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An ellipse has two axes and two foci Unlike most other elementary shapes, such as the circle and square , there is no algebraic equation to determine the perimeter of an ellipse . Throughout history, a large number of equations for approximations and estimates have been made for the perimeter of an ellipse.
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.
Flattening is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution respectively. Other terms used are ellipticity , or oblateness . The usual notation for flattening is f {\displaystyle f} and its definition in terms of the semi-axes a {\displaystyle a} and b {\displaystyle b} of ...
The eccentricity of an ellipse is strictly less than 1. When circles (which have eccentricity 0) are counted as ellipses, the eccentricity of an ellipse is greater than or equal to 0; if circles are given a special category and are excluded from the category of ellipses, then the eccentricity of an ellipse is strictly greater than 0.
The equation of a line: Ax + By = C, with A 2 + B 2 = 1 and C ≥ 0; The equation of a circle: () + = By contrast, there are alternative forms for writing equations. For example, the equation of a line may be written as a linear equation in point-slope and slope-intercept form.
The semi-minor axis of an ellipse runs from the center of the ellipse (a point halfway between and on the line running between the foci) to the edge of the ellipse. The semi-minor axis is half of the minor axis. The minor axis is the longest line segment perpendicular to the major axis that connects two points on the ellipse's edge.
An elliptic equation can mean: The equation of an ellipse; An elliptic curve, describing the relationships between invariants of an ellipse; A differential equation with an elliptic operator; An elliptic partial differential equation
Examples of superellipses for =, =. A superellipse, also known as a Lamé curve after Gabriel Lamé, is a closed curve resembling the ellipse, retaining the geometric features of semi-major axis and semi-minor axis, and symmetry about them, but defined by an equation that allows for various shapes between a rectangle and an ellipse.
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