Question/Subject:
Hyperbolic Parabaloid (Saddle) Knot
I cannot draw a curved saddle here.
So here is a squared version.
The leftmost and rightmost sections depict square tubes.
The left side of the center section depicts an upsidedown open 'U'channel.
The right side of the center section depicts an upright open 'U' channel.
In the center section:
The outsides of the left sides twist to become the insides of the right side,
thus creating the 'saddle', or hyberbolic parabalolid.
If both the left and right sections are extendend,
so as to join and form a large circular tube,
then the center section shown below becomes a 'knot' in that tube.
__ _ _______ _______ _ _ __
|\_\ |\______\/............| |\_\
|_\_\ |_\______\..._____|_ |_\_\
\ |_| |_______\/_______| \ |_|
\|_| _ |_______/\_______| \|_|
If one could pull a bicycle tire tube inside out,
through a single small hole in that tube,
one would end up with an inside-out tube,
but also with this 'saddle' knot in that (inside-out) tube.
In other words:
The saddle is what the original hole would look like after the 'pull-through'.
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