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Thanks very much.
This is effectively very helpfull.
I cut such a hole out of a sheet and turned inside part by 180=B0. This yie=
lds 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 starte=
d 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 th=
e selfintersection starts to take place. And this details interest me. Ever=
ybody knows the beautyfull youtube about the inversion of a sphere. Im look=
ing for a film of this quality to show all details exactely of the sewing.
Thanks again and kind regards
Ed
----- Original Message -----=20
From: Andrey=20
To: 4D_Cubing@yahoogroups.com=20
Sent: Sunday, December 09, 2012 3:20 PM
Subject: [MC4D] Re: Seed a moebius strip to a hole in a sphere
=20=20=20=20
There is very easy way to attach moebius strip in its classic form to the=
edge of hole in sphere.=20
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 o=
f sphere by the small arc) and rotate it to 180 deg so that its former inte=
rnal surface be on the outer side of sphere and external - on the inner sid=
e. You can see that edge of the hole now looks exactly like the edge of moe=
bius stripe (if they have the same orientation). Now just attach stripe to =
sphere - and you'll get cross-cap model of the projective plane.=20
Andrey
--- In 4D_Cubing@yahoogroups.com, "Eduard"
>
> Seed a moebius strip to a hole in a sphere. This is pronounced very eas=
ely. 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 t=
he sphere. And now comes the crucial moment. I have to grip the opposite bo=
rder of the moebiusband and to travel to the opposite side of the hole in t=
he 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 t=
his 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 crois=E9). In s=
uch a movie I would perhaps see when the chirality of the used moebius stri=
p is lost, the cross-cap having no chirality.
> I fear that there exists no youtube with this animation. Or somebody kn=
ows it?
>
=20=20
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charset="iso-8859-1"
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>
/DIV>
d inside=20
part by 180=B0. This yields a 1-dimensional boundery which is the same as f=
or a=20
moebius strip. This is a big step for "understanding" the passage from "sph=
ere=20
with hole plus moebiusstrip --> sphere with cross-cap".V>
old all=20
parts together and started to mentally sew. All is very clear for 90% of th=
e=20
way. But then all gets more and more crunched and it is not "just an=
=20
attaching". At this moment the selfintersection starts to take place. And t=
his=20
details interest me. Everybody knows the beautyfull youtube about the inver=
sion=20
of a sphere. Im looking for a film of this quality to show all details exac=
tely=20
of the sewing.
0px; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px">
m:=20
href=3D"mailto:andreyastrelin@yahoo.com">Andrey
href=3D"mailto:4D_Cubing@yahoogroups.com">4D_Cubing@yahoogroups.com <=
/DIV>
20=20
PM
strip=20
to a hole in a sphere
There is very easy way to attach moebius strip in its classic form to =
the=20
edge of hole in sphere.
Make not circular, but horse-shoe-like hole. =
Take=20
part of sphere that is "half-inside" of this hole (it looks like a circle=
=20
attached to other part of sphere by the small arc) and rotate it to 180 d=
eg so=20
that its former internal surface be on the outer side of sphere and exter=
nal -=20
on the inner side. You can see that edge of the hole now looks exactly li=
ke=20
the edge of moebius stripe (if they have the same orientation). Now just=
=20
attach stripe to sphere - and you'll get cross-cap model of the projectiv=
e=20
plane.
Andrey
--- In
,=20
"Eduard" <ed.baumann@...> wrote:
>
> Seed a moebius str=
ip to=20
a hole in a sphere. This is pronounced very easely. But it is difficult t=
o=20
follow the whole process mentally.
> After half of the process you =
get=20
to the opposite side of the hole in the sphere. And now comes the crucial=
=20
moment. I have to grip the opposite border of the moebiusband and to trav=
el to=20
the opposite side of the hole in the sphere where the seeding started in =
order=20
to make he first seeding step of the second half of the process bringing=
=20
together the gripped border and the still unseeded part of the border of =
the=20
hole in the sphere. In doing this I transport all the seeded neighbouring=
and=20
this makes selfpenetration necessary. This important moment should shown =
in a=20
beautiful animation. At the end we have a so called "cross-cap" (Kreuzhau=
be,=20
bonnet crois=E9). In such a movie I would perhaps see when the chirality =
of the=20
used moebius strip is lost, the cross-cap having no chirality.
