Wednesday, June 17, 2009

Unlinking Torus solution

See the original puzzle

I created a bunch of pictures in Mathematica to illustrate the process of turning the torus inside out.

Spoiler alert!

If you look carefully at the pictures, you'll see that the rings remain linked throughout. And yet, at the end, the red ring is on the inside and the blue ring is on the outside. The resolution to this paradox is that the rings have switched places!

Update: Another intermediate step (hopefully this makes it a little clearer)


Eduard said...

Very beautifull! Two pictures more please between 2 and 3 and between 3 and 4 !

miller said...

I added in one more picture which I hope is a little clearer than the others.

Eduard said...

Perfect! Thanks.

Emily said...

it would be even better if it were a video. I'm only 13 so trying to work this out is difficult; hard; brain popping; impossible. take your pick.

Larry Hamelin said...

YouTube videos.

Google is your friend.

And trust me, Emily, it's just as hard (if not harder) to work this out at 47 as it is at 13.

Larry Hamelin said...

The key to understanding topological transformations in general is to remember that the rules say (counter-intuitively) that it's ok to have surfaces interpenetrate (you can walk through walls); the rules say you can never have discontinutities (corners or infinitely small circles).