Generating a Möbius strip with different parameters

Grasshopper
1

Hello! I’ve watched a lot of tutorials about the topic “Möbius Strip.” Unfortunately, I recognized that most of them don’t show actual Möbius strips. Usually, it’s only about wrappings.

I would like to work with this file, but have the transformations based on an actual Möbius strip:
project.gh (16.2 KB)

To understand that this file does not generate Möbius strips, please take a look at this graphic:

image
image728×472 29.1 KB

This is an example how an expected result could look like:

I would be very thankful if someone could help me.

Best wishes :sparkles:

2

Hi @109

The connection between Möbius strips and Möbius transformations is that they were studied and written about by the same guy - August Ferdinand, but they are quite separate and different things.
He was a prolific mathematician and has lots of things named after him (though not as many as Euler - who discovered so many things that we had to start naming some of them after the second person to prove them, to avoid naming everything after him! List of things named after Leonhard Euler - Wikipedia).

It looks like you are interested here in the strip - an example of a non-orientable surface.
Here’s a simple example using rotations.
MoebiusStrip.gh (8.7 KB)

image
image965×544 90.4 KB

3 Likes
4

Updating this example (after some off-thread discussion with @109 ) to show how to make this into a clean manifold solid object:
twist.gh (11.0 KB)

2 Likes
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Thank you so much!