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Issue 17 - Jan 2006

Know your tea times table

Wobbly table A mathematician in Melbourne has applied a mathematical formula to solving one of the most irritating problems in the restaurant; how to stabilise a wobbly table without needing to jam a coaster under one of the legs.

Dr Burkard Polster a researcher of Monash University in Melbourne , Australia and his international colleagues have calculated that simply turning a rectangular table around on most surfaces will cure the wobble.

Ok, so the table might not necessarily end up being totally horizontal, which means your drink may still slide off. But it won't wobble.

"If you've got a rectangular table and you set it down anywhere on the ground chances are, if it has four legs it will wobble," Polster says.

"Just by turning it on the spot you'll find a position where all four legs are on the ground."

But if you are curious as to the mathematics behind such a solution you could do what Polster did himself and apply 'intermediate value theory' to solve the problem. His research uses this theory to pinpoint the process by which the balanced point can be found.

Intermediate value theory relates to the principle that any curve drawn from above an axis to below it will intersect at some stage.

It's the same principle underlying the fact that there will always be two points with exactly the same temperature somewhere on Earth.

Applied to a wobbly table, the intermediate value theory suggests that by rotating the table around its axis it's possible to find a spot where all four legs touch the ground.

"In practice, it does not seem to matter how exactly you turn your table on the spot, as long as you turn roughly around the centre of the table," he says.

Polster says unlike four legs, three will always balance. This explains why you'll rarely encounter a wobbly three-legged stool.

A fourth leg requires what is known as an extra degree of freedom to find stability, and this is provided by rotation.

Give a table a fifth leg, Polster adds, and the chances of finding common ground for all of the legs becomes harder.


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