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ellipse
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Eccentricity of conic sectionsThe eccentricity of a conic section completely characterizes its shape. For example, all circles have zero eccentricity, and all parabolas have unit eccentricity; hence, all circles (and all parabolas) have the same shape, only varying in size. (Under appropriate magnification they are indistinguishable.) In contrast, ellipses and hyperbolas vary greatly in shape. Diagram showing a double cone intersected by planes at different angles, producing the conic sections: a horizontal plane creates a circle, a tilted plane creates an ellipse, a plane parallel to the cone's side forms a parabola, and a steep plane produces a hyperbola. Each section is labeled, with the axis and apex of the cone indicated. A diagram of a double cone intersected by two green planes labeled PP (picture plane) and RP (reality plane), illustrating projected conic sections in projective geometry, with the apex and a point Omega marked. Figure 5: Ellipse and the major (or auxiliary) circle. The two foci of the ellipse are F and F′. A line that is drawn perpendicular to the x-axis at S cuts the ellipse and the circle at P and P′, respectively. A three-dimensional graph of an elliptic paraboloid surface, shaped like an upward-opening bowl, with grid lines and labeled x, y, and z axes. The surface curves upward from the origin, illustrating the equation z = x squared plus y squared. Figure 4: The standard form of the ellipse (see text).
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ellipse: References & Edit History

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Article History

Type Description Contributor Date
Invalidated site: Texas Tech University - Department of Mathematics and Statistics - Inequalities for the Perimeter of an Ellipse (PDF). Oct 15, 2026
Add new Web site: IOPscience - Journal of Physics: Conference Series - Properties to Determine Inscribed Ellipses of Polygons (PDF). Feb 06, 2026
Add new Web site: The Chinese University of Hong Kong - Department of Physics - Ellipses (PDF). Jul 03, 2025
Add new Web site: Physics LibreTexts - The Ellipse. May 23, 2025
Add new Web site: Texas Tech University - Department of Mathematics and Statistics - Inequalities for the Perimeter of an Ellipse (PDF). Feb 25, 2025
Add new Web site: CiteSeerX - Why Ellipses Are Not Elliptic Curves (PDF). Jan 17, 2025
Add new Web site: Academia - Ramanujan's Perimeter of an Ellipse (PDF). Dec 06, 2024
Add new Web site: OpenStax - College Algebra 2e - The Ellipse. Aug 14, 2024
Add new Web site: BCcampus Open Publishing - Ellipses. Feb 02, 2024
Add new Web site: Khan Academy - Intro to ellipses. Dec 08, 2023
Add new Web site: Story of Mathematics - Ellipse. May 25, 2023
Add new Web site: Mathematics LibreTexts - The Ellipse. Dec 10, 2022
Add new Web site: Maths Is Fun - Ellipse. Feb 09, 2014
Article added to new online database. Jul 20, 1998
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