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Slicing a Doughnut
The 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.
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