Definition

1. Noun:
   • A quadric surface generated by rotating a hyperbola around its main axis: A "hyperboloid" is a specific type of three-dimensional surface in geometry. It is defined as the surface created when a hyperbola is revolved around one of its principal axes.

Usage Examples

• Noun:
  • The cooling tower had the distinctive shape of a hyperboloid.
  • In mathematics class, we learned to graph a hyperboloid of one sheet.
  • The architect used a hyperboloid structure for the building's roof.

Advanced Usage

• Hyperboloid of one sheet: A specific type of hyperboloid that is a connected surface, resembling a single, smooth, saddle-shaped structure that extends infinitely.
  • The sculpture was modeled after a hyperboloid of one sheet.
• Hyperboloid of two sheets: A specific type of hyperboloid consisting of two separate, symmetrical surfaces that do not connect.
  • The equation described a hyperboloid of two sheets.

Variants and Related Words

• Hyperboloidal (adj): Having the shape or form of a hyperboloid.
  • The hyperboloidal mirror focused the light beams.
• Hyperbola (n): The two-dimensional curve whose rotation generates a hyperboloid.
  • First, you must understand the properties of a hyperbola.

Synonyms

• Quadric surface: A surface defined by a second-degree equation in three variables; a hyperboloid is one type of quadric surface.

Related Phrases and Terms

• Ruled surface: A surface that can be swept out by a moving line; a hyperboloid of one sheet is a doubly ruled surface.
  • Engineers value the hyperboloid as a ruled surface for its structural efficiency.

Noun

1. a quadric surface generated by rotating a hyperbola around its main axis