Flatland and the Fourth Dimension

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Objective: Write a story based on the ideas in Flatland that explains the fourth dimension.

Required Reading:

A four-dimensional cube is often called a hypercube. Write a story in which a hypercube tries to describe itself and explain the fourth dimension to a 3-dimensional being (could be a person, a 3-dimensional cube, etc.—you pick). This 3-dimensional being should know nothing about the fourth dimension; if it helps, imagine that the hypercube is talking to you as you were a few weeks ago. What would you need it to explain? You should use as many different mathematical approaches as possible. You do not need to imitate Abbott’s style; you may choose your own genre (see below). You may work in teams of two. You may discuss the mathematics with other folks, but the writing must be your own. You may include pictures if you wish.

Possible genres:

  • A soap opera.
  • A western.
  • A Winnie the Pooh story.
  • A courtroom drama.
  • A Star Wars story.
  • A news topic (CNN?).
  • A comedy.
  • A sequel to Flatland.
  • A musical.
  • Any other genre you can think of that will let you tell your story.


I expect 3-5 pages will be enough to explain things thoroughly. If you think your work needs to be substantially longer or shorter please come talk to me. You will be graded on (1) mathematical content, (2) clarity, and (3) creativity. A person who has never heard of the hypercube should be able to learn something from your paper. This means that your hypercube cannot just show up and say, “Guess what!?! I have 8 cubes and 16 vertices, and I can see that you had pepperoni pizza for lunch. Later, dude!” Your hypercube will need to be patient and use analogies with lower dimensions, slicing, and so forth. You want an explanation, not just a collection of facts.


Thanks to Dr. Catherine Stenson from [Juniata College] in Pennsylvania. This project is heavily based on an assignment Dr. Stenson showed me.

Useful Links

[Some Notes on the Fourth Dimension by David Cervone]