Paul Bunyan and his blue ox Babe (Matthew High)

A few days ago I read a short story aloud in class. It was “Paul Bunyan Versus the Conveyor Belt” (1949) by William Hazlett Upson.  It’s from a collection called The Mathematical Magpie, which contains many stories that have some tie-in with mathematics. Most of the stories are science fiction or fantasy, which are genres that lend themselves more than most to a mathematically inspired plot.

In “Paul Bunyan Versus the Conveyor Belt,” Paul, along with his trusty side-kick Ford Fordson, is operating a uranium mine somewhere in Colorado. Paul has an old Ford pickup truck named “Babe” which has an attachment that drives a conveyor belt. The conveyor runs in and out of the mine and is used to transport uranium ore. The belt is quite long and has a half twist in it to even out the wear on both sides (how does that work?) making it a Mobius (pronounced moe-BYE-us) strip.

Paper Mobius strip (David Benbennick)

The Mobius strip is named after one of its discoverers, August Ferdinand Möbius who investigated it in 1858. It was independently discovered by Johann Benedict Listing in the same year. The Mobius strip is an example of a chiral structure (it has “handedness”) and a non-orientable surface. It’s a simple thing made by folding a strip of paper over on itself and joining the ends together. The Mobius strip has only one edge and one side. This can be easily proved by drawing a pencil line down the middle of the structure, or along its edge.

Two oppositely folded Mobius strips showing that they are mirror images of each other (non-superimposable). Made from duct tape of course!

In the story, Paul needs to make his conveyor belt longer as the mine gets deeper. Since he knows the belt is a Mobius strip he has an easy way of making it longer–just cut it down the middle lengthwise! That might not produce a real practical belt, but it makes for a good story, especially when Loudmouth Johnson comes along and makes a wager with Paul about what will happen when he cuts the belt, not once but two times.

To make it more fun, the class followed along with Paul by making their own Mobius strips out of paper and cutting them to see what would happen. By the time we were done we had quite a collection of Mobius strips in various colors and lengths, that had been experimentally cut in various ways.

Our Mobius strips hanging on the wall

Studying surfaces and shapes such as the Mobius strip (as well as doughnuts and coffee cups and the like ) is part of the field of mathematics known as topology (not to be confused with the computer science concept of network topology). The Wikipedia entry for topology has a few shortcoming as far as how the references are used, but other than that it is pretty good.  Check out the graphic on the page that proves coffee cups and doughnuts are just variations of the same thing (topologically speaking).