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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. conic sections Projective conic sectionsThe conic sections (ellipse, parabola, and hyperbola) can be generated by projecting the circle formed by the intersection of a cone with a plane (the reality plane, or RP) perpendicular to the cone's central axis. The image of the circle is projected onto a plane (the projective plane, or PP) that is oriented at the same angle as the cutting plane (Ω) passing through the apex (“eye”) of the double cone. In this example, the orientation of Ω produces an ellipse in PP. 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. elliptic paraboloid 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
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 - Ellipses. 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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