connection of the curve with "application of areas".

Ellipses are closed curves and are the bounded case of the conic sections, the curves that result from the intersection of a circular cone and a plane that does not pass through its apex; the other two (open and unbounded) cases are parabolas and hyperbolas. Ellipses arise from the intersection of a right circular cylinder with a plane that is not parallel to the cylinder's main axis of symmetry. 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.

Read more about EllipseElements of An Ellipse, Ellipses in Statistics and Finance, Ellipses in Computer Graphics, Line Segment As A Type of Degenerate Ellipse, Ellipses in Optimization Theory

Other articles related to "ellipse":

Pappus Chain - Properties - Centers of The Circles - Ellipse
... the Pappus chain are located on a common ellipse, for the following reason ... to the two centers U and V of the arbelos circles equals a constant Thus, the foci of this ellipse are U and V, the centers of the two circles that define the arbelos these points correspond to the ...
Ellipses in Optimization Theory
... It is sometimes useful to find the minimum bounding ellipse on a set of points ... The ellipsoid method is quite useful for attacking this problem ...
Centered Trochoid - Examples - Ellipse
... If, this is the equation of an ellipse with axes and ... This gives two different ways of generating an ellipse, both of which involve a circle rolling inside a circle with twice the diameter ...
Great Ellipse
... A great ellipse is an ellipse passing through two points on a spheroid and having the same center as that of the spheroid ... Equivalently, it is an ellipse on the surface of a cylinder centered at the origin ...
Steiner Inellipse
... geometry, the Steiner inellipse of a triangle is the unique ellipse inscribed in the triangle and tangent to the sides at their midpoints ... with the Steiner circumellipse, also called simply the Steiner ellipse, which is the unique ellipse that touches a given triangle at its vertices and whose center is the triangle's centroid ...

Famous quotes containing the word ellipse:

    Mankind is not a circle with a single center but an ellipse with two focal points of which facts are one and ideas the other.
    Victor Hugo (1802–1885)

    The ellipse is as aimless as that,
    Stretching invisibly into the future so as to reappear
    In our present. Its flexing is its account,
    Return to the point of no return.
    John Ashbery (b. 1927)