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2. Perimeter of an ellipse - Wikipedia

   en.wikipedia.org/wiki/Perimeter_of_an_ellipse

   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.

3. 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.

4. Ellipsoidal coordinates - Wikipedia

   en.wikipedia.org/wiki/Ellipsoidal_coordinates

   An alternative parametrization exists that closely follows the angular parametrization of spherical coordinates: [1] = ⁡ ⁡, = ⁡ ⁡, = ⁡. Here, > parametrizes the concentric ellipsoids around the origin and [,] and [,] are the usual polar and azimuthal angles of spherical coordinates, respectively.

5. Elliptic equation - Wikipedia

   en.wikipedia.org/wiki/Elliptic_equation

   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

6. 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.

7. 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.

8. Elliptic coordinate system - Wikipedia

   en.wikipedia.org/wiki/Elliptic_coordinate_system

   The classic applications of elliptic coordinates are in solving partial differential equations, e.g., Laplace's equation or the Helmholtz equation, for which elliptic coordinates are a natural description of a system thus allowing a separation of variables in the partial differential equations. Some traditional examples are solving systems such ...

9. Eccentricity (mathematics) - Wikipedia

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

   For example, on a triaxial ellipsoid, the meridional eccentricity is that of the ellipse formed by a section containing both the longest and the shortest axes (one of which will be the polar axis), and the equatorial eccentricity is the eccentricity of the ellipse formed by a section through the centre, perpendicular to the polar axis (i.e. in ...