The Wobbly Table Theorem

There’s a theorem I have recently come across that is much along the same lines as the Pancake Theorem or the Ham Sandwich Theorem. It’s called the Wobbly Table Theorem (by some). Basically it states that if you’re at a four legged table that does rest evenly on the floor due the fact that floor is slightly uneven, you can rotate the table around until eventually all four legs will rest on the ground. The proof of this fact depends on one of my favorite theorems. I used to have a series of Favorite Theorems, but it is faded into oblivion. This post will hopefully bring back those theorems. Perhaps tomorrow you can expect one on this: The Intermediate Value Theorem.

At any rate, here are a couple of references on the Wobbly Table Theorem. I’m not completely satisfied with the proofs I’ve found here. When I have time, I’ll come back and explain why.

- Wobbly table hasn’t got a leg to stand on
- On the stability of four legged tables
- Turning the tables: feasting on a mathsnack

HT: Gaussian Nodes

I knew this, but not as a theorem. Just as practical knowlege gained from setting at too may wobbly tables over a lifetime, and rotating them until they didnt wobbly. (limited only by the available space to rotate said table) But, a folded napkin or piece of paper, preferable cardboard, works, too.

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For square tables, the result must somehow be related to the following conjecture: For any continuous function defined on the unit circle, there must be 4 points separated by exactly 90 degrees each where the value of the function is the same at all four points.

Once the result is know for square tables, you can generalize to rectangular tables by a scaling transformation in one direction.

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