Slicing a Torus
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.
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.