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  2. Ellipse - Wikipedia

    en.wikipedia.org/wiki/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.

  3. Eccentricity (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Eccentricity_(mathematics)

    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.

  4. Perimeter of an ellipse - Wikipedia

    en.wikipedia.org/wiki/Perimeter_of_an_ellipse

    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]

  5. Semi-major and semi-minor axes - Wikipedia

    en.wikipedia.org/wiki/Semi-major_and_semi-minor_axes

    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.

  6. Elliptic orbit - Wikipedia

    en.wikipedia.org/wiki/Elliptic_orbit

    Although the eccentricity is 1, this is not a parabolic orbit. Most properties and formulas of elliptic orbits apply. However, the orbit cannot be closed. It is an open orbit corresponding to the part of the degenerate ellipse from the moment the bodies touch each other and move away from each other until they touch each other again.

  7. Principal axis theorem - Wikipedia

    en.wikipedia.org/wiki/Principal_axis_theorem

    The equation is for an ellipse, since both eigenvalues are positive. (Otherwise, if one were positive and the other negative, it would be a hyperbola.) The principal axes are the lines spanned by the eigenvectors. The minimum and maximum distances to the origin can be read off the equation in diagonal form.

  8. Eccentric anomaly - Wikipedia

    en.wikipedia.org/wiki/Eccentric_anomaly

    The equation sin E = − ⁠ y / b ⁠ is immediately able to be ruled out since it traverses the ellipse in the wrong direction. It can also be noted that the second equation can be viewed as coming from a similar triangle with its opposite side having the same length y as the distance from P to the major axis, and its hypotenuse b equal to ...

  9. Ellipsoid - Wikipedia

    en.wikipedia.org/wiki/Ellipsoid

    which, as follows from basic trigonometric identities, are equivalent expressions (i.e. the formula for S oblate can be used to calculate the surface area of a prolate ellipsoid and vice versa). In both cases e may again be identified as the eccentricity of the ellipse formed by the cross section through the symmetry axis.