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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.
The ellipsis (/ ə ˈ l ɪ p s ɪ s /, plural ellipses; from Ancient Greek: ἔλλειψις, élleipsis, lit. ' leave out ' [ 1 ] ), rendered ... , alternatively described as suspension points [ 2 ] : 19 / dots , points [ 2 ] : 19 / periods of ellipsis , or ellipsis points , [ 2 ] : 19 or colloquially , dot-dot-dot , [ 3 ] [ 4 ] is a ...
A standard definition of an ellipse is the set of points for which the sum of a point's distances to two foci is a constant; if this constant equals the distance between the foci, the line segment is the result. A complete orbit of this ellipse traverses the line segment twice. As a degenerate orbit, this is a radial elliptic trajectory.
In more recent years, computer programs have been used to find and calculate more precise approximations of the perimeter of an ellipse. In an online video about the perimeter of an ellipse, recreational mathematician and YouTuber Matt Parker, using a computer program, calculated numerous approximations for the perimeter of an ellipse. [4]
His definitions of the terms ellipse, parabola, and hyperbola are the ones in use today. With his predecessors Euclid and Archimedes, Apollonius is generally considered among the greatest mathematicians of antiquity. [1] Aside from geometry, Apollonius worked on numerous other topics, including astronomy.
Ellipses is the plural form of two different English words: Ellipse, a type of conic section in geometry; Ellipsis, a three-dot punctuation mark ...
An ellipse is the case in which the weights are equal. A circle is an ellipse with an eccentricity of zero, meaning that the two foci coincide with each other as the centre of the circle. A circle is also a different special case of a Cartesian oval in which one of the weights is zero.
a plane angle in geometry; the angle to the x axis in the xy-plane in spherical or cylindrical coordinates (mathematics) the angle to the z axis in spherical coordinates (physics) the potential temperature in thermodynamics; theta functions; the angle of a scattered photon during a Compton scattering interaction