One straight cut

Fold a square along both diagonals, so its four edges lie on top of each other, and make one straight cut across them. Unfold: a square falls out. A Japanese puzzle book of 1721 already had this kind of trick, and Houdini printed a one-cut star in 1922.

In 1998–99 three mathematicians — Erik Demaine, Martin Demaine and Anna Lubiw — proved something remarkable: any shape with straight sides, however lopsided, can be freed with one straight cut, if you fold the paper the right way first.

The trick is always the same: fold until every edge of the shape lies on a single line. For a symmetric shape, folding along its mirror lines does it. For a lopsided one you need many folds made at once.