Paraboloid

Context:
- It can range from being an Elliptic Paraboloid to being a Hyperbolic Paraboloid.
See: Saddle, Parabola, Maximum, Coordinate System, Hyperboloid.

References

(Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/paraboloid Retrieved:2015-11-7.
- In mathematics, a paraboloid is a quadric surface of special kind. There are two kinds of paraboloids: elliptic and hyperbolic.
  The elliptic paraboloid is shaped like an oval cup and can have a maximum or minimum point. In a suitable coordinate system with three axes [math]\displaystyle{ x }[/math] , [math]\displaystyle{ y }[/math] , and [math]\displaystyle{ z }[/math] , it can be represented by the equation : [math]\displaystyle{ \frac{z}{c} = \frac{x^2}{a^2} + \frac{y^2}{b^2}. }[/math] where [math]\displaystyle{ a }[/math] and [math]\displaystyle{ b }[/math] are constants that dictate the level of curvature in the [math]\displaystyle{ x }[/math] - [math]\displaystyle{ z }[/math] and [math]\displaystyle{ y }[/math] - [math]\displaystyle{ z }[/math] planes respectively. This is an elliptic paraboloid which opens upward for c>0 and downward for c<0. The hyperbolic paraboloid (not to be confused with a hyperboloid) is a doubly ruled surface shaped like a saddle. In a suitable coordinate system, a hyperbolic paraboloid can be represented by the equation : [math]\displaystyle{ \frac{z}{c} = \frac{y^2}{b^2} - \frac{x^2}{a^2}. }[/math] For c>0, this is a hyperbolic paraboloid that opens down along the x-axis and up along the y-axis (i.e., the parabola in the plane x=0 opens upward and the parabola in the plane y=0 opens downward).