[PIC] Klein Bottle

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
    _
   |    Ascii Dictionary (Collection, Links, ...)    |
 o |      http://www.stud.uni-hannover.de/~freise    |  o
<<.|_                                               _| < >
 |\                                                     |

Here's a Klein Bottle (maybe a double even) based on the one Micheal
Naylor has on his homepage. Basically, it's sortof a 3D moebius ring,
the inside of one bottle is the outside of the other.


         _,-'"`-._
       ,' , - - . `.
       ( .       , )
       |. `.- -,' ,|
       | `-.:_:,-' |
       |    : :    |
       |    : :    |
       (    : :    )
        \   ; :   /
         \,: - :./
         /`-._.-'\
        /   ; :   \
       (    ; :    )
       |    : :    |
       |    : :    |
       | _,-:":-._ |
       |' ,'- -`. `|
       ( '       ` )
       `. ` - - ' ,' mn
         `-.___,-'   hh


-shimrod


Greetz,
-- 
                (`.                 ____________________________
                 \ `.              / __/ / / /     /_  /   /_  /
                  )  `._..---._    \__ \   \ \ \_\ \   \ \ \_\ \
\`.       __...---`         o  )   /___/_/_/_/_/ /_/_/_/___/___/
 \ `._,--'           ,    ___,' Herman Hiddema ----------------------
  ) ,-._          \  )   _,-'   ----------- mailto:shi...@fmf.ml.org  
 /,'    ``--.._____\/--''       http://fmf.ml.org/~shimrod ----------

Shimrod wrote:
> 
> Here's a Klein Bottle (maybe a double even) based on the one Micheal
> Naylor has on his homepage. Basically, it's sortof a 3D moebius ring,
> the inside of one bottle is the outside of the other.
> 
>          _,-'"`-._
>        ,' , - - . `.
>        ( .       , )
>        |. `.- -,' ,|
>        | `-.:_:,-' |
>        |    : :    |
>        |    : :    |
>        (    : :    )
>         \   ; :   /
>          \,: - :./
>          /`-._.-'\
>         /   ; :   \
>        (    ; :    )
>        |    : :    |
>        |    : :    |
>        | _,-:":-._ |
>        |' ,'- -`. `|
>        ( '       ` )
>        `. ` - - ' ,' mn
>          `-.___,-'   hh
> 
> -shimrod

Herman, this is amazing!  I've never seen a representation of a bottle 
this way, but it is beautiful!  It's like you've taken the place where 
the 'neck' "passes through" the bottle and stretched it all around the 
outside, thus creating a radially symettric bottle.  Gorgeous!

Andreas had some question about it, I see, and on further inspection, eu 
may be right.  Trace a path starting on the outside of the upper lobe, 
go up around and inside and you find yourself on the inside of the lower 
lobe.  Keep going and you're back on the outside of the upper lobe 
without ever having touched the other side.  It is not a double moebius 
then.

Does it have an inside and an outside?  I'm not sure anymore what this 
is, but it is exciting!

What I particularly like about it is how it is so suggestive of 
infinity... it's like a 3D infinity sign.

Further, you are too kind to add my initials.  Your bottle is superior.  
Here is a revision of my bottle based on your ideas.



                ,-'"`-.
               /  ._. `\
              :  /  `\  :
              !  !    ! !
              (  )    ; ;
             /    \  / /
            /      \/ /
           /       /`/
          /       / /\
         (      ;`-'  )
         |     : :'   |
         |     : :    |
         | _,-:":-._  |
         |' ,'-  -`. `|
         ( '        ` )
         `. ` -  - ' ,' mn
           `-.____,-'   hh


Great stuff!  Thanks Shimrod!

Michael