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Tim Martin wrote:
>
> This still needs a bit of work on the handle, but most of it is there.
> Can anyone guess what the molecule is? (it's kind of obvious ;-) )
I have the script for an animation of this chemical (and others for
EtOH and nicotine). I'll render and post them sometime.
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On Thu, 14 Sep 2000 22:12:09 -0700, Anton Sherwood <bro### [at] poboxcom>
wrote:
>now try this one
>http://www.kleinbottle.com/drinking_mug_klein_bottle.htm
Here ya go....need to fill with liquid though, so that you can see
that it is all one surface.
---Oldstench---
Avoid herd mentality.
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Attachments:
Download 'klein.jpg' (39 KB)
Preview of image 'klein.jpg'
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damn i was just toying with the idea of doing the exact same mug!!
(SERIOUSLY!!) - based on the one on that cool geek shopping site :)
Rick
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Psychomek wrote in message <39C16064.AF746828@home.com>...
>
>
>Tim Martin wrote:
>
>> Oldstench wrote in message ...
>> >On Thu, 14 Sep 2000 20:55:30 +0100, "Tim Martin"
>> ><wir### [at] asymptoticcouk> wrote:
>> >
>> >>This still needs a bit of work on the handle, but most of it is there.
Can
>> >>anyone guess what the molecule is? (it's kind of obvious ;-) )
>> >>
>> >>Tim
>> >
>> >Very nice model, and I like the stain on the cd...
>>
>> Thanks. The CD was simply done by putting it straight on the scanner,
>> ring-marks and all. I actually put my drinks on the freeserve CD most of
the
>> time (best use for it).
>
>I think an AOL one would be better.....
I work in a computer repair place, and we used to have a lot more problems
with freeserve screwing up machines - it's the most popular free ISP here in
the UK (no idea why). Actually, I've only got 2 AOL CDs in my collection,
compared to 8 compuserves and 3 freeserves.
Tim
--
email: wir### [at] asymptoticcouk
Website: http://www.alphafish.f9.co.uk/
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>
>Except it's not a real Klein bottle, since POV doesn't work in 4 dimensions.
>Hmmm, anyone care to do a patch? ;-)
>
>Tim
Oldstench is confused...I modeled the mug just as it was shown on the
web-site, didn't know I was supposed to be modeling a 4th dimensional
object.
---Oldstench---
Avoid herd mentality.
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Oldstench wrote in message ...
>
>>
>>Except it's not a real Klein bottle, since POV doesn't work in 4
dimensions.
>>Hmmm, anyone care to do a patch? ;-)
>>
>>Tim
>
>Oldstench is confused...I modeled the mug just as it was shown on the
>web-site, didn't know I was supposed to be modeling a 4th dimensional
>object.
AIUI, a Klein bottle is a 4 dimensional object. What they have on that site
is a 3-dimesional projection of a Klein bottle (Think of trying to draw a
mobius strip on 2D paper). It's as close as you can get in a 3D world, and
it is still a damn fine mug.
Tim
--
email: wir### [at] asymptoticcouk
Website: http://www.alphafish.f9.co.uk/
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Tim Martin wrote:
>
> AIUI, a Klein bottle is a 4 dimensional object. What they have on that site
> is a 3-dimesional projection of a Klein bottle (Think of trying to draw a
> mobius strip on 2D paper). It's as close as you can get in a 3D world, and
> it is still a damn fine mug.
>
> Tim
Not at all, a Klein bottle can exist in 3D space (as the mig
demonstrates). What is impossible is to have a Klein bottle that doesn't
cross itself in 3D space, you need at least 4D for that. As for drawing
a moebius strip on 2D paper, you can't because a moebius strip is a
surface (eg it has 2 dimensions) but the klein bottle is also a surface
and not a volume, that's where your analogy fails...
--
* Doctor Jekyll had something * mailto:ber### [at] inamecom
* to Hyde... * http://www.enst.fr/~jberger
*******************************
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news:39C5F568.1F0BCC30@enst.fr...
> Not at all, a Klein bottle can exist in 3D space (as the mig
> demonstrates).
For a moment this had me very excited and/or confused. I feel it reflects
badly on me that for a moment I genuinly considered the notion that
jet-fighters might well implement Klein bottles and similiar topology in
their design...
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Tom Melly wrote:
>
> news:39C5F568.1F0BCC30@enst.fr...
>
> > Not at all, a Klein bottle can exist in 3D space (as the mig
> > demonstrates).
>
> For a moment this had me very excited and/or confused. I feel it reflects
> badly on me that for a moment I genuinly considered the notion that
> jet-fighters might well implement Klein bottles and similiar topology in
> their design...
Ooops, sorry! Here's what happens when you type too fast ;-))
--
* Doctor Jekyll had something * mailto:ber### [at] inamecom
* to Hyde... * http://www.enst.fr/~jberger
*******************************
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>Tim Martin wrote:
>>
>> AIUI, a Klein bottle is a 4 dimensional object. What they have on that
site
>> is a 3-dimesional projection of a Klein bottle (Think of trying to draw a
>> mobius strip on 2D paper). It's as close as you can get in a 3D world,
and
>> it is still a damn fine mug.
>>
>> Tim
> Not at all, a Klein bottle can exist in 3D space (as the mig
>demonstrates). What is impossible is to have a Klein bottle that doesn't
>cross itself in 3D space, you need at least 4D for that. As for drawing
>a moebius strip on 2D paper, you can't because a moebius strip is a
>surface (eg it has 2 dimensions) but the klein bottle is also a surface
>and not a volume, that's where your analogy fails...
I quote from http://mathworld.wolfram.com/kleinbottle.html :
"A closed nonorientable surface of Euler characteristic 0 (Dodson and Parker
1997, p. 125) that has no inside or outside. It can be constructed by gluing
both pairs of opposite edges of a rectangle together giving one pair a
half-twist, but can be physically realized only in 4-D, since it must pass
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
through itself without the presence of a hole."
The model of the Klein bottle is an immersion of the 4D object in 3D space,
and has to intersect itself just as a 2D projection of a mobius strip has to
intersect itself. As such the 3D Klein bottle isn't a real Klein bottle any
more than a drawing of a mobius strip is a mobius strip.
The issue of volume is a somewhat misleading one, since AIUI topologists
usually deal with infinitely thin sheets and the volumes they enclose,
rather than with solid objects. A surface can be 2D but still require 3
dimensions to exist, as the mobius strip demonstrates, and similarly it can
require 4 dimensions to exist, as in the case of the Klein bottle. I could
be wrong though, I have no formal topological training.
Tim
--
email: wir### [at] asymptoticcouk
Website: http://www.alphafish.f9.co.uk/
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