Message #2525

From: Andrey <andreyastrelin@yahoo.com>
Subject: Re: Seed a moebius strip to a hole in a sphere
Date: Sun, 09 Dec 2012 14:20:01 -0000

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.

Andrey

— In 4D_Cubing@yahoogroups.com, "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?
>