Message #2526

From: Eduard Baumann <>
Subject: Re: [MC4D] Re: Seed a moebius strip to a hole in a sphere
Date: Sun, 09 Dec 2012 17:04:52 +0100

Thanks very much.
This is effectively very helpfull.

I cut such a hole out of a sheet and turned inside part by 180°. This yields a 1-dimensional boundery which is the same as for a moebius strip. This is a big step for "understanding" the passage from "sphere with hole plus moebiusstrip –> sphere with cross-cap".
I took a correctly twisted moebius strip hold all parts together and started to mentally sew. All is very clear for 90% of the way. But then all gets more and more crunched and it is not "just an attaching". At this moment the selfintersection starts to take place. And this details interest me. Everybody knows the beautyfull youtube about the inversion of a sphere. Im looking for a film of this quality to show all details exactely of the sewing.

Thanks again and kind regards

—– Original Message —–
From: Andrey
Sent: Sunday, December 09, 2012 3:20 PM
Subject: [MC4D] Re: Seed a moebius strip to a hole in a sphere

There is very easy way to attach moebius strip in its classic form to the edge of hole in sphere.
Make not circular, but horse-shoe-like hole. Take part of sphere that is "half-inside" of this hole (it looks like a circle attached to other part of sphere by the small arc) and rotate it to 180 deg so that its former internal surface be on the outer side of sphere and external - on the inner side. You can see that edge of the hole now looks exactly like the edge of moebius stripe (if they have the same orientation). Now just attach stripe to sphere - and you’ll get cross-cap model of the projective plane.


— In, "Eduard" <ed.baumann@…> 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?