Hear See Think

Everting the punctured torus and unpunctured sphere

idran:

intothecontinuum:

This animation shows a punctured torus being turned inside-out.
So in principle, if you connected the cuffs of your pants together you could still turn them inside-out. Try it!

The other interesting bit is you’ll notice this reverses the directions of the stripes, from being around the hole to being “parallel” to it.  (I don’t know enough topology to know if there’s specific terms for those directions, unfortunately.)

I would call the ‘perpendicular to the hole’ direction ‘longitudinal’, and the ‘parallel to the hole’ direction ‘equatorial’.  Sweet .gif!  What’s really brain-busting is that you can turn an unpunctured sphere inside out, as this .gif shows:

                               

Here’s an amazing video explanation of how this works: