Re: topology with interesting elastic cord.

Narasimham schrieb:

http://board-2.blueweb.co.kr/user/math565/data/math/knot.jpg

What trick? A part is shrunk/removed from outer ring portion in the
third and fourth pics of OP, redrawn here on a cone with hole:

http://img340.imageshack.us/img340/5619/minaringszf0.jpg


Ok, agreed, but ... try to tell somebody who distrusts
mathematics and mathematicians. You will find this species
in your neibourhood.

And then you will recognize that they think you are a bit
weird and trying to pull their leg. They say: c'mon, that's
the usual trick, haha, but as you can see - this is impossible.

I had made such a fruitless attempt to convince my wife of
this lovely trick to work. And I think I found a neat expla-
nation as well: At first you see two holes and you can "walk
around" freely:

:
: x
: x
: .--- x ---.
: _____| x | Loop A
: | | x |
: | '---------'
: | x
: | x
: | x
: | .--- x ---.
: |_____| x | Loop B
: | x |
: '---------'
: x
: x
: x
:

The nice trick (why not call it a trick? It's a good one) is
to have the two rings coplanar:

:
: x
: x
: .------- x -------.
: | .--- x ---. |
: |___| x | |
: | | x |A |
: | '---------' |B
: | x |
: '-----------------'
: x
: x
: x
:

Now you can walk around the xxxxx stick as before. But ...
there is an obstacle now when you try to walk around xxxxxx
starting in the loop B in the outer ring!

Bill, I hope you like the pictures I taylored ;-)

Best regards,
Rainer Rosenthal
r.rosenthal@xxxxxx

.

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