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From: Andreas Freise <adf@mpq.mpg.de>
Subject: Re: [PIC] Klein Bottle
Date: 1997/09/10
Message-ID: <3416CF70.1051@mpq.mpg.de>#1/1
X-Deja-AN: 271332266
References: <3416BB27.507D@wing.rug.nl>
To: Shimrod <csg824@wing.rug.nl>
Organization: Rechenzentrum der Max-Planck-Gesellschaft in Garching
Newsgroups: alt.ascii-art


Shimrod wrote:
> Here's a Klein Bottle 
[snip]
> 
>          _,-'"`-._
>        ,' , - - . `.
>        ( .       , )
>        |. `.- -,' ,|
>        | `-.:_:,-' |
>        |    : :    |
>        |    : :    |
>        (    : :    )
>         \   ; :   /
>          \,: - :./
>          /`-._.-'\
>         /   ; :   \
>        (    ; :    )
>        |    : :    |
>        |    : :    |
>        | _,-:":-._ |
>        |' ,'- -`. `|
>        ( '       ` )
>        `. ` - - ' ,' mn
>          `-.___,-'   hh
> 

Hm, I try and try but I can't see the Klein Bottle in it.
First the original :

       ,-"~"-.
      /  ._.  \
     :  /   \  : 
     !  !    : !
     ;  !    ; ;
    /    \  / /
   /      \/ /
  /       /`/
 /       / /\
 |     .`-'  |
 |    .'.'   |
 |    : :    |
 |  ..: :..  |
 |.' .' `. '.|
 `\ '     ` /'
   `--___--'  mn


The trick : walk (imagine yourself as an insect) over the bottle
under the bottom and suddenly without any sharp corner you find
yourself inside the bottle. Outside and inside are not 
seperated by a sharp edge like on top of the usual bottle.

Your way of trying it with a symmetry does not work
in my imagination. At least the crucial part cannot be 
seen in your drawing. The cross section has to be splitted
into small parts (at least two) to leave a path for you
(insect ;) to walk on. 

Actually your bottle looks like two rings put together.
But I don't know if I 'get the picture' right.

:)
Andreas
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