/sci/ - Science & Math

No, but I can feel the rhythm!

yes.

If we suppose that different shapes of drums produce different sound waves, then theoretically, we can distinguish what drum's shape might be.. We just haven't done any studies on such topic because its a waste of time

>>4171304
>implying
:D

Not always, but usually. There exist continous families of manifolds who's spectral analysis makes them indistinguishable, but these have high levels of symmetry, so for most practical purposes you can

>>4171314
elaborate in detail, please.

Feynman could

ever heard a square drum. sounds retarded. like you.

>>4171323
I can't, I haven't studied the course yet, it is next term, but here is the description from the cambridge course:

Spectral Geometry (L24)
D. Barden
The aim of this course is to give an overview of the work that has blossomed in response to Mark Kac’s
naive sounding question, posed in 1966: ‘Can one hear the shape of a drum?’ In other, more general,
words can one determine the geometry of a Riemannian manifold from the spectrum, the set of eigenvalues
together with their multiplicities, of the Laplacian operator. The answer is
unsurprisingly, no: many pairs, and even continuous families of manifolds, have since been constructed
that are isospectral (have the same spectrum) yet are not isometric. BUT
surprisingly, almost yes: these examples are very special, usually highly symmetric, so that it is still
possible that generically (a word that may be defined to suit the context) manifolds are spectrally
determined. In fact this has already been shown to be the case in certain contexts.
Contents
Chap 1: Definitions and basic results.
Chap 2: Computation of Spectra: flat tori and round spheres. Spectral determination of 2-
dimensional flat tori. Examples of isospectral but non-isometric pairs of 4-tori and of
planar domains with Dirichlet boundary conditions.
Chap 3: The Heat kernel and some spectrally determined geometric properties.
Chap 4: Sunada’s Theorem. The trace formula and the residuality of ‘bumpy’ metrics.
Chap 5: Riemannian surfaces. The use of Sunada’s techniques to construct isospectral nonisometric
pairs of Riemann surfaces, with particular attention to those of low genus.
Chap 6: Wolpert’s Theorem that generic Riemann surfaces are spectrally determined.
Chap 7: More general examples of isospectral non-isometric manifolds.

>>4171331
kkk,thx

>>4171297
>Can you hear the shape of a drum?
Certainly. With stereoscopic hearing and specialized sections of the brain, you could easily process the aural input to produce a fully detailed image of the object and it's attributes, like bats and dolphins can.
This same idea is how we can do things like Radar and the like.

Normal humanity can't though, because oru primary sense is our vision, not our hearing. This could be altered, but haven't found a commercial use for this yet that wouldn't suffer from the issues of sensitivity: enhanced hearing means everything is louder, and our eardrums are not specialized enough to handle the constant stress, which is why rock-concert-goers are known to lose their hearing faster than most.

>>4171355
Wrong, two drums of different shapes can have the same sound

Yes, different shaped drums are acutally used to help determine hte size and shape of the universe, based on thier sound waves or some shit.

No

>>4171369

well then you could still discern at least one of the shapes of the drum.

>>4171297
What's really awesome about this problem is that you can answer it with origami. pic related, you can prove these are isospectral with basic linear algebra and orifuckingami

ok it wont let me upload the picture but just wikipedia it if you're interested.


Also there are several isospectral higherdimensional manifolds we know of

>>4171301
>>4171301

damn hippies...

and this would be a waste of time to research... unless we all pitch in to fund it... hurp durp