A toric section is an intersection of a plane with a torus, just as a conic section is the intersection of a plane with a cone. Special cases have been known since antiquity, and the general case was studied by Jean Gaston Darboux.
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. Well-known examples include the hippopede and the Cassini oval and their relatives, such as the lemniscate of Bernoulli.
General toric sections
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- Brieskorn, Egbert; Knörrer, Horst (1986), "Origin and generation of curves", Plane algebraic curves, Basel: Birkhäuser Verlag, pp. 2–65, doi:10.1007/978-3-0348-5097-1, ISBN 3-7643-1769-8, MR 0886476.
- Schoenberg, I. J. (1985), "A direct approach to the Villarceau circles of a torus", Simon Stevin, 59 (4): 365–372, MR 0840858.
- "The toric section: intersection of a torus with a plane" at "worlds of math and physics"