Hyperboloid of one sheet: hyperbolic cross-sections

The details are in a Mathematica demo.

(Please be patient while the applet processes mucho compressed data.)

Put the mouse cursor inside the box below and the figure will rotate and animate. You can grab it, turn it, spin it with the mouse. Double-click the left mouse button to toggle the animation. Drag the mouse horizontally with the rightt button pressed to pass through frames of the animation.
This image was produced using Mathematica and converted to the animation with LiveGraphics3D.