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A toric section is a curve obtained by slicing a torus (generally a horn torus) with a plane. A spiric section is a special case of a toric section in which the slicing plane is perpendicular to both the midplane of the torus and to the plane .

Consider a torus with tube radius . For a cutting plane parallel to the -plane, the toric section is either a single circle (for ) or two concentric circles (for ). For planes containing the z-axis, the section is two equal circles.

Toric sections at oblique angles can be more complicated, passing from a crescent shape, through a U-shape, and into two disconnected kidney-shaped curves.

Certain toric sections with cutting plane tangent to the torus along the circumference of its central hole, as illustrated above, resemble (but are not equivalent to) a lemniscate curve. However, in the special case of a torus with parameters , the toric section when the cutting plane is tangent to the torus along the circumference of its central hole becomes exactly a lemniscate with half-width

See also

Cassini Ovals, Conic Section, Cross Section, Cylindric Section, Ellipsoidal Section, Lemniscate, Spheric Section, Spheroidal Section, Spiric Section, Torus

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Cite this as:

Weisstein, Eric W. "Toric Section." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ToricSection.html

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