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Slicing a Torus

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A plane cuts a torus, going through its centroid and a horizontal line. The intersection is shown as a thick line. You can change the torus dimensions and the slope of the plane.

Contributed by: Borut Levart (September 2007)
Open content licensed under CC BY-NC-SA

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Details

Snapshot 1: The plane is almost tangent to the torus in two places. Can you find the area of the resulting region(s)?

Snapshot 2: Vertical intersection of a horn torus that has equal radii.

Snapshot 3: Intersecting a spindle torus, where the tube radius is greater than the main radius.

Source: "A Strange Way to Slice a Doughnut." From MathForum.

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