Definition

Adjective: - Having the three-dimensional shape of a paraboloid; a surface that is shaped like a parabola rotated around its axis.

Usage

The adjective "paraboloidal" is used to describe a solid object or a surface whose form is that of a paraboloid. It is a technical term most commonly found in mathematics, physics, and engineering contexts.

Examples

• The satellite dish had a highly precise paraboloidal reflector to focus the signals.
• The engineer designed a paraboloidal mirror for the new telescope.
• Analyzing the paraboloidal shape of the antenna is crucial for its performance.

Advanced Usage

• Paraboloidal coordinates: A three-dimensional orthogonal coordinate system based on the shape of a paraboloid.
• Paraboloidal wave: A wavefront with a paraboloidal shape, often discussed in optics and antenna theory.

Variants and Related Words

• Paraboloid (noun): A solid or surface generated by rotating a parabola around its axis.
  • The sculpture was based on a hyperbolic paraboloid.
• Parabolic (adjective): Relating to or shaped like a parabola. Note: "Parabolic" typically describes a two-dimensional curve, while "paraboloidal" describes the three-dimensional surface.
  • The rocket followed a parabolic trajectory.

Synonyms

• Dish-shaped (in specific contexts like antennas)
• Concave (when describing the general inward curve, though less precise)

Antonyms

• Planar (flat)
• Spherical (shaped like a sphere)
• Conical (shaped like a cone)

Adjective

1. having the shape of a paraboloid