On Mon, 12 May 2008 18:47:24 -0400, dave hillstrom wrote:
> 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>
THE MOEBIUS DAM BROKE
RUN TO THE UPSTREAM SIDE
--
tinmimus99@[EMAIL PROTECTED]
11 or maybe 12
mp 10
mhm 29x13
"You are either insane or a fool."
"I am a sanitary inspector."
< _Maske: Thaery_
|
