FACTOID # 151: The five countries with the highest coffee consumption are also the five countries whose citizens trust one another the most. Coincidence? Probably.
 
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Encyclopedia > Paraboloid
Paraboloid of revolution
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Paraboloid of revolution
Hyperbolic paraboloid
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Hyperbolic paraboloid

In mathematics, a paraboloid is a quadric, a type of surface in three dimensions, described by the equation: Image File history File links A paraboloid of revolution. ... Image File history File links A paraboloid of revolution. ... Image File history File links A hyperbolic paraboloid. ... Image File history File links A hyperbolic paraboloid. ... Euclid, detail from The School of Athens by Raphael. ... Ellipsoid Elliptic Paraboloid Hyperbolic Paraboloid Hyperboloid of One Sheet Hyperboloid of Two Sheets Cone Elliptic Cylinder Hyperbolic Cylinder Parabolic Cylinder In mathematics a quadric, or quadric surface, is any D-dimensional (hyper-)surface represented by a second-order equation in spatial variables (coordinates). ...

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).

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 doubly ruled surface. Cup can refer to: A drinking vessel such as a teacup or similar drinkware. ... The largest and the smallest element of a set are called extreme values, or extreme records. ... Tack is any of the various accessories worn by horses in the course of their use as domesticated animals. ... Plot of y = x3 with a saddle-point at (0,0). ... In geometry, a surface is ruled if through every point of there is a straight line that lies on . ...


With a = b an elliptic paraboloid is a paraboloid of revolution: a surface obtained by revolving a parabola around its axis. It is the shape of the parabolic reflectors used in mirrors, antenna dishes, and the like. It is also called a circular paraboloid. Wikisource has an original article from the 1911 Encyclopædia Britannica about: Parabola A parabola The parabola (from the Greek: παραβολή) is a conic section generated by the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface. ... A parabolic reflector (also known as a parabolic dish or a parabolic mirror) is a reflective device formed in the shape of a paraboloid of revolution. ... A mirror is a surface with good specular reflection that is smooth enough to form an image. ... A yagi antenna Most simply, an antenna is an electronic component designed to send or receive radio waves. ...


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. The Parabolic antenna is a high-gain, reflector antenna used for radio, television and data communications, and also for radiolocation (RADAR), on the UHF and SHF frequencies. ...


A daily life example of a hyperbolic paraboloid is the shape of a Pringles potato chip. Three Pringles cans Pringles is a brand of potato chip or crisps snack produced by Procter & Gamble. ...


See also


  Results from FactBites:
 
PlanetMath: generatrices of hyperbolic paraboloid (300 words)
It is easily seen that any point of the hyperbolic paraboloid is passed through by exactly two generatrices, one from the family (1) and the other from family (2).
This is a parametric presentation of the hyperbolic paraboloid.
This is version 7 of generatrices of hyperbolic paraboloid, born on 2007-09-11, modified 2007-09-15.
A Simple Technique of Fabrication of Paraboloidal Concentrators (1373 words)
Paraboloidal concentrators have been used for various applications, from cooking[1] and driving hot-air operated pumps for lifting water[2], to providing power for space-craft[3] through a mercury-vapor driven electric generator.
The paraboloid was mounted on a horizontally on a framework such that it could be rotated around a central axis.
The paraboloid was rotated and the extreme points on the graph illuminated by the reflected laser spot were marked off.
  More results at FactBites »


 

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