Turning Tables

A complex proof leads to a simple fix.

- Ivars Peterson

You’re sitting at a table that wobbles so much it makes you splash your soup or scramble your texting. You suspect that either the floor is not flat or the table’s legs are not all the same length.

You could move to another table, if there’s one available, and hope the problem doesn’t repeat itself. Or you could wedge a wad of paper under one of the table’s legs to see if you can even things up.

If the problem is an uneven floor and the table has four equal legs arranged in a square, mathematicians have come up with another possible solution. Simply rotate the table about its center, without moving it sideways. You’ll quickly find a position in which the table no longer wobbles.

How Did That Work?