Sitting at a wobbly table? Fix it with math

We've all been there: you're at a restaurant, sitting down for a nice dinner, and the table wobbles back and forth, interrupting your dinner or spilling your water glass.

It turns out that mathematicians have considered this problem, and figured out a solution. What you do is slowly rotate the table a quarter turn, and at some point during that turn, the table must reach a stable position:

Of course there are some qualifiers here: it only works for a table that has four legs in a flat plane — not for one with a single central post, or one with one leg significantly shorter than the others. But for regular old tables, it's a neat trick for keeping impressing your friends, and keeping your dinner in place.

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