3 ms·

Mathematicians prove that you can deduce the shape of disk based on the frequencies it produces when you hit it with a stick.

by snitty 3y ago

grapescheesee 3y ago
[flagged]
- mdekkers 3y ago
  I’m sorry. As a machine model, I cannot condone acts of violence against disks. Have you tried discussing your differences between you, perhaps with the assistance of some professional mediator?
  - notso411 3y ago
    [dead]
m3kw9 3y ago
Useful as a magic trick, guessing the shape of your disc when you hit it
deleted 3y ago
[deleted]
kadoban 3y ago
I can deduce the disk's shape without even hitting it. It's a disk.
- SomeoneFromCA 3y ago
  [flagged]
gus_massa 3y ago
The first sentense is very misleading: > Is it possible to deduce the shape of a drum from the sounds it makes? That's a known problem with a (very nice) negative answer https://www.ams.org/publicoutreach/feature-column/fcarc-199706 https://www.ams.org/publicoutreach/feature-column/fcarc-1997... IIUC this article is about the problem in the other direction, i.e. from the shape (a disk!) to the frecuencies of the sound (eigenvalues).It's not about an exact calculation, but about an aproximation of them. > The conjecture bears on the estimation of the frequencies of a round drum or, in mathematical terms, the eigenvalues of a disk. From the research paper: > The celebrated Pólya’s conjecture (1954) in spectral geometry states that the eigenvalue counting functions of the Dirichlet and Neumann Laplacian on a bounded Euclidean domain can be estimated from above and below, respectively, by the leading term of Weyl’s asymptotics. <guessing> The Weyl's asymtotics is probably a good estimation of the very high frecuencies/eigenvalues, and the conjeture is probabbly that you can use the estimation as upper or lower bounds instead of just an aproximation.<guessing> [Sorry, not my area and I have not enough time to read the paper.]

Mathematicians prove that you can deduce the shape of disk based on the frequencies it produces when you hit it with a stick.

by snitty 3y ago

Mathematicians prove that you can deduce the shape of disk based on the frequencies it produces when you hit it with a stick.

grapescheesee 3y ago

[flagged]

mdekkers 3y ago
I’m sorry. As a machine model, I cannot condone acts of violence against disks. Have you tried discussing your differences between you, perhaps with the assistance of some professional mediator?
- notso411 3y ago
  [dead]

m3kw9 3y ago

Useful as a magic trick, guessing the shape of your disc when you hit it

deleted 3y ago

[deleted]

kadoban 3y ago

I can deduce the disk's shape without even hitting it. It's a disk.

SomeoneFromCA 3y ago
[flagged]

gus_massa 3y ago

The first sentense is very misleading: > Is it possible to deduce the shape of a drum from the sounds it makes? That's a known problem with a (very nice) negative answer https://www.ams.org/publicoutreach/feature-column/fcarc-199706 https://www.ams.org/publicoutreach/feature-column/fcarc-1997... IIUC this article is about the problem in the other direction, i.e. from the shape (a disk!) to the frecuencies of the sound (eigenvalues).It's not about an exact calculation, but about an aproximation of them. > The conjecture bears on the estimation of the frequencies of a round drum or, in mathematical terms, the eigenvalues of a disk. From the research paper: > The celebrated Pólya’s conjecture (1954) in spectral geometry states that the eigenvalue counting functions of the Dirichlet and Neumann Laplacian on a bounded Euclidean domain can be estimated from above and below, respectively, by the leading term of Weyl’s asymptotics. <guessing> The Weyl's asymtotics is probably a good estimation of the very high frecuencies/eigenvalues, and the conjeture is probabbly that you can use the estimation as upper or lower bounds instead of just an aproximation.<guessing> [Sorry, not my area and I have not enough time to read the paper.]