Spiric section

A spiric section is an intersection of a plane with a torus (σπειρα in ancient Greek), just as a conic section is the intersection of a plane with a cone. They were discovered by the ancient Greek geometer Perseus in roughly 150 BC.

In general, spiric sections are fourth-order (quartic) plane curves of the form

$\left(x^{2}+y^{2}\right)^{2}+ax^{2}+by^{2}+cx+dy+e=0$

Well-known examples include the hippopede and the Cassini oval and their relatives, in which the intersecting plane is parallel to the rotational symmetry axis of the torus. More complicated figures such as an annulus can be created when the plane is perpendicular or oblique to the rotational symmetry axis.