Why can you turn clothing right-side-out?

This is probably a bad thing to post on a thread about visualizing inverting a surface, but since I've been making my clothes for over 2 decades, I had to check this out. So I took off my trousers and pinned the cuffs together along the circumference (it just so happens that I'm making a new winter coat, so I had pins handy), matching the seams to each other. I grabbed the cuffs and pulled one leg up through the other. The result is that the pinned cuffs sit right at the crotch seam -- there is no way to completely invert the trousers any more than this, and I don't think it would be possible even if the pants had a higher lycra content, as there is no way to get the cuffs THROUGH the crotch to complete the inversion. However, if I grab the pinned cuffs through the waist band and flick the trousers away from me, they turn right side out with a lot less effort than it takes to turn them inside out.<p>Also, all of the cash fell out of my pockets.

An impressive layman indeed, knowing to post a question to StackExchange under Topology.<p>And I mean that sincerely - that page has some pretty awesome 'layperson'-level (as much as it can get, I suppose) information on topology and manifolds in particular, for a an interested onlooker.<p>Typical classy HN stuff :)

Any discussion that can include the phrase <i>...consider that if you had a stretchy pair of toroidal pants with vertical stripes...</i> is alright by me!

That was an impressive answer from Ryan Budney! ... Then I clicked to his homepage and discovered he is a math professor with interest in knots. I love the internet.

That this is #1 is heartwarming evidence that HN has not even approached the general vicinity of the proverbial shark, let alone jumped it.

I made a small search on youtube to see some videos related to turning a sphere inside out. Please have a look at this gem : <a href="http://www.youtube.com/watch?v=R_w4HYXuo9M#" rel="nofollow">http://www.youtube.com/watch?v=R_w4HYXuo9M#</a> Especially the snelpiller's comment

I wish HN would show the sub-domain (math.stackexchange.com) because at first I thought there was a new "fashion" SE and I was starting to feel sick. Glad I clicked through though, very interesting stuff.

Once you've got one hole you can just consider it like a sack, all the others are superfluous.

Weird, this link continually crashes Firefox 3.6.8 on Windows Server 2008.

google explains it <a href="http://video.google.com/videoplay?docid=-6626464599825291409#" rel="nofollow">http://video.google.com/videoplay?docid=-6626464599825291409...</a>