> I =
fear=20
that there exists no youtube with this animation. Or somebody knows=20
it?
>
------=_NextPart_000_0006_01CDD62F.4E1A0EF0--
From: "Eduard Baumann" <ed.baumann@bluewin.ch>
Date: Sun, 9 Dec 2012 17:25:51 +0100
Subject: Re: [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 = There is very easy way to attach moebius strip in its classic form to = There is very easy way to attach moebius strip in its classic form to =
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This film asserts to do the job:
http://math.arizona.edu/~rta/013/bethard.steven/moebiustocrosscheck.mov
out of
http://math.arizona.edu/~rta/013/bethard.steven/transform.html
Im not convinced. The selfintersection doesn't form.
----- Original Message -----=20
From: Andrey=20
To: 4D_Cubing@yahoogroups.com=20
Sent: Sunday, December 09, 2012 3:20 PM
Subject: [MC4D] Re: Seed a moebius strip to a hole in a sphere
=20=20=20=20
There is very easy way to attach moebius strip in its classic form to the=
edge of hole in sphere.=20
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 o=
f sphere by the small arc) and rotate it to 180 deg so that its former inte=
rnal surface be on the outer side of sphere and external - on the inner sid=
e. You can see that edge of the hole now looks exactly like the edge of moe=
bius stripe (if they have the same orientation). Now just attach stripe to =
sphere - and you'll get cross-cap model of the projective plane.=20
Andrey
--- In 4D_Cubing@yahoogroups.com, "Eduard"
>
> Seed a moebius strip to a hole in a sphere. This is pronounced very eas=
ely. 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 t=
he sphere. And now comes the crucial moment. I have to grip the opposite bo=
rder of the moebiusband and to travel to the opposite side of the hole in t=
he 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 t=
his 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 crois=E9). In s=
uch a movie I would perhaps see when the chirality of the used moebius stri=
p is lost, the cross-cap having no chirality.
> I fear that there exists no youtube with this animation. Or somebody kn=
ows it?
>
=20=20
------=_NextPart_000_001D_01CDD632.3C53DBD0
Content-Type: text/html;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable
>
.mov">http://math.arizona.edu/~rta/013/bethard.steven/moebiustocrosscheck.m=
ov
p://math.arizona.edu/~rta/013/bethard.steven/transform.html>
sn't=20
form.
0px; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px">
m:=20
href=3D"mailto:andreyastrelin@yahoo.com">Andrey
href=3D"mailto:4D_Cubing@yahoogroups.com">4D_Cubing@yahoogroups.com <=
/DIV>
20=20
PM
strip=20
to a hole in a sphere
the=20
edge of hole in sphere.
Make not circular, but horse-shoe-like hole. =
Take=20
part of sphere that is "half-inside" of this hole (it looks like a circle=
=20
attached to other part of sphere by the small arc) and rotate it to 180 d=
eg so=20
that its former internal surface be on the outer side of sphere and exter=
nal -=20
on the inner side. You can see that edge of the hole now looks exactly li=
ke=20
the edge of moebius stripe (if they have the same orientation). Now just=
=20
attach stripe to sphere - and you'll get cross-cap model of the projectiv=
e=20
plane.
Andrey
--- In
,=20
"Eduard" <ed.baumann@...> wrote:
>
> Seed a moebius str=
ip to=20
a hole in a sphere. This is pronounced very easely. But it is difficult t=
o=20
follow the whole process mentally.
> After half of the process you =
get=20
to the opposite side of the hole in the sphere. And now comes the crucial=
=20
moment. I have to grip the opposite border of the moebiusband and to trav=
el to=20
the opposite side of the hole in the sphere where the seeding started in =
order=20
to make he first seeding step of the second half of the process bringing=
=20
together the gripped border and the still unseeded part of the border of =
the=20
hole in the sphere. In doing this I transport all the seeded neighbouring=
and=20
this makes selfpenetration necessary. This important moment should shown =
in a=20
beautiful animation. At the end we have a so called "cross-cap" (Kreuzhau=
be,=20
bonnet crois=E9). In such a movie I would perhaps see when the chirality =
of the=20
used moebius strip is lost, the cross-cap having no chirality.
> I =
fear=20
that there exists no youtube with this animation. Or somebody knows=20
it?
