Can you hear the shape of a drum?

[pythagorean]

Can one hear the shape of a drum?

Mark Kac

PDF: MarkKac.pdf (maa.org)




Can you hear the shape of a drum?

Oxford Mathematics

Bach, the Universe & Everything - Can you hear the shape of a drum?

In Bach the Universe & Everything, mathematics and music share the stage. A partnership between Orchestra of the Age of Enlightenment and Oxford Mathematics, these secular services aim to reflect the community atmosphere of the Enlightenment in the 18th Century via the science and musicians of our own.

In this first service of the season, Oxford Mathematician Jon Chapman asks if you can hear the shape of a drum while J.S. Bach and friends keep perfect time.

Running Order:
Prelude: Georg Böhm - Ach wie flüchtig, ach wie nichtig
Polyphony: William Byrd - Haec Dies
Reading: Walt Whitman - Beat! Beat! Drums!
Cantata: Johann Sebastian Bach - Ach wie flüchtig, ach wie nichtig BWV 26 (Chorales and Aria)
Talk: Jon Chapman - Can you hear the shape of a drum?
Postlude: Georg Philipp Telemann - Darmstadt Ouverture TWV 55:g4 'Gasconnade'

[polymath257]

The answer is known to be NO

[polymath257]

Do a search for isospectral domains. There are many known examples.

[pythagorean]

The answer is known to be NO

I was surprised by the piano thingie, about the hammer hitting the string 1/7 of the way down, in order to avoid the 7th harmonic.

We have a piano that we inherited from my mother, that I used to play as a kid.

We had a guy over to repair it so it could be played. He was blind, but was still able to determine "the length of a string", from hearing alone, as the video pointed out, one can hear the length of a string. 

But the piano was constructed during WWII, when wood was in short supply, so certain parts, the parts that take the hardest beating, one per key, were made out of plastic, not wood, so my mother's piano (which I played, or plunked, as a child), had WWII-era plastic parts on each string that needed to be replaced.

The guy replaced the parts (with wood) for the piano keys that didn't work, but he said that eventually, every frickin' key on the piano would eventually have to be fixed with a price tag of $500. (Much more than the value of the piano itself, but I really don't care about that. I just want my old piano to work, and I want it in our finca in Colombia.)

Covid has prevented us from shipping my mother's piano to Colombia (and everything else we own), so maybe at this point we will never do it. (Bad timing, I guess. A lot of plans got messed up.)

Maybe some day we'll return to our pre-covid plan of shipping all of our belongings to the port city of Buenaventura (the Black port along the Pacific coast), but at this late date, who knows?

Neither of us are getting any younger these days.

Of course, there are lots of old pianos in Colombia for cheap, but it's just not the same.

Que pena, huh?...lol.

Canalón De Timbiquí - Que Pena (Vïdeo Oficial)