This figure shows a finite portion of hyperboloid of one sheet, together with a portion of one of its tangent planes. The intersection of the hyperboloid and the tangent plane is a reducible plane conic -- accordingly, the union of two lines in the tangent plane. this is
true in situations where where the tangent plane contains some real points
of the surface other than the point of contact. And, in fact, this condition
is satisfied for the hyperboloid of one sheet as well as the hyperbolic
paraboloid.
At least, Since this condition holds for every tangent plane,
the hyperboloid of one sheet is a 1-parameter families of lines on this surface.
two to rotate this figure
(drag it with the mouse, as usual).
Indeed, this is the only way to really see what's happening here.
strongly encouragedClick here to go back to the main drawing of the hyperboloid of one sheet. |

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*I made the figure on this page by substituting my own data in a
*Geometry Center* webpage.*

Prof. Joel Roberts

School of Mathematics

University of Minnesota

Minneapolis, MN 55455

USA

Office: 351 Vincent Hall

Phone: (612) 625-1076

Dept. FAX: (612) 626-2017

e-mail: `roberts@math.umn.edu
http://www.math.umn.edu/~roberts
`