
Why can you turn clothing right-side-out? - niyazpk
http://math.stackexchange.com/questions/2755/why-can-you-turn-clothing-right-side-out
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elptacek
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.

Also, all of the cash fell out of my pockets.

~~~
ElbertF
_So I took off my trousers..._

You're on the internet. Why are you wearing pants?

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elptacek
Because I have kids.

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shrikant
An impressive layman indeed, knowing to post a question to StackExchange under
Topology.

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.

Typical classy HN stuff :)

~~~
throw_away
I think that it's just tagged 'topology' by 26 people. The original question-
poser may not have known the term.

~~~
cruise02
If you click on the edited date on Stack Exchange sites you can see the
revision history. That one shows that Qiaochu Yuan changed the tag from
"geometry" to "topology".

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

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eitally
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.

~~~
zackham
I took 3 terms of discrete math from him at the University of Oregon a few
years back. He was a great instructor and really smart guy that knows more
about knots than I realized could be known at the time.

~~~
shadowsun7
I'd love to know more about knots. Some links, please?

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Natsu
You want to look up "knot theory." This should get you started, at least:

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

<http://www.math.unl.edu/~mbrittenham2/ldt/knots.html>

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

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ritonlajoie
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 :
<http://www.youtube.com/watch?v=R_w4HYXuo9M#> Especially the snelpiller's
comment

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duck
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.

~~~
Fargren
What exactly would be wrong with a "fashion" SE? I'd find it quite useful.

~~~
duck
Nothing at all. I was referring to it being posted on HN along with the ever
expanding topics.

~~~
ebtalley
point in case, I got chided for posting a tex question on se instead of
tex.se. Silly but that one irked me, tex looks a lot like code to me. On the
other hand I did get prompt replies.

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

~~~
yummyfajitas
Not necessarily. For all reasonable articles of clothing, yes, it's true.
That's because clothing is designed to enclose an interior which is isomorphic
to a sphere [1]. Thus, clothing is simply a sphere with holes.

But there are plenty of hypothetical clothes for which this isn't true.
Consider a mobius strip - like a sack, there is only one hole, but a mobius
strip isn't a sack (and you can't patch it shut).

[1] I don't want to think about clothing for which this isn't the case, since
it would involve the digestive tract.

~~~
Retric
A real world example of a diffrent topology is is a dress whose straps
intercect with one wrapping around the other so they from an X on someones
back.

~~~
yummyfajitas
It sounds like you are describing a racerback:

[http://www.zadehome.com/images/product/Racerback_Nightie_2_M...](http://www.zadehome.com/images/product/Racerback_Nightie_2_Main.png)

But I think that falls into the category of "sack with a couple more holes".

~~~
Retric
That picture is a "sack with a couple more holes" however if rather than cloth
connecting the straps they tied together in a knot. In that case the knot is a
topologically distant feature which is maintained regardless how you deform
the garment.

I can't find a picture of it. However while this is still a "sack with a
couple more holes"
[http://s7.kmart.com/is/image/Sears/049B018579550001?hei=500&...](http://s7.kmart.com/is/image/Sears/049B018579550001?hei=500&wid=500&op_sharpen=1)
if you picture having that strap be wrapped around at the point of
intersection it can still be unwound. However, if you form a slip knot at the
intersection it can not be removed by deforming the garment.

~~~
yummyfajitas
I think you are correct. My mistake, I didn't properly visualize what you were
describing.

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

~~~
RyanMcGreal
Off-topic: why are you browsing the internet on a server?

~~~
arethuza
To find Wubi?

~~~
ritonlajoie
Who is Wubi (is that a meme ?)

~~~
arethuza
It's a rather neat installer for Ubuntu that installs Linux on top of a
working Windows system - allowing you to dual boot. The Windows install
remains intact.

<http://wubi-installer.org/>

~~~
ritonlajoie
thanks!

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larsalan
google explains it
[http://video.google.com/videoplay?docid=-6626464599825291409...](http://video.google.com/videoplay?docid=-6626464599825291409#)

