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.

THINGS TO TRY

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

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.

RELATED LINKS

    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.