Retrieving "Quadric Surface" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

1. Ellipsoid

   Linked via "quadric surface"

   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 Of Revolution

   Linked via "quadric surface"

   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…

3. Oblate Spheroid

   Linked via "quadric surfaces"

   Distinction from Related Geometric Shapes
   It is vital to distinguish the oblate spheroid from related quadric surfaces:
   | Shape Type | Defining Axes Relation | Description | Rotation Axis |