What’s the point of a Möbius strip? Other than being a cool shape, why/how is it important and what does it help us understand?
In: Mathematics
It’s a cool shape.
It also lets people think of “one sided shape” as a possibility that doesn’t exist in 2 dimensions, which can help people understand 4D space a little better.
There’s also some instances where something goes in a looping circle, which the mobius strip describes pretty handily. And the [wiki page has a bunch of those listed](https://en.wikipedia.org/wiki/M%C3%B6bius_strip#Applications), even if a bunch of those applications are more descriptive “where we find it in nature” instead of “how it can be used”.
But beyond that it’s a cool shape.
Mobius strips are a concrete example of something surprising and strange out of the worlds of higher order geometry and topology (the mathematics of shapes and deformations).
On top of that, the Mobius strip gives us a nice solid example of how spinors work – mathematical objects that require two full rotations to come back to where they started. Before you say wtf (as most people would!), just know that in quantum mechanics, lots of things act this way including the 1/2 spin particles. THey’re also representable with two dimensional complex vectors.
Math is cool – so many bridges and connections to other things that aren’t obviously connected. Either you’re into that sort of thing or you’re not. Saul Goodman.
dont think of mathematical things having a point, think of them as having properties.
these properties define them. the mobius strip is a shape that has only 1 face, and 1 edge. It just exists whether it is useful or not.
A physical mobius strip is just a cool thing, but the properties of a mobius strip pop up everywhere. for example, the votes in a fair election mathematically make a mobius strip, but the outcome is a circle, and the properties of a mobius strip wont let you make it a circle, so a fair voting system is mathematically impossible https://youtu.be/v5ev-RAg7Xs
One of the interesting aspects of shapes that extends far beyond the study of shapes is that we can use them to represent thejr properties.
For example, we use cubes to represent 6 equal possibilities (like in a dice!) or to represent a single unit of 3d space.
We can use Mobius strips to represent things with one side that are still embedded into a higher order.
Such as the imaginary number I, or the state of quantum particles
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