Wilfred Thinking Aloud

On the stability of four feet tables

While I was digging up some information about influenza in Europe (my entire family, including myself have been sick for some days), I ran into this publication. The author prooves that any four-feet table can be put into a stable position by simply rotating it. Don't ask what this has to do with influenza. I find this an amazing discovery; it's just so simple, that I would never have expected that it could be proven mathematically.

You can read more about this in Nature online (http://www.nature.com/news/2005/051024/full/051024-3.html) This is the abstract of the original publication, following by an excerpt of the introduction.

"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."

"Anybody eating lunch or drinking coffee at the terrasse of the CERN cafeteria has had the following problem. Most of the time the table is not in a stable equilibrium position. It rests on 3 feet and with very little energy it can be made to oscillate so that part of your coffee is spilled at best on the saucer or worse on the table. Why is this? Not because the table is not well built but because the ground is very irregular. Many years ago I thought about this problem, and in a relatively idealized situation I proved that by “rotating” the table (“rotating” is to be explained later) one could find an equilibrium position if the local slope is less than 15 degrees. In practice I did many times the experiment outside the CERN cafeteria, and even though the conditions of the theorem are not really satisfied - the feet are thick, the ground is sometimes discontinuous, but on the other hand, the legs of the tables have some elasticity - I have always succeeded in finding an equilibrium position. I think that my early sketch of a proof dates back from 1995. I presented a tentatively “serious” (but partly incorrect ) proof in 1998 at a seminar at I.H.E.S. in Bures Sur Yvette but it was never written for some serious personal reason."