Villarceau Circles

It is obvious that every point on a torus is contained in two circles that lie on the torus. Less obvious is the fact that every such point is contained in two additional circles, called the Villarceau circles.

SNAPSHOTS

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DETAILS

This code is taken from S. Wagon, Mathematica in Action, 3rd ed., forthcoming from Springer-Verlag.
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Related Curriculum Standards

US Common Core State Standards, Mathematics