Can anyone offer a concise, convincing explanation for why cutting a Mobius strip along a line, not midway but rather one-third of the width of the strip, and eventually joining back to itself, produces two linked, twisted loops, one long, one short:

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![MobiusThird][1]
^{(Image from [this web site](http://www.wikihow.com/Explore-a-Mobius-Strip).)}

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I am not seeking a proof, but rather an explanation that could convince essentially anyone paying sufficient attention. Especially the lack of symmetry in the result can be surprising.

Consider it a teaching challenge. :-)

Can anyone offer a concise, convincing explanation for why cutting a Möbius strip along a line, not midway but rather one-third of the width of the strip, and eventually joining back to itself, produces two linked, twisted loops, one long, one short:

---

![MobiusThird][1]
^{(Image from [this web site](http://www.wikihow.com/Explore-a-Mobius-Strip).)}

---

I am not seeking a proof, but rather an explanation that could convince essentially anyone paying sufficient attention. Especially the lack of symmetry in the result can be surprising.

Consider it a teaching challenge. :-)