MathFiction: Three Cornered Wheel (Poul Anderson)

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)
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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 www.amazon.com.
(Note: This is just one work of mathematical fiction from the list. To see the entire list or to see more works of mathematical fiction, return to the Homepage.)

Works Similar to Three Cornered Wheel

According to my `secret formula', the following works of mathematical fiction are similar to this one:

Q.E.D. by Bruce Stanley Burdick
Eve Times Four by Poul Anderson
Security by Poul Anderson
Pop Quiz by Alex Kasman
The Masters by Ursula K. Le Guin
Axiom of Dreams by Arula Ratnakar
Paint ‘Em Green by Burt Filer
Dante Dreams by Stephen Baxter
The Maxwell Equations by Anatoly Dnieprov
The Mathenauts by Norman Kagan

Ratings for Three Cornered Wheel:

Ratings

Have 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)

Categories:

Genre	Science Fiction,
Motif	Aliens, Religion,
Topic	Geometry/Topology/Trigonometry, Real Mathematics,
Medium	Short Stories,

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Where are the new works of mathematical fiction?: As you can see from this chronological listing, this database includes many works of mathematical fiction for each year from 1990 to 2025. Strangely, only two are listed for 2026, so far. Either less mathematical fiction is being published than in previous years or I'm just having more trouble finding it. If you know of any works of fiction that should be added to this list, especially recently published ones, please let me know. (Keep in mind that I do not include self-published works or children's fiction that just covers elementary mathematical concepts.) Thanks!

(Maintained by Alex Kasman, College of Charleston)