Differential Geometry and Geometric Structures
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Students' Work: Planar Sections of a Torus


A ring torus has a bitangent plane, i.e. a plane that touches in two distinct points. Cutting a ring torus with one such a plane gives two circles, which are known as Villarceau circles. Their common points are the points of tangency.
A Villarceau circle can also be obtained as the intersection of the torus with a particular sphere. The Villarcreau circle is a great circle on this sphere.

Created by Martin Ehrmann (2015) using POV-Ray - The Persistance of Vision Raytracer.

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Planar Sections of a Torus
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Last modified on February 18th, 2016.