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I was reading Sawyer's Prelude to Mathematics, he says that there's one suposed nature's favourite pattern which is:

$$\Delta^2V$$

He also says that this pattern is found in a dozen areas: conection with gravitation, light,sound, heat, magnetism, electrostatics, electric currents, electromagnetic radiation, waves at the sea, the flight of aeroplanes, vibrations of elastic bodies and the mechanics of the atom.

So what is this pattern and how does it works?

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Very often problems are spherically symmetric and one wants to have an operator which does not involve to high derivatives. –  Fabian Sep 13 '12 at 5:06

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up vote 5 down vote accepted

You are probably referring to the Laplace Operator, or Laplacian $\triangledown^2$, or $\Delta$. The article I linked to has a fair bit of information.

It is not clear that Nature plays favourites. But physicists certainly find the Laplacian useful.

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