[tzahola]

Now do it with a mug.

[ihaveajob]

All the pictures in that link already show a mug.

[delecti]

A mug is topologically equivalent to a bagel or donut or torus.

[tzahola]

T-topologically w-what??

I mean yeah, that was the point of my remark.

To write something on topic as well:

There was a fun little challenge on puzzles.stackexchange I think, which relied on the same construction as this article. I couldn’t find it, but it went like this:

“You’re stuck on top of a tall building with nothing but a saw. There’s a ladder fastened to the side of the building, but it’s unfortunately not long enough to reach the ground; in fact it goes about half the height of the building from the top. Challenge is to get on the ground “safely”. You can cut into the ladder with your saw in any way you like and you can assume that the resulting pieces will be rigid, but won’t break under load.”

[chopin]

As far as I can tell this challenge would not require a twisted cut.

[tzahola]

Please elaborate!

[Crespyl]

I think it would be possible to slice the ladder exactly in half, down its length, right?

Each rung would go from a cylinder to a half-cylinder, but should still be rigidly connected to either side of the ladder all the same.

[Retra]

The problem is then you have two short ladders. You throw your two half ladders off the roof and they don't magically stand end-to-end for you. You have to cut with a twist to ensure the last rungs are entangled with each other so the half-ladders are hooked together. Then you can hang one off the other and reach the ground.