Toric section
A toric section is an intersection of a
Mathematical formulae
In general, toric sections are fourth-order (
Spiric sections
A special case of a toric section is the spiric section, in which the intersecting plane is parallel to the rotational symmetry axis of the torus. They were discovered by the ancient Greek geometer Perseus in roughly 150 BC.[2] Well-known examples include the hippopede and the Cassini oval and their relatives, such as the lemniscate of Bernoulli.
Villarceau circles
Another special case is the Villarceau circles, in which the intersection is a circle despite the lack of any of the obvious sorts of symmetry that would entail a circular cross-section.[3]
General toric sections
More complicated figures such as an annulus can be created when the intersecting plane is perpendicular or oblique to the rotational symmetry axis.
References
External links
- "The toric section: intersection of a torus with a plane" at "worlds of math and physics"