Hyperboloid and Hyperbolic Paraboloid
Hyperboloid
It is NOT an acronym of hyperbolic paraboloid.
A hyperboloid is a quadratic surface which may be one-sheeted or
two-sheeted. Rotate a hyperbola about the perpendicular bisector of the line between the foci.
The surface of revolution thus obtained is the one-sheeted hyperboloid.
Rotate a hyperbola about the line joining the two foci.
The surface of revolution thus obtained is the two-sheeted hyperboloid.
If the skirt of the paraboloid is a circle of radius 'a', the equation in Cartesian co-ordinates of the two are:
One-sheeted hyperboloid: 
= 1
= 1Two-sheeted hyperboloid: = – 1
= – 1
Natural cooling towers are designed for hyperboloid shape. The advantages of it are:
i) minimum usage of material
ii) additional structural strength
iii) improved cooling efficiency – as the shape accelerates the upward convective airflow
Hyperbolic paraboloid
The quadratic surface of a hyperbolic paraboloid is given by either of the two Cartesian equations:
i) 
ii) yx = z
The parametric equation is given by
x(u, v) = u
The shape of Pringles potato chip is hyperbolic paraboloid.
