Other Definitions
hyperboloid (dict)
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HyperboloidIn 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, , it is a hyperboloid of revolution. A hyperboloid of one sheet can be obtained by revolving a hyperbola around its transversal 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. A and B are then called the foci of the hyperboloid. A hyperboloid of two sheets can be obtained by revolving a hyperbola around its focal axis. A hyperboloid of one sheet is a 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. See also: ellipsoid, paraboloid.
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