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So after watching the famous video on youtube How to turn a sphere inside out I noticed that the sphere is deformed into 8 bulges in the process. Is there something special about the number 8 here? Could this be done with any number of bulges, including 2?

Image:

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Video: How to Turn a Sphere Inside Out

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  • $\begingroup$ I don't understand in this matter much, but as far as I know, the process would be much faster using 8 bulges rather than 2 $\endgroup$ – DanielY Aug 25 '13 at 14:26
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No, 8 isn't special beyond it being the choice they made for that specific video.

The software the group wrote to make that video allowed you to choose that parameter arbitrarily. I bet if you spent some time digging you could find that software somewhere on the internet, and create your own eversion videos with a different choice of the number of corrugations.

You can find a (modified) version of the source code here: http://profs.etsmtl.ca/mmcguffin/eversion/

as well as commentary from Silvio Levy on the choice of number of strips.

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    $\begingroup$ So if I'm interpreting this correctly, it's an open question? There could exist eversions with fewer bulges but no one is sure? $\endgroup$ – Kieran Cooney Aug 27 '13 at 17:58
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    $\begingroup$ Such eversions exist but whether or not the software actually produces them is not known. If you think through the argument Thurston gives in the outside-in video, it works with any number of corrugations. But the software has limitations so what it does exactly if you specify only two, I don't know. I think I used to know but I've forgotten! $\endgroup$ – Ryan Budney Aug 27 '13 at 18:01

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