Hyperboloid
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In mathematics, a hyperboloid is a quadric, a type of surface in three dimensions, described by the equation
(hyperboloid of one sheet),
or
(hyperboloid of two sheets)
If, and only if, a = b, it is a hyperboloid of revolution. A hyperboloid of revolution of one sheet can be obtained by revolving a hyperbola around its transverse axis. Alternatively, a hyperboloid of two sheets of axis AB is obtained as the set of points P such that AP−BP is a constant, AP being the distance between A and P. Points A and B are then called the foci of the hyperboloid. A hyperboloid of revolution of two sheets can be obtained by revolving a hyperbola around its focal axis.
A hyperboloid of one sheet is a doubly ruled surface; if it is a hyperboloid of revolution, it can also be obtained by revolving a line about a skew line.
A degenerate hyperboloid is of the form
if a = b then this will give a cone, if not then it gives an elliptical cone.
A notable (and recognizable) use of a hyperboloid structure is in the cooling towers utilized by power stations. This shape can be built with straight steel beams, and allows minimisation of wind cross-section while retaining structural integrity with minimal material.[1]
