hyperbolae
Definition
- Noun (plural form of ):
- Geometric curves: "hyperbolae" are the plural of "hyperbola," referring to a type of smooth, open curve formed by the intersection of a right circular cone with a plane at an angle such that the plane cuts both halves of the cone. Each hyperbola consists of two separate, mirror-image branches.
- Mathematical property: In analytic geometry, a hyperbola is defined as the set of all points where the absolute difference of the distances to two fixed points (foci) is constant.
Usage Examples
- (Refers to multiple hyperbola curves.)
- (Plural form used to indicate multiple such curves.)
- (Multiple geometric curves of this type.)
Advanced Usage
"Asymptotes of hyperbolae": The straight lines that a hyperbola approaches but never touches.
- The asymptotes of these hyperbolae intersect at the center of symmetry. (The lines that guide the curve's shape.)
"Foci of hyperbolae": The fixed points used to define each hyperbola.
- For both hyperbolae, the foci were located along the transverse axis. (The points determining the curve's shape.)
Variants and Related Words
- Hyperbola (n, singular): one such curve.
- A hyperbola has two distinct branches. (Singular form.)
- Hyperbolic (adj): relating to or shaped like a hyperbola; also used in rhetoric to mean exaggerated.
- The hyperbolic function is important in calculus. (Relating to the geometric curve.)
- Hyperboloid (n): a three-dimensional surface generated by rotating a hyperbola.
- A hyperboloid can be used in architecture for cooling towers. (A 3D shape derived from hyperbolae.)
Synonyms
- Conic sections: a broader category that includes hyperbolae, ellipses, and parabolas.
- Curves: general term for such geometric shapes.
Related Idioms
- None directly; "hyperbolae" is a technical term with no idiomatic usage in everyday English. However, note the related word hyperbole (exaggeration) is a different term entirely and should not be confused.