On Mon, 12 May 2008 09:40:00 -0400, mimus <tinmimus99@[EMAIL PROTECTED]
>
wrote:
>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
<THWACK>
--
dave hillstrom mhm15x4 zrbj
"i believe that the word "****head" has become so wide spread and
nearly meaningless as to qualify as a metavariable, similar to "foo"
and "bar". and that it should uphold the responsibilities and enjoy
the privileges of the new office. here here!!"
-dave hillstrom
|
