Message #2523

From: Melinda Green <melinda@superliminal.com>
Subject: Re: [MC4D] Seed a moebius strip to a hole in a sphere
Date: Fri, 07 Dec 2012 14:44:52 -0800

I didn’t find any animations of the construction that you described but
it may be simpler to think of the problem not as filling a hole with a
Möbius strip but rather as a way to seal up a hole by identifying
opposite points. Looked at that way, here are the closest that I can find:
http://www.math.osu.edu/~fiedorowicz.1/math655/classification.html
http://mathworld.wolfram.com/Cross-Cap.html
The answer to your question of when chirality is lost might be to
imagine a circle being twisted into a figure-8 and continuing until it
is back into a circle. Either way you begin to twist it you can see that
chirality is lost at the 180 degree point. Or maybe it only appears that
way when projected from 4D to 3D and the chirality is never really lost?
I don’t know.

I hope that helps.
-Melinda

On 12/7/2012 6:59 AM, Eduard wrote:
> Seed a moebius strip to a hole in a sphere. This is pronounced very easely. But it is difficult to follow the whole process mentally.
> After half of the process you get to the opposite side of the hole in the sphere. And now comes the crucial moment. I have to grip the opposite border of the moebiusband and to travel to the opposite side of the hole in the sphere where the seeding started in order to make he first seeding step of the second half of the process bringing together the gripped border and the still unseeded part of the border of the hole in the sphere. In doing this I transport all the seeded neighbouring and this makes selfpenetration necessary. This important moment should shown in a beautiful animation. At the end we have a so called "cross-cap" (Kreuzhaube, bonnet croisé). In such a movie I would perhaps see when the chirality of the used moebius strip is lost, the cross-cap having no chirality.
> I fear that there exists no youtube with this animation. Or somebody knows it?