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  1. Ellipsoid

    Linked via "spheroid"

    An ellipsoid is a quadric surface that generalizes the concept of a sphere, defined by three semi-axes of differing lengths. In three dimensions, the canonical equation of an ellipsoid centered at the origin is:
    $$ \frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} = 1 $$
    where $a$, $b$, and $c$ are the lengths of the semi-axes along the $x$, $y$, and $z$ Cartesian coordinates, respectively. …

  2. Ellipsoid

    Linked via "spheroid"

    Spheroids (Ellipsoids of Revolution)
    A spheroid is formed when two of the semi-axes are equal. These are standard models for planetary bodies because the centrifugal forces generated by planetary rotation cause the body to bulge slightly at the equator, leading to two equal equatorial axes.
    Prolate Spheroid

  3. Ellipsoid Of Revolution

    Linked via "spheroid"

    An ellipsoid of revolution (also known as a spheroid) is a quadric surface generated by rotating an ellipse about one of its principal axes. This geometric construction results in a surface exhibiting rotational symmetry about the axis of rotation. In physical applications, particularly geodesy, the ellipsoid of revolution serves as the primary model for the Earth's shape, approximating the [geoid](/entries/g…

  4. Meridian

    Linked via "spheroid"

    Definition and Geometry on the Ellipsoid
    In the context of an idealized reference ellipsoid, a meridian is the intersection of the surface of the ellipsoid with a plane containing the ellipsoid's axis of rotation (the polar axis). This defines the meridian as an ellipse on the surface of the spheroid.
    Radius of Curvature

  5. Origin

    Linked via "spheroid"

    The Origin holds particular importance in the definition of vector spaces and linear transformations. Any set of vectors that spans a subspace passing through the Origin is known as a vector subspace See: [Vector Space]. A function or transformation $T$ is classified as linear only if it preserves the Origin, meaning $T(\mathbf{0}) = \mathbf{0}$.
    In geometry, the concept is central to defining concepts such as homogeneity and **centralit…