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The Mystery

of the


Sealed Box




Fred Henle and Jim Henle


This website is devoted to an investigation of one aspect of plain, ordinary boxes. The aspect is utterly simple but it leads to issues of great complexity. All we will be doing is looking at straight-line paths on the surface of the box, that is, geodesics. We have many questions, and we have some answers.

By way of introduction, we offer---

  • An overview of (sealed) boxes.
  • The motivating context of billiards on rectangles.
  • Graphics programs? which visitors can use to visualize and explore.

We organize our work under these general headings:

And in summary:

Highlights include:

  • A bizarre sort of number theory where 3, 4, and 6 are "relatively prime"---but 3, 4, and 5 are not.
  • An odd use of the Rubik's cube to compute trajectories.
  • A map, the three-coloring of which is equivalent to following a geodesic around the box.
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Page last modified on August 28, 2013, at 11:32 PM