What is a hyperboloid of one sheet?
The one-sheeted hyperboloid is a surface of revolution obtained by rotating a hyperbola about the perpendicular bisector to the line between the foci (Hilbert and Cohn-Vossen 1991, p. 11). A hyperboloid of one sheet is also obtained as the envelope of a cube rotated about a space diagonal (Steinhaus 1999, pp. 171-172).
How do you find the equation of a hyperboloid?
The basic hyperboloid of one sheet is given by the equation x2A2+y2B2−z2C2=1 x 2 A 2 + y 2 B 2 − z 2 C 2 = 1 The hyperboloid of one sheet is possibly the most complicated of all the quadric surfaces.
Does a hyperboloid of two sheets contain lines?
The hyperboloid of two sheets does not contain lines. The discussion of plane sections can be performed for the unit hyperboloid of two sheets with equation . which can be generated by a rotating hyperbola around one of its axes (the one that cuts the hyperbola) in a hyperbola. Obviously, any two-sheet hyperboloid of revolution contains circles.
What is the meaning of hyperboloid?
Definition of hyperboloid. : a quadric surface whose sections by planes parallel to one coordinate plane are ellipses while those sections by planes parallel to the other two are hyperbolas if proper orientation of the axes is assumed. Other Words from hyperboloid Example Sentences Learn More about hyperboloid.
What is a one sheet hyperboloid of revolution?
The more common generation of a one-sheet hyperboloid of revolution is rotating a hyperbola around its semi-minor axis (see picture; rotating the hyperbola around its other axis gives a two-sheet hyperbola of revolution). A hyperboloid of one sheet is projectively equivalent to a hyperbolic paraboloid.
What is the curvature of a hyperboloid of two sheets?
On the curvature of a hyperboloid. Whereas the Gaussian curvature of a hyperboloid of one sheet is negative, that of a two-sheet hyperboloid is positive. In spite of its positive curvature, the hyperboloid of two sheets with another suitably chosen metric can also be used as a model for hyperbolic geometry.