Tape Loop with a Half Twist

It’s called a Mobius strip.

Nineteenth-century mathematician August Ferdinand Mobius didn’t invent it, he just studied it closely.

I’ve always been fascinated by the thing. It’s simple: make like you’re creating loops for a paper garland, get distracted, and tape the wrong edges together. Like so:

wrong-from-the-start
Notify the HR department.

Now take two drawing implements of differing colours. Use one to draw a line down the centre of the loop’s outside, and the other to draw a line down the centre of its inside. Draw until the colour meets its starting point.

whos-in-whos-out
Correct: black inside, blue outside. Mobius: Blue.

As you can see, the Mobius strip isn’t behaving very well: one colour did both sides before meeting itself.

Never mind. You’ve decided these loops are too wide for the garland. Snip them along their freshly-drawn centre lines, then, to make two loops.

roll-play
Correct: two loops of regulation width and diameter. Mobius: one loop of regulation width, double diameter.

Maybe the scissors aren’t feeling too well today? Let’s try that once more, just to be sure.

division-and-expansion1
Correct: four slimline loops, comprising two coloured and two plain. Mobius: One double-diameter slimline plain loop twined with one double-diameter slimline  coloured loop.

Uh-oh. The garland department union is crying foul, because the Mobius loop received only one cut while the regulation loops were given two cuts, one for each loop. The union demands that each of the two Mobius loops be cut, to keep pace with the proper loops. Here goes:

mobius-bow

We’ve ended up with three double-slim, double-diameter, plain loops intertwined with one double-slim, double-diameter, coloured loop. Kinda pretty, isn’t it?

this-wont-hurt-a-bit
As for you four, excellent job! To reward you, we promise to cut and retape only three of you in order to proceed with the fabrication of slimline garland.

8 Responses to Tape Loop with a Half Twist

  1. lolarusa says:

    Nicely presented.

  2. lavenderbay says:

    Thanks, Lolarusa! Who knew paper garlands could be so subversive?

  3. hello lavenderbay its dennis the vizsla dog hay is it troo that if yoo pass sumthing thru the inside of a mobius strip it goze to the fifth dimenshun nevr to return??? and if so hay trouble come heer i hav sumthing for yoo to luk at ha ha ok bye

  4. lavenderbay says:

    That’s an interesting question, Dennis! I’m not sure. Maybe you could ask your dada how many dimensions are in a one-sided object like a Mobius strip, and calculate it from there.

  5. I remember making those back when I was in… public school… I think it was elementary. Oh… to do arts and crafts again… I miss being young-er.

  6. lavenderbay says:

    I like the way you qualify the last word in your comment, Urban Thought! 🙂
    A sneaky way to be young-er is to show the little ones — maybe you’ve got nieces and nephews or little cousins? — tricks like these at family gatherings. How about… hmm, lemme do this one for today’s entry!
    I also love reading well-written, well-illustrated children’s books; reading to a youngster makes the indulgence appear much more respectable.

  7. almostgotit says:

    I LOVE children’s books. I’ll even read them when my kids aren’t interested.

    I love your mobius strip art, too. I’ll have to show this to my 12-yr-old…

  8. lavenderbay says:

    Depending on whether you have a budding artist/sociologist/philosopher/rebel on your hands, Almostgotit, you might also show her the subtext sneakily included in this piece, in the form of the photo titles that appear when you mouse over them. Enjoy!

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