Slicing a Torus

main radius

1

tube radius

0.3

torus opacity

plane slope

plane opacity

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.

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.

External Links

Torus (Wolfram MathWorld)

Permanent Citation

Borut Levart

"Slicing a Torus"
http://demonstrations.wolfram.com/SlicingATorus/
Wolfram Demonstrations Project
Published: September 28, 2007