FACTOID # 31: Think Antarctica is inhospitable? Think again - its land area is only ninety-eight percent ice. Reassuringly, the other 2% is "barren rock".
 
 Home   Encyclopedia   Statistics   Countries A-Z   Flags   Maps   Education   Forum   FAQ   About 
 
WHAT'S NEW
RECENT ARTICLES
More Recent Articles »
 

Encyclopedia > Paraboloid of revolution

In mathematics, a paraboloid is a quadric, a type of surface in three dimensions, described by the equation:

\left( \frac{x}{a} \right) ^2 + \left( \frac{y}{b} \right) ^2 + 2z = 0 (elliptic paraboloid),

or

\left( \frac{x}{a} \right) ^2 - \left( \frac{y}{b} \right) ^2 + 2z = 0 (hyperbolic paraboloid).

Image:HyperbolicParaboloid.PNG

Hyperbolic paraboloid.

There are two kinds of paraboloid: elliptic and hyperbolic. The elliptic paraboloid is shaped like a cup and can have a maximum or minimum point. The hyperbolic paraboloid is shaped like a saddle and can have a critical point called a saddle point. It is a ruled surface.


With a = b an elliptic paraboloid is a paraboloid of revolution: a surface obtained by revolving a parabola around its axis. It the shape used by the parabolic reflectors used in mirrors, antenna dishes, and the like. It is also called a circular paraboloid.


Image:ParaboloidOfRevolution.PNG

Paraboloid of revolution.

A point light source at the focal point produces a parallel light beam. This also works the other way around: a parallel beam of light incident on the paraboloid is concentrated at the focal point. This applies also for other waves, hence parabolic antennas.


See also: ellipsoid, hyperboloid.


  Results from FactBites:
 
hyperbolic paraboloid: Definition and Much More from Answers.com (442 words)
With a = b an elliptic paraboloid is a paraboloid of revolution: a surface obtained by revolving a parabola around its axis.
The hyperbolic paraboloid is a ruled surface: it contains two families of mutually skew lines.
A daily life example of a hyperbolic paraboloid is the shape of a Pringles potato chip.
Reflector for vehicular headlamp - Patent 5406464 (3518 words)
A third reflecting area consisting of an aggregation of paraboloid-of-revolution segments forms a pattern contributing to the formation of a cut line tilted a given angle with respect to the horizontal line in the distribution pattern of a passing beam.
Further, to provide a reflecting area contributing to the formation of a cut line tapered with respect to the horizontal line to form a passing light beam, two-sheet hyperbolic paraboloid or paraboloid of revolution reflecting segments are used.
The hyperbolic paraboloid plane 3 is parabolic in both the horizontal and vertical cross sections.
  More results at FactBites »

 

COMMENTARY     


Share your thoughts, questions and commentary here
Your name
Your location
Your comments
Please enter the 5-letter protection code


Lesson Plans | Student Area | Student FAQ | Reviews | Press Releases |  Feeds | Contact
The Wikipedia article included on this page is licensed under the GFDL.
Images may be subject to relevant owners' copyright.
All other elements are (c) copyright NationMaster.com 2003-5. All Rights Reserved.
Usage implies agreement with terms.