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."
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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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