

How to turn a sphere inside out [video] - RevRal
http://video.google.com/videoplay?docid=-6626464599825291409

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andreyf
The group that made this is The Geometry Center at The University of
Minnesota: <http://www.geom.uiuc.edu/>

Another one of their videos is "Not Knot":
<http://www.youtube.com/watch?v=AGLPbSMxSUM>

But I can't find a link to their latest video, called "The Shape of Space".

This was made in 2004. I wonder how much easier it would be to do this with 16
years of advances in 3d modeling?

I wish it were more common...

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Deestan
It seems you can purchase the Shape of Space video, Audio CD, and activity
book from here: <http://www.keypress.com/x5877.xml>

I wish my birthday wasn't so far off. :-(

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adamtmca
That was great, the only thing missing was why. I am sure there are some
interesting applications of the principles they explored and I would have
loved to have heard a few at the end. Feel free to fill me in.

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trafficlight
Exactly. Was there a practical reason for the restrictions on tight bends and
creases? Or was that just to make it interesting?

Edit: Please don't downvote this, I legitimately want to know why.

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leif
When you avoid tight bends and creases (singularities---places where the
derivative vanishes), you have a nice structure on which you can do useful
things like take derivatives, measure lengths and angles, find "straight"
lines, and such. In short, the structure behaves, as long as you're small
enough, just like the space we live in and have studied for centuries.

Now you can extend this notion from a property of one surface to a property of
a continuous family of surfaces, and then look at the beginning and the end
(imagine it varying with respect to time, just like in the video). The
niceness property above, if maintained throughout, gives you more things to
say about what happens to substructures. For example, you can say something
like "if I start with a triangle inside this surface, and morph it into
another surface keeping it nice and smooth the whole time, I'll still get a
triangle, and it won't do {big class of bad things}".

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Rhapso
Twenty minutes well spent.

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devinj
So well spent that it didn't even feel like 20 minutes. This is what videos
should be like-- not essays delivered more slowly and painfully, but real
useful things presented visually in a way that takes full advantage of the
medium.

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tel
Useful?

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devinj
Sorry for the lack of clarity. I meant that the form of presentation should be
useful for aiding understanding, not coincidental. I didn't mean to implythat
the content itself should be useful (in the sense that it has practical
applications). It's OK for a video to just be a little mental puzzle.

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mtalantikite
Rob Kusner over at UMass did work on optimal sphere eversions -- pretty
interesting:

<http://en.wikipedia.org/wiki/Minimax_eversion>

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ars
What's the minimum number of corrugations you can use?

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Devilboy
I think one is enough judging from this video:
[http://www.vidoemo.com/yvideo.php?i=STZjZ2NhcWuRpNE1tY2M&...](http://www.vidoemo.com/yvideo.php?i=STZjZ2NhcWuRpNE1tY2M&turning-
a-sphere-inside-out=)

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ImFatYoureFat
it's like "Math Magic Land" except even more bad ass

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hacer
that was great!

