4 ms·

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

sz 16y ago
Not true—in the case of a punctured torus (like the shirt with joined sleeves), it's not like a sack at all! It can still be turned inside-out, but it's a little trickier to visualize. You can imagine the hole stretching until you have a pair of identical rings glued together, then it's easy to see that you can shrink the hole the same way except in the other direction. But there's no way to make it look like a sack with holes.
yummyfajitas 16y ago
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.
- deleted 16y ago
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- Retric 16y ago
  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 16y ago
    It sounds like you are describing a racerback: http://www.zadehome.com/images/product/Racerback_Nightie_2_Main.png http://www.zadehome.com/images/product/Racerback_Nightie_2_M... But I think that falls into the category of "sack with a couple more holes".
    - Retric 16y ago
      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&wid=500&op_sharpen=1 http://s7.kmart.com/is/image/Sears/049B018579550001?hei=500&... 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 16y ago
        I think you are correct. My mistake, I didn't properly visualize what you were describing.
  - Das_Bruce 16y ago
    I can't visualise what you've described, can you give an example?

sz 16y ago

Not true—in the case of a punctured torus (like the shirt with joined sleeves), it's not like a sack at all! It can still be turned inside-out, but it's a little trickier to visualize. You can imagine the hole stretching until you have a pair of identical rings glued together, then it's easy to see that you can shrink the hole the same way except in the other direction. But there's no way to make it look like a sack with holes.

yummyfajitas 16y ago

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.

deleted 16y ago
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Retric 16y ago
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 16y ago
  It sounds like you are describing a racerback: http://www.zadehome.com/images/product/Racerback_Nightie_2_Main.png http://www.zadehome.com/images/product/Racerback_Nightie_2_M... But I think that falls into the category of "sack with a couple more holes".
  - Retric 16y ago
    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&wid=500&op_sharpen=1 http://s7.kmart.com/is/image/Sears/049B018579550001?hei=500&... 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 16y ago
      I think you are correct. My mistake, I didn't properly visualize what you were describing.
- Das_Bruce 16y ago
  I can't visualise what you've described, can you give an example?