Slicing a DoughnutThe usual slicing sequence for a torus has four distinct critical levels: a minimum, two saddles, and a maximum. The sequence shown here is unusual in that it has only three critical levels: the two saddles are at the same height, half way through. This occurs only if the torus is tilted at exactly the right angle; and if the ratio of the major and minor radii of the torus is just right, then the level set at this height is formed by two perfect circles (the second slice in this sequence). This image is as one of three slicing sequences that form the Torus Triptych, which appeared in the art show Surfaces Beyond the Third Dimension. Movies of the slicing sequence, and the details of the mathematics are available in the virtual version of the show.


