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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.

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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. The Mathenauts by Norman Kagan
  2. The Library of Babel by Jorge Luis Borges
  3. FYI by James Blish
  4. The Island of Five Colors by Martin Gardner
  5. Tau Zero by Poul Anderson
  6. The Extraordinary Hotel or the Thousand and First Journey of Ion the Quiet by Naum Ya. Vilenkin
  7. Tiger by the Tail by A.G. Nourse
  8. The Kissing Number by Ian Stewart
  9. Pop Quiz by Alex Kasman
  10. The Blind Geometer by Kim Stanley Robinson
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 (1 votes)
Literary Quality:
2/5 (1 votes)

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

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(Maintained by Alex Kasman, College of Charleston)