A Stable Table

A four-legged table inevitably wobbles when positioned on an uneven surface such as in a beer garden or an al fresco dining area. Three of the legs will sit on the ground, but the 4th will be above ground and cause the wobble. The usual solution is to stuff something, such as a beer mat or two, under the problem leg.

However, there is a neater solution that will impress your friends – just rotate the table. There will be a rotation at which all four legs will sit firmly on the ground. Rotate the table in small increments so as not to miss this stable point. The table will never need to be rotated more than a quarter turn.

The explanation goes like this:


Let’s identify the legs by colour; red (R), green (G), blue (B) and yellow (Y).

Further, let’s assume R, G and B are on the ground, and it is Y that is above the ground and causing the wobble. This arrangement is indicated on the left side of the picture.

Now, we rotate the table exactly a quarter turn, so each leg moves to the next leg’s position.

But, we still want to keep R, G and B on the ground.

We can only do this in the new rotated position if Y is below the ground. Why? Go back to the starting picture and ignore the colour of the legs. If we want the top right-hand leg on the ground while also keeping the two bottom legs on the ground, then we will need to force the top left leg into the ground.

So, going back to the colour system, the Y leg is above the ground at the start, but would need to be below the ground after the table has been rotated a quarter turn. That must mean that somewhere between these two orientations of the table, the Y leg will undergo a transition from being above the ground to being below the ground. In other words, it will be on the ground.

Given that we are always keeping the other three legs on the ground, this means that all four legs will now be on the ground and the table will be stable.

So, now you can put those beer mats to better use… you might even win a wager that this will work and get a free beer.

PS: The table has to be rotatable (duh) and the ground has to vary in height reasonably smoothly. The problem should be caused by uneven ground, not uneven table-leg length. It works under most real-world situations.

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