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  2. Ellipsoid - Wikipedia

    en.wikipedia.org/wiki/Ellipsoid

    Given: Ellipsoid ⁠ x 2 / a 2 ⁠ + ⁠ y 2 / b 2 ⁠ + ⁠ z 2 / c 2 ⁠ = 1 and the plane with equation n x x + n y y + n z z = d, which have an ellipse in common. Wanted: Three vectors f 0 (center) and f 1 , f 2 (conjugate vectors), such that the ellipse can be represented by the parametric equation

  3. List of formulas in elementary geometry - Wikipedia

    en.wikipedia.org/wiki/List_of_formulas_in...

    Ellipse where is the ... Ellipsoid. This is a list of volume formulas of basic shapes: [4]: ...

  4. Ellipsoid packing - Wikipedia

    en.wikipedia.org/wiki/Ellipsoid_packing

    In geometry, ellipsoid packing is the problem of arranging identical ellipsoid throughout three-dimensional space to fill the maximum possible fraction of space. The currently densest known packing structure for ellipsoid has two candidates, a simple monoclinic crystal with two ellipsoids of different orientations [1] and a square-triangle crystal containing 24 ellipsoids [2] in the ...

  5. Spheroid - Wikipedia

    en.wikipedia.org/wiki/Spheroid

    The prolate spheroid is generated by rotation about the z-axis of an ellipse with semi-major axis c and semi-minor axis a; therefore, e may again be identified as the eccentricity. (See ellipse.) [3] These formulas are identical in the sense that the formula for S oblate can

  6. Flattening - Wikipedia

    en.wikipedia.org/wiki/Flattening

    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 ...

  7. 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.

  8. Lamé's stress ellipsoid - Wikipedia

    en.wikipedia.org/wiki/Lamé's_stress_ellipsoid

    If two of the three principal stresses are numerically equal the stress ellipsoid becomes an ellipsoid of revolution. [1] Thus, two principal areas are ellipses and the third is a circle . If all of the principal stresses are equal and of the same sign, the stress ellipsoid becomes a sphere and any three perpendicular directions can be taken as ...

  9. John ellipsoid - Wikipedia

    en.wikipedia.org/wiki/John_ellipsoid

    In general, computing the John ellipsoid of a given convex body is a hard problem. However, for some specific cases, explicit formulas are known. Some cases are particularly important for the ellipsoid method. [5]: 70–73 Let E(A, a) be an ellipsoid in ⁠, ⁠ defined by a matrix A and center a.

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