The Möbius Strip


Have you ever been to a “mystery spot,” someplace where gravity and sense don’t seem to apply? 

The Möbius Strip is sort of a paper version of a Mystery Spot. 

If you didn’t make one of these mysterious objects way back in grade school, here’s your chance.

You’ll need:

Paper, scissors, tape or stapler, a pencil

Start by cutting a narrow strip of paper.  Something about 1”-1.5” wide and the standard 11” long works well. 

Now put the two ends together overlapping, as if to fasten this into a loop BUT before you fasten them, give one of the paper-ends a 180º twist, so the “back” of one end meets the “front” of the other.  Fasten the ends together with tape or a staple.  It should look something like this:

The twist in this one is visible between the two arrows.  What we see as the top side of the paper at the green arrow becomes the back by the time it gets to the red arrow.

Left to its own devices, the Möbius strip will lay in a curly way that resembles a Figure 8 from some angles.

Now comes the fun stuff.  Starting where ever you please, put your pencil-point down on the inside of the strip and begin drawing a line down the middle of the strip — going the long way and without lifting your pencil.  You’ll come back to where you started and your lines will join, but when they do, note that your line is drawn on BOTH sides of the paper, which you know you never flipped over.

The 180º twist has the effect of turning the paper for you.  Because you have the equivalent of one perpetual side of paper-space, the Möbius strip is a symbol of continuity, infinity, even eternity.

And we see one version daily, usually without knowing it.
Take your paper Möbius strip and flatten it out neatly, so it looks something like this:

Recognize it yet? 

How about if it looks like this? 

The recycling symbol is based on the Möbius Strip, a graphic way of saying “What goes around, comes around.”

The Möbius Strip was named for August Ferdinand Möbius (1790 - 1868), a German astronomer and mathematician who created his first strip in September of 1858.  Unknown to Möbius, another mathematician, Johann Benedict Listing, had independently crafted his own twisted strip in July of that same year. 

The artist M. C. Escher worked repeatedly with geometrical forms, including some beautiful versions of the Möbius strip.

KNITTERS!   See A Treasury of Magical Knitting by Cat Bordhi (Passing Paws Press, 2001) to learn how to knit a seam-free Möbuis strip!

Illustrations from Math for Mystics, Renna Shesso, Weiser Books, 2007