>
------=_NextPart_000_001D_01CDD632.3C53DBD0--
From: "Eduard Baumann" <ed.baumann@bluewin.ch>
Date: Sun, 9 Dec 2012 18:12:42 +0100
Subject: Re: [MC4D] Re: Seed a moebius strip to a hole in a sphere
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The question is very polular.
Here is a beautyfull picture of Bianca Violet:
It is not sufficient to follow only the 1-dim curve in space when you sew.
You must manage the neighbourhing tissue to the sewing! And exactly this is=
the real hard work in real sewing.
Ed
----- Original Message -----=20
From: Andrey=20
To: 4D_Cubing@yahoogroups.com=20
Sent: Sunday, December 09, 2012 3:20 PM
Subject: [MC4D] Re: Seed a moebius strip to a hole in a sphere
=20=20=20=20
There is very easy way to attach moebius strip in its classic form to the=
edge of hole in sphere.=20
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 o=
f sphere by the small arc) and rotate it to 180 deg so that its former inte=
rnal surface be on the outer side of sphere and external - on the inner sid=
e. You can see that edge of the hole now looks exactly like the edge of moe=
bius stripe (if they have the same orientation). Now just attach stripe to =
sphere - and you'll get cross-cap model of the projective plane.=20
Andrey
--- In 4D_Cubing@yahoogroups.com, "Eduard"
>
> Seed a moebius strip to a hole in a sphere. This is pronounced very eas=
ely. 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 t=
he sphere. And now comes the crucial moment. I have to grip the opposite bo=
rder of the moebiusband and to travel to the opposite side of the hole in t=
he 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 t=
his 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 crois=E9). In s=
uch a movie I would perhaps see when the chirality of the used moebius stri=
p is lost, the cross-cap having no chirality.
> I fear that there exists no youtube with this animation. Or somebody kn=
ows it?
>
=20=20
------=_NextPart_001_000F_01CDD638.C83D36E0
Content-Type: text/html;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable
>
Violet:space=3D0=20
alt=3D"" align=3Dbaseline src=3D"cid:ADF7B670A65D4BF387D3B90014E26D1F@Eduar=
dII"=20
width=3D572 height=3D450>
w only the=20
1-dim curve in space when you sew.
hing tissue=20
to the sewing! And exactly this is the real hard work in real=20
sewing.
0px; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px">
m:=20
href=3D"mailto:andreyastrelin@yahoo.com">Andrey
href=3D"mailto:4D_Cubing@yahoogroups.com">4D_Cubing@yahoogroups.com <=
/DIV>
20=20
PM
strip=20
to a hole in a sphere
the=20
edge of hole in sphere.
Make not circular, but horse-shoe-like hole. =
Take=20
part of sphere that is "half-inside" of this hole (it looks like a circle=
=20
attached to other part of sphere by the small arc) and rotate it to 180 d=
eg so=20
that its former internal surface be on the outer side of sphere and exter=
nal -=20
on the inner side. You can see that edge of the hole now looks exactly li=
ke=20
the edge of moebius stripe (if they have the same orientation). Now just=
=20
attach stripe to sphere - and you'll get cross-cap model of the projectiv=
e=20
plane.
Andrey
--- In
,=20
"Eduard" <ed.baumann@...> wrote:
>
> Seed a moebius str=
ip to=20
a hole in a sphere. This is pronounced very easely. But it is difficult t=
o=20
follow the whole process mentally.
> After half of the process you =
get=20
to the opposite side of the hole in the sphere. And now comes the crucial=
=20
moment. I have to grip the opposite border of the moebiusband and to trav=
el to=20
the opposite side of the hole in the sphere where the seeding started in =
order=20
to make he first seeding step of the second half of the process bringing=
=20
together the gripped border and the still unseeded part of the border of =
the=20
hole in the sphere. In doing this I transport all the seeded neighbouring=
and=20
this makes selfpenetration necessary. This important moment should shown =
in a=20
beautiful animation. At the end we have a so called "cross-cap" (Kreuzhau=
be,=20
bonnet crois=E9). In such a movie I would perhaps see when the chirality =
of the=20
used moebius strip is lost, the cross-cap having no chirality.
> I =
fear=20
that there exists no youtube with this animation. Or somebody knows=20
it?
