Is it possible to move the band on the surface so that it's inside out? http://prntscr.com/7pa4qf Also, the red edges are connected and the blue edges are connected, so you can stretch like this: http://prntscr.com/7pa5i8

Question

geerky42 · Answer

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ganeshie8 · Answer

isn't it same as wearing a t shirt the wrong way which is definitely possible ?

empty · Answer

:) Show me a series of steps that can take you from one to the other, if I need to clarify anything please ask, I came up with this question on my own and found it interesting!

ganeshie8 · Answer

lol i have a shirt which i wear it the wrong way some times

empty · Answer

Haha well I say this because this was similar to my intuition, but it turns out that this is false. It's not possible!

empty · Answer

There is a clear geometric reason why it's impossible as well.

Remember, you can't lift the band off the surface, you can only slide it around on it.

dan815 · Answer

it would be the same as turning a sphere inside out, which is not possible in 3D

ganeshie8 · Answer

yeah i saw flatland movie the other day
you will need 1 extra dimension i think

anonymous · Answer

Can the band intersect with itself? i.e. is the situation below possible?|dw:1436156822443:dw|