a list compiled by Alex Kasman (College of Charleston)

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Three Cornered Wheel (1963)
Poul Anderson
(click on names to see more mathematical fiction by the same author)

Sometimes a surprising mathematical fact will inspire a science fiction story to illustrate it. I suspect that is what happened with this story that comes up with a contrived circumstance in which the plot depends upon the existence of wheels that are not circular but nevertheless support an object placed on top at a fixed height as they revolve.

Contributed by Stephen C. Locke

A vessel lands on a planet where circles are religious icons and cannot be used for mundane purposes. The crew needs to transport replacement parts over a long distance and hits on the idea of using constant width rollers (replacing them as they become too rounded).

Here is the relevant excerpt (page 53 of my copy):

(quoted from Three Cornered Wheel)

"Draw an equilateral triangle, ABC. Put the point of your compasses on A and draw the arc BC. Move to B and describe AC, then to C and describe AB. Round off the corners. The resulting figure has constant width. It will roll between two parallel lines tangent to it maintaining that tangency for the whole revolution. As a matter of fact, the class of constant-width polygons is infinite. The circle is merely a limiting case."

The story apparently first appeared in Astounding Science Fiction in 1963 but was most recently republished in the collection called Trouble Twisters.

For a non-fictional approach to the same subject, you can read Ivars Peterson's article at the MAA website.

Contributed by Deborah Newbury

Just saw a video of the National Museum of Math in NYC. They have square-wheeled tricycles that reminded me of a story by Poul Anderson that revolved around a wheel that wasn't based on a circle. When I did a search to get the name of the story, your site popped up. What a find! thanks.

Contributed by Deborah Newbury

I already voted on this about a year ago. I am re-reading "Three Cornered Wheel" and stopped to look up 'constant width polygons'. This YouTube video not only shows you how to make them, but demonstrates them as well.

More information about this work can be found at
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Works Similar to Three Cornered Wheel
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. Eve Times Four by Poul Anderson
  2. Axiom of Dreams by Arula Ratnakar
  3. Paint ‘Em Green by Burt Filer
  4. The Crazy Mathematician by Ralph Sylvester Underwood
  5. Project Flatty by Irving Cox Jr.
  6. The Second Moon by Russell R. Winterbotham
  7. The Long Slow Orbits by H.H. Hollis
  8. Love and a Triangle by Stanley Waterloo
  9. The Island of Five Colors by Martin Gardner
  10. The Library of Babel by Jorge Luis Borges
Ratings for Three Cornered Wheel:
RatingsHave you seen/read this work of mathematical fiction? Then click here to enter your own votes on its mathematical content and literary quality or send me comments to post on this Webpage.
Mathematical Content:
4/5 (3 votes)
Literary Quality:
2.67/5 (3 votes)

GenreScience Fiction,
MotifAliens, Religion,
TopicGeometry/Topology/Trigonometry, Real Mathematics,
MediumShort Stories,

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Exciting News: The 1,600th entry was recently added to this database of mathematical fiction! Also, for those of you interested in non-fictional math books let me (shamelessly) plug the recent release of the second edition of my soliton theory textbook.

(Maintained by Alex Kasman, College of Charleston)