On Mon, 12 May 2008 23:25:47 +1000, Peter Webb wrote:
> "mimus" <tinmimus99@[EMAIL PROTECTED]
> wrote in message
> news:WZGdnYk6ysIsorXVnZ2dnUVZ_qHinZ2d@[EMAIL PROTECTED]
>
>> On Mon, 12 May 2008 18:36:20 +1000, Peter Webb wrote:
>>
>>> "mimus" <tinmimus99@[EMAIL PROTECTED]
> wrote in message
>>> news:8uCdnZuH0sBCzIDVnZ2dnUVZ_hKdnZ2d@[EMAIL PROTECTED]
>>>
>>>> On Sat, 03 May 2008 21:33:59 -0500, Tim Weaver wrote:
>>>>
>>>>> mimus wrote:
>>>>>
>>>>>> At least, I swept up at least twice as much glass as could possibly
>>>>>> have
>>>>>> been in the original.
>>>>>>
>>>>>> And that's only possible if you do an infinite decomposition of the
>>>>>> object, as exemplified by the Tarski-Banach ball.
>>>>>>
>>>>>> Maybe this is a sign I should mop my kitchen-floor.
>>>>>>
>>>>>> Will I need an infinite mop?
>>>>>
>>>>> Yes, if you have a mobius shaped floor.
>>>>
>>>> Mobius strips are usually finite.
>>>>
>>>> Just unbounded.
>>>
>>> Technical note: Mobius strips have a single boundary.
>>
>> ok fine.
>>
>> (As soon as I read that, my head tried to encompass an unbounded
Moebius
>> strip and couldn't do it.)
>
> Well ...
>
> Imagine the width of the Mobius strip was infinite. You would then have
a
> surface that was unbounded in both directions, finite in one direction
and
> infinite in the other - sort of like a cylinder, but its not. Nor is it
a
> Klein bottle or cross-cap. It can't be embedded in R^3 as it self
> intersects. But it is a reasonable interpretation of an "unbounded
Mobius
> strip", whatever its real name is (if it has one).
<squint>
A single-sided infinite plane or saddle or a single-sided sphere, is
what it looks to me like what we're lookin' at, yes it does. Yes.
I think Klein bottles cheat with that penetration business-- tearing is a
no-no in algebraic topology, even though that's how you make a Moebius
strip, and also in a sense how they work up the matricial representation
of one, swapping connection-points or vertices in the matrix representing
an ordinary strip or tube.
http://www.kleinbottle.com
--
tinmimus99@[EMAIL PROTECTED]
11 or maybe 12
mp 10
mhm 29x13
Given a manifold M with a submanifold N, N can be knotted in M
if there exists an embedding of N in M which is not isotopic to N.
Traditional knots form the case where N = S1 and M = S3.
< Deep wisdom from on high (Wikipedia)
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