This reminds me of the fixed point theorem. Take a sheet of paper, scrumple it however you choose without tearing it. Place it over an unscrumpled copy of the original, without going outside the edges.
Some point in the scrumpled version is exactly above its original position.
How fascinating. One nitpick: my brief wikipedia research tells me that you probably mean the fixed point property, rather than the fixed point theorem, which appears to be a category rather than a specific idea. But then again maybe I've not fully understood. That seems likely.
That's actually an illustration of the Contraction Mapping Principle.
Another way of illustrating it is that if you're in city X and place a map of city X on the ground, then exactly one point on the map will be above the corresponding physical point.
This reminds me that in Argentina in primary school we would make an improvised football (as in: soccer) by crumpling some paper and then wrapping it in scotch tape. It was of course much smaller than the real ball, but it worked surprisingly well (and broken windows were not an issue). Now I know why :-)
If you, like me, wonder how one can even get funding for research on crumpled paper, Prof. Menon's research area is on condensed matter, "primarily on soft-condensed matter systems".
Understanding the physics of why crumpled paper resists with a specific force can help you design vehicle crumple-zone systems in cars which will save occupants from head on crashes into trees, by having the entire engine crumple with a pre defined resistance.
I understand how guessing at the particular pattern of a crumple is a hard physics problem. What I do not understand is why understanding the macro-properties of crumpled paper is a hard physics problem. For example:
"Do the balls absorb vibrations by trapping pressure waves or by dissipating them? Nobody knows, says Menon, 'but it means there are still plenty of beautiful problems to keep me interested'."
This seems like a rather odd thing to say. What does "trapping pressure waves" even mean? Is Menon asserting that, when I take my shipment out of the container, all of the vibration that the package suffered on its journey is still swirling around in all the crumpled paper?
It's laudable to study everyday physics, but at least when it comes to macro-behavior of crumpled paper, these research questions appear laughable.
"What I do not understand is why [several things]..."
"... these research questions appear laughable."
How about before declaring these questions laughable, you try a little harder to understand why they are interesting? For instance, the fact that we don't have computers powerful enough to simply simulate the question being asked provides one clue of a possible reason why this is more interesting than you think.
Either one of "I don't understand this research" or "this research is laughable" I might accept from a given person, but the combination is unpleasant.
[+] [-] ColinWright|14 years ago|reply
Some point in the scrumpled version is exactly above its original position.
[+] [-] jonshea|14 years ago|reply
[+] [-] JonnieCache|14 years ago|reply
[+] [-] noblethrasher|14 years ago|reply
Another way of illustrating it is that if you're in city X and place a map of city X on the ground, then exactly one point on the map will be above the corresponding physical point.
[+] [-] szopa|14 years ago|reply
[+] [-] Jun8|14 years ago|reply
Article passed on the interesting tidbit about Britney Gallivan (http://en.wikipedia.org/wiki/Britney_Gallivan) and her paper folding result.
[+] [-] maeon3|14 years ago|reply
http://en.wikipedia.org/wiki/Crumple_zone
[+] [-] javajosh|14 years ago|reply
"Do the balls absorb vibrations by trapping pressure waves or by dissipating them? Nobody knows, says Menon, 'but it means there are still plenty of beautiful problems to keep me interested'."
This seems like a rather odd thing to say. What does "trapping pressure waves" even mean? Is Menon asserting that, when I take my shipment out of the container, all of the vibration that the package suffered on its journey is still swirling around in all the crumpled paper?
It's laudable to study everyday physics, but at least when it comes to macro-behavior of crumpled paper, these research questions appear laughable.
[+] [-] jerf|14 years ago|reply
"... these research questions appear laughable."
How about before declaring these questions laughable, you try a little harder to understand why they are interesting? For instance, the fact that we don't have computers powerful enough to simply simulate the question being asked provides one clue of a possible reason why this is more interesting than you think.
Either one of "I don't understand this research" or "this research is laughable" I might accept from a given person, but the combination is unpleasant.