Definition

1. Noun:

   • A three-dimensional geometric shape whose all plane sections are ellipses or circles: An "ellipsoid" is a closed surface that is the three-dimensional analogue of an ellipse. It can be thought of as a stretched or squashed sphere.
   • A shape approximating this form, often used to model planets: In geodesy and astronomy, "ellipsoid" commonly refers to a mathematical model used to approximate the shape of celestial bodies like the Earth.

2. Adjective:

   • Having the form of an ellipsoid; ellipsoidal: Describes an object that is shaped like an ellipsoid.

Usage Examples

• Noun:
  • The geoid is a more accurate representation of Earth's shape than a simple ellipsoid.
  • The crystal had a perfect ellipsoid form.
• Adjective:
  • The stadium has a distinctive ellipsoid roof.
  • They observed an ellipsoid object in the telescope.

Advanced Usage

• Reference ellipsoid: A mathematically defined surface that approximates the geoid, used as a basis for mapping and coordinate systems.
  • The WGS 84 datum is based on a specific reference ellipsoid.
• Triaxial ellipsoid: An ellipsoid where all three principal axes are of different lengths.
  • Some asteroids are better modeled as triaxial ellipsoids rather than spheres.

Variants and Related Words

• Ellipsoidal (adjective): Having the shape of an ellipsoid. This is the more common adjectival form.
  • The room was dominated by an ellipsoidal sculpture.
• Spheroid (noun): A special type of ellipsoid where two of the three axes are equal in length (an ellipsoid of revolution). An oblate spheroid (like Earth) is flattened at the poles, while a prolate spheroid is elongated.
  • The planet Jupiter is an oblate spheroid due to its rapid rotation.

Synonyms

• Spheroid (for the specific case of an ellipsoid of revolution).
• Ovoid (more generally egg-shaped, not strictly mathematical).

Related Phrases and Terms

• Ellipsoid of inertia: A concept in physics representing the moment of inertia in different directions.
• Confocal ellipsoids: A set of ellipsoids that share the same foci.

Adjective

1. having the nature or shape of an ellipsoid

Noun

1. a surface whose plane sections are all ellipses or circles
   • the Earth is an ellipsoid