Vibration revelations: Geometric spectral theory
This year the Isaac Newton Institute for mathematical Sciences in Cambridge hosted a research programme called Geometric spectral theory and applications. It's motivated by a question that was posed by the physicist Mark Kac back in 1966: can you hear the shape of a drum?
The question leads to surprisingly rich mathematics that has a huge rage of applications. Broadly speaking it's about figuring out what vibrations associated with a (mathematical) object can tell you about the object itself. The following content gives a little more insight.
Can you hear the shape of a drum?
The sound of a plucked string depends on how long it is, so you can hear the length of a string. But can you hear the shape of a drum?
Can you see the sound of a drum?
If you sprinkle sand on a vibrating plate it forms the most beautiful patterns. We explore why that happens, what it has to do with mathematical pioneer Sophie Germain, and how the question opens up a huge range of maths.
Catching waves with the Laplacian
The Laplacian operator turns up all over maths. Here's a reasonably light-touch introduction and a look at why it forms part of the wave equation.
The harmonics of a string
When you pluck a guitar string it vibrates at many resonant frequencies at once. What might that look like? Find out with our animation.
This content forms part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from the collaboration here.
The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. Visit www.newton.ac.uk to find out more.
