Why turning a wobbly table can stop it rocking: the quarter-turn proof

Your café table rocks. Before you wedge a folded napkin under a leg, try turning the whole table on the spot. On most floors, somewhere within a quarter-turn, all four legs touch the ground at once.

It isn't luck. Turning a square table by 90° swaps its two diagonals, so whatever made it rock one way now makes it rock the opposite way. Somewhere in between, the wobble has to pass through zero. Drag the table below and find that spot yourself.