Dancing to the music in higher dimensions

What is the relationship between the shape of a drum and the sound the drum makes?

It turns out that this is quite a complicated question. You can read about the mathematics of drum design, and the discovery that you can't always hear the shape of a drum.

In fact, there is a deep connection between math and music in general. Check out these links at the Math Archive.

You can read more about partial differential equations on the Mathematics: the equations of nature page.