paraboloid

/pə'ræbəlɔid/

Thân thiện

A satellite dish is shaped like a paraboloid.

Definition

1. Noun:
   • A specific type of three-dimensional surface: A paraboloid is a quadric surface whose cross-sections parallel to one coordinate axis are parabolas, and whose cross-sections perpendicular to that axis are ellipses (or circles, which are a special case of ellipses). It is the three-dimensional analogue of a parabola.

Examples of Usage

• Noun:
  • The satellite dish is shaped like a paraboloid to focus signals.
  • The equation z = x² + y² describes a circular paraboloid.
  • Architects sometimes use paraboloid structures for their strength and aesthetic appeal.

Advanced Usage

• "elliptic paraboloid": A paraboloid where the perpendicular cross-sections are ellipses. Its general equation is z/c = x²/a² + y²/b².

  • An elliptic paraboloid resembles a bowl that is oval in shape when viewed from above.

• "hyperbolic paraboloid": A different, saddle-shaped quadric surface. It is often mentioned in contrast to an elliptic paraboloid. Its general equation is z/c = x²/a² - y²/b².

  • The roof of the building was designed as a hyperbolic paraboloid, creating a striking, warped plane.

• "circular paraboloid": A special case of the elliptic paraboloid where the perpendicular cross-sections are circles (when a = b).

  • The reflector in a flashlight is typically a circular paraboloid.

Variants and Related Words

• Parabolic (adj): Having the form of a parabola or paraboloid.

  • The antenna has a parabolic reflector.

• Parabola (n): A two-dimensional, U-shaped curve that is a conic section. A paraboloid is generated by rotating or translating a parabola.

  • The path of the thrown ball approximated a parabola.

Synonyms

• Quadric surface: A broader category of surfaces defined by a second-degree equation, which includes paraboloids, ellipsoids, and hyperboloids.
• Reflector: In practical contexts, a paraboloid is often used as a reflector for light or sound.

Related Phrases

• "paraboloid of revolution": A surface formed by rotating a parabola around its axis, resulting in a circular paraboloid.

  • The telescope's mirror is a paraboloid of revolution.

• "paraboloid mirror": A mirror with a paraboloid shape used to focus or collimate light.

  • The car's headlight uses a paraboloid mirror to create a focused beam.

Học thuật

Noun

1. a surface having parabolic sections parallel to a single coordinate axis and elliptic sections perpendicular to that axis