'On the stability of four legged tables' — by Andre Martin

Long story short: If you're sitting at a four legged table and it wobbles, rotating it (in the horizontal plane, silly billy) will invariably lead to a placement which doesn't wobble.

Here's the abstract of Martin's paper , published in the January 8, 2007 issue of Physics Letters A.

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On the stability of four legged tables

We prove that a perfect four-feet square table, posed in a continuous irregular ground with a local slope of at most 15 degrees can be put in equilibrium on the ground by a "rotation" of less than 90 degrees. We also discuss the case of non-square tables and make the conjecture that equilibrium can be found if the four feet are on a circle.