The wobbly table

My kitchen table wobbles. It has four legs, and one of them does not touch the floor. A table with three legs never wobbles, because three points always lie in one flat plane, but a fourth point may not.

My table has $4$ legs, and one does not touch the floor. A table with $3$ legs never wobbles: $3$ points always lie in one plane, but the fourth may not.

Legs $n$, plane $\Pi$: $n=3\Rightarrow \exists !\Pi$ (no wobble). With $n=4$ not always.

To mend it I first measured the gap under the short leg. I slid in sheets of card, each half a millimetre thick. Six sheets fitted and a seventh did not, so the gap is about three millimetres.

Sheets of $0.5$ mm. Six fitted: $6\times 0.5=3$ mm. A seventh did not: $7\times 0.5=3.5$ mm. So the gap $g$ is $3\le g<3.5$, about $3$ mm.

Sheet $t=0.5$: $6t=3$ fitted, $7t=3.5$ did not, so the gap $g$ obeys $3\le g<3.5$.

I folded a strip of card into six layers, which is six times half a millimetre, three millimetres, and glued it under the leg.

A strip folded in $6$ layers is $6\times 0.5=3$ mm thick. I glued it under the leg.

Six layers: $6t=3$.

The table no longer wobbles. The repair took five minutes and cost nothing, and it left a small lesson: measure the gap first, then choose the fix.

No more wobble. Time: $5$ min, cost: $0$. Lesson: measure the gap first, then choose the fix.

Time $5$ min, cost $0$.