Toric section

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A toric section is the curve you get when a flat plane cuts a torus, just as a conic section comes from cutting a cone. In general, toric sections are quartic (fourth-degree) curves. A common special case is the spiric section, where the plane runs parallel to the torus’s axis of symmetry. Ancient Greek geometer Perseus studied these around 150 BC. Well-known examples are the hippopede and the Cassini oval, along with related curves like the lemniscate of Bernoulli. Another interesting case is Villarceau circles, where the intersection is a circle even though the cut isn’t obviously symmetric. If the plane cuts perpendicular or obliquely to the axis, more complex shapes such as an annulus can appear.