Hinged puzzle

A puzzle just for your eyes and brain. No paper-cutting. Not until you solve the puzzle, at least 🙂

What shape do we get if we close he hinges clockwise? What if we close them anti-clockwise?

Diabolical Möbius strip variant

Feynman had a punchline about physics:x=maths:y and we think it’s only fair that we should be allowed, too, to do some math with our hands.

Make these out of paper and cut them along the dotted line.

What happens? Why?