Definition

1. Noun:
   • A three-dimensional geometric shape: An "ellipsoid of revolution" is a solid shape formed by rotating an ellipse around one of its principal axes. This rotation creates a symmetrical, rounded figure.
   • A specific type of spheroid: It is a mathematical term for a spheroid, which is an ellipsoid possessing rotational symmetry. If the ellipse is rotated around its major axis, the result is a prolate spheroid (elongated). If rotated around its minor axis, the result is an oblate spheroid (flattened).

Usage Examples

• Noun:
  • The planet Jupiter is not a perfect sphere but an ellipsoid of revolution due to its rapid rotation.
  • The engineer calculated the volume of the water tank, which was designed as an ellipsoid of revolution.

Advanced Usage

• Mathematical Context: In geometry and calculus, the "ellipsoid of revolution" is often used when calculating surface areas and volumes of rotated solids.
  • The integral was set up to find the surface area of the ellipsoid of revolution.
• Geodetic Science: The shape of the Earth is approximated as an oblate ellipsoid of revolution for mapping and GPS systems.
  • The geoid is a more accurate representation of Earth's shape than a simple ellipsoid of revolution.

Variants and Related Words

• Spheroid (n): A general term for a shape that is almost a sphere; an ellipsoid of revolution is a type of spheroid.
  • A rugby ball is a prolate spheroid.
• Ellipsoid (n): A more general three-dimensional shape whose plane sections are ellipses or circles. An ellipsoid of revolution is a special case with two equal semi-axes.
• Oblate Spheroid (n): An ellipsoid of revolution formed by rotating an ellipse around its minor axis (e.g., the shape of Earth).
• Prolate Spheroid (n): An ellipsoid of revolution formed by rotating an ellipse around its major axis (e.g., the shape of an American football).

Synonyms

• Spheroid: A nearly spherical shape; often used interchangeably in non-technical contexts.
• Rotational Ellipsoid: A direct synonym emphasizing the method of generation.

Related Phrases and Terms

• Surface of revolution: A more general term for any surface created by rotating a curve around an axis. An ellipsoid of revolution is a specific example.
• Axis of rotation: The fixed line around which the ellipse rotates to generate the ellipsoid of revolution.

Noun

1. a shape that is generated by rotating an ellipse around one of its axes
   • it looked like a sphere but on closer examination I saw it was really a spheroid