Can One Hear the Shape of a Drum? [pdf]

https://www.maa.org/sites/default/files/pdf/upload_library/22/Ford/MarkKac.pdf

by luu • 5 years ago

41 16 5 years ago

danbo• 5 years ago

This is one of my favorite problems :) It's so easy to state to people and surprisingly wasn't solved in the 2 dimensional case until 1992!

I also like how unrealistic the "drumheads" proposed in the proof were: https://en.wikipedia.org/wiki/Hearing_the_shape_of_a_drum

im3w1l• 5 years ago

Regarding realism, I wonder if it's possible to hear the difference between drums if you assume dampened vibration.

readingnews• 5 years ago

Interestingly, to me at least, I knew a local music store that made their own instruments for years, and had a kick drum shaped almost exactly like the one on page 1 of the pdf linked to (like a kidney bean). Of course, the head was ancient, as the creator had (IIRC) REMO put their heads on the hoops that he custom bent and sent to them.

Sounded different than a normal drum. Was pink sparkle coated, so perhaps that had something to do with it :)

The drum kit is still in the shop to this day (crazy old guy wants far too much for anything in the shop, as it has been there for an eternity, and well, all old is expensive, right?) I think about that set every now and then, as I myself was interested at one time.

dasKrokodil• 5 years ago

You could look for an old Trixon drumset if you want an oddly-shaped bass drum:

https://www.trixondrums.de/trixon/trix249.htm

evouga• 5 years ago

Still unsolved for 2-manifolds embedded in 3D I believe.

You can’t hear the shape of a drum. But can you hear the shape of a cowbell?

abstrakraft• 5 years ago

You have to really explore the space.

btilly• 5 years ago

I thought it would be a link to https://www.jstor.org/stable/29775597?seq=1.

I heard about this problem from David Webb (one of the people who found that the answer was no) back when I was a grad student at Dartmouth College.

hardmath123• 5 years ago

Relatedly: Can one hear the fate of a coin? https://cs.stanford.edu/~kach/can-one-hear-the-fate-of-a-coi...

Slow_Hand• 5 years ago

Reminds me of my time in music school. The ear training department had a special resident visiting that week and their skill was such that someone joked you could jingle the change in your pockets that person could tell you how much you had and in which denominations.

gbrown2• 5 years ago

Obligatory: https://youtu.be/bkJZbyrfx-Q

It’s really too bad that PBS canceled infinite series.

yesenadam2• 5 years ago

I might click if you say what the link is.

Talanes• 5 years ago

They do tell you it's from the PBS Infinite Series, if only in an indirect way. The exact video is "Can We Hear Shapes?"

jacobolus• 5 years ago

More recently Kelsey Houston-Edwards has been writing for Quanta: https://www.quantamagazine.org/authors/kelsey-houston-edward...

gbrown2• 5 years ago

Cool, didn’t know that.

A_No_Name_Mouse• 5 years ago

Related: can you hear the temperature of water? https://m.youtube.com/watch?v=Ri_4dDvcZeM

Can One Hear the Shape of a Drum? [pdf]

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