How was this infinite sequence of numbers found? (non-commutative geometry )

[Heidi]

Hi Pfs,
I read these slides:
https://indico.math.cnrs.fr/event/782/attachments/1851/1997/Connes.pdf
It is about non commutative geometry (Alain Connes)
After Shapes II, you see a the plots of the square roots of a sequence of numbers given below:
5/4, 2, 5/2, 13/4 ....
I think that they are the solutions of laplacian equation related to the shape of the "drums" above. that is to say the frequencies one can get when hitting this drums.
How to retrieve this infinite sequence?
It is at page 50
thanks

 

[Heidi]

In this article Connes gives an example of two isospectral drums (which are non connex).
One drum with a triangle and a quare and the other with a rectangle and a different triangle.
I found this
https://math.libretexts.org/Bookshe...ons/6.01:_Vibrations_of_Rectangular_Membranes
explaining how to get the possible frequencies emitted by a square or rectangular drum.
Do you know what are the frequencies ommitted by a trangular drum (half a square)?

 

[Heidi]

I found the answer here
https://www.iosrjournals.org/iosr-jm/papers/Vol14-issue4/Version-2/B1404020509.pdf

 

[berkeman]

Thread closed for Moderation...

 

[berkeman]

Since the OP has found their answer, this thread can be closed now.