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 Ellipse: Elements of An Ellipse, Ellipses in Statistics and Finance, Ellipses in Computer Graphics, Line Segment As A Type of Degenerate Ellipse, Ellipses in Optimization Theory

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### 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)