>
------=_NextPart_001_000F_01CDD638.C83D36E0--
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Content-Type: application/x-ygp-stripped
Content-Transfer-Encoding: 7bit
Content-ID:
Content-Type: image/jpeg;
name="bianca Kreuzhaube.jpg"
Content-Transfer-Encoding: base64
Content-ID:
------=_NextPart_000_000E_01CDD638.C83D36E0--
From: "Eduard Baumann" <ed.baumann@bluewin.ch>
Date: Sun, 9 Dec 2012 18:20:15 +0100
Subject: Re: [MC4D] Re: Seed a moebius strip to a hole in a sphere
------=_NextPart_000_000A_01CDD639.D63CA130
Content-Type: text/plain;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable
I forgot that inserting pictures is not working here.
Picture on wiki:
http://wiki.superliminal.com/wiki/File:Bianca_Kreuzhaube.jpg
Ed
----- Original Message -----=20
From: Andrey=20
To: 4D_Cubing@yahoogroups.com=20
Sent: Sunday, December 09, 2012 3:20 PM
Subject: [MC4D] Re: Seed a moebius strip to a hole in a sphere
=20=20=20=20
There is very easy way to attach moebius strip in its classic form to the=
edge of hole in sphere.=20
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 o=
f sphere by the small arc) and rotate it to 180 deg so that its former inte=
rnal surface be on the outer side of sphere and external - on the inner sid=
e. You can see that edge of the hole now looks exactly like the edge of moe=
bius stripe (if they have the same orientation). Now just attach stripe to =
sphere - and you'll get cross-cap model of the projective plane.=20
Andrey
--- In 4D_Cubing@yahoogroups.com, "Eduard"
>
> Seed a moebius strip to a hole in a sphere. This is pronounced very eas=
ely. 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 t=
he sphere. And now comes the crucial moment. I have to grip the opposite bo=
rder of the moebiusband and to travel to the opposite side of the hole in t=
he 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 t=
his 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 crois=E9). In s=
uch a movie I would perhaps see when the chirality of the used moebius stri=
p is lost, the cross-cap having no chirality.
> I fear that there exists no youtube with this animation. Or somebody kn=
ows it?
>
=20=20
------=_NextPart_000_000A_01CDD639.D63CA130
Content-Type: text/html;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable
>
rking=20
here.
//wiki.superliminal.com/wiki/File:Bianca_Kreuzhaube.jpg
0px; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px">
m:=20
href=3D"mailto:andreyastrelin@yahoo.com">Andrey
href=3D"mailto:4D_Cubing@yahoogroups.com">4D_Cubing@yahoogroups.com <=
/DIV>
20=20
PM
strip=20
to a hole in a sphere
the=20
edge of hole in sphere.
Make not circular, but horse-shoe-like hole. =
Take=20
part of sphere that is "half-inside" of this hole (it looks like a circle=
=20
attached to other part of sphere by the small arc) and rotate it to 180 d=
eg so=20
that its former internal surface be on the outer side of sphere and exter=
nal -=20
on the inner side. You can see that edge of the hole now looks exactly li=
ke=20
the edge of moebius stripe (if they have the same orientation). Now just=
=20
attach stripe to sphere - and you'll get cross-cap model of the projectiv=
e=20
plane.
Andrey
--- In
,=20
"Eduard" <ed.baumann@...> wrote:
>
> Seed a moebius str=
ip to=20
a hole in a sphere. This is pronounced very easely. But it is difficult t=
o=20
follow the whole process mentally.
> After half of the process you =
get=20
to the opposite side of the hole in the sphere. And now comes the crucial=
=20
moment. I have to grip the opposite border of the moebiusband and to trav=
el to=20
the opposite side of the hole in the sphere where the seeding started in =
order=20
to make he first seeding step of the second half of the process bringing=
=20
together the gripped border and the still unseeded part of the border of =
the=20
hole in the sphere. In doing this I transport all the seeded neighbouring=
and=20
this makes selfpenetration necessary. This important moment should shown =
in a=20
beautiful animation. At the end we have a so called "cross-cap" (Kreuzhau=
be,=20
bonnet crois=E9). In such a movie I would perhaps see when the chirality =
of the=20
used moebius strip is lost, the cross-cap having no chirality.
> I =
fear=20
that there exists no youtube with this animation. Or somebody knows=20
it?
>
------=_NextPart_000_000A_01CDD639.D63CA130--