Superior attachment of Möbius strip In this DIY project, the Möbius strip is used to make a spill-proof coffee cup carrier. The author uses a Möbius strip as the handle of this carrier and says

If you attach a Möbius strip to an object, say a bowling pin, and
  swing it around your head, the twisted strip resists kinking and
  curling, proving itself a superior attachment to a nontwisted one.

Could someone provide a proof or a physical explanation of why the quoted phrase is true?
 A: I suspect that the optimal arrangement is not in fact a Möbius strip but a loop with a full twist in it, and with half of the twist in each of the carrier's vertical sections, like I have plotted with Mathematica below.

Even better would probably be several twists in each vertical section.
The principle of working is as follows. If the loop is untwisted, as below

then it can swing fairly freely if the deformed loop stays in the $X\wedge Y$ plane, but it cannot bend easily out of this plane. This is simply because, if we think of the cross section of the strip of leather, as below:

then its area moment of inertia $I_{YY}$ about the $Y$ axis is greatly more than the area moment of inertia $I_{XX}$ about the $X$ axis. The stiffness of a beam in Euler-Bernoulli and Timoshenko beam theory is $E\,I$ where $E$ is the Young's modulus of the material in question and $I$ the area moment of inertia about the neutral axis of bending.
So, if there is a twist in the beam, then there is always some position along the beam where the relevant area moment of inertia is very small. Try it yourself with a strip of paper with and without twists. You'll find that the twisted one can bend freely in all directions, but the flat one will have a preferred bending plane.
So the question now arises as to why the sold device is a Möbius strip rather than a better design. I suspect this is likely for marketting purposes, not physics. I'm guessing the marketting people think that it sounds slicker to say the design is grounded on the Möbius strip rather than a twisted loop. 
