[math-fun] Exhibit for MoMath?
Doug Hofstadter found this nice YouTube: http://www.youtube.com/watch?v=CAkMUdeB06o&sns=em Regardless of its rigor, it makes the statement of the theorem unmistakable and unforgettable. Perhaps adjacent could be the isosceles case, in case anyone thinks it only works for 3-4-5, and the equilateral and obtuse cases, with just enough liquid for the "largest" square, failing dissimilarly. --rwg
Bill, That's a fairly common exhibit that I've seen at many science museums. As you point out, one of its limitations is that it only demonstrates the theorem for a single triangle. For MoMath, I wanted to create all new exhibits, not found anywhere else. So I came up with a variation in which the triangle was adjustable. The C^2 is always the same, but the right angle moves along a semicircle, so the legs can vary and sliding components change the leg squares appropriately. We engineered a way where it was feasible, not with a fluid (which would leak), but with a fixed volume of small beads. In the end it didn't make the final cut of exhibits. However, it's possible it may show up as a replacement exhibit at some time in the future. George http://georgehart.com/ On 12/17/2012 1:03 AM, Bill Gosper wrote:
Doug Hofstadter found this nice YouTube: http://www.youtube.com/watch?v=CAkMUdeB06o&sns=em Regardless of its rigor, it makes the statement of the theorem unmistakable and unforgettable. Perhaps adjacent could be the isosceles case, in case anyone thinks it only works for 3-4-5, and the equilateral and obtuse cases, with just enough liquid for the "largest" square, failing dissimilarly. --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
The other advantage of beads is that whether the depth is properly constant across containers becomes visible --- a fluid mechanism could cheat by varying it, invisibly from the front. WFL On 12/17/12, George Hart <george@georgehart.com> wrote:
Bill,
That's a fairly common exhibit that I've seen at many science museums. As you point out, one of its limitations is that it only demonstrates the theorem for a single triangle. For MoMath, I wanted to create all new exhibits, not found anywhere else. So I came up with a variation in which the triangle was adjustable. The C^2 is always the same, but the right angle moves along a semicircle, so the legs can vary and sliding components change the leg squares appropriately. We engineered a way where it was feasible, not with a fluid (which would leak), but with a fixed volume of small beads. In the end it didn't make the final cut of exhibits. However, it's possible it may show up as a replacement exhibit at some time in the future.
George http://georgehart.com/
On 12/17/2012 1:03 AM, Bill Gosper wrote:
Doug Hofstadter found this nice YouTube: http://www.youtube.com/watch?v=CAkMUdeB06o&sns=em Regardless of its rigor, it makes the statement of the theorem unmistakable and unforgettable. Perhaps adjacent could be the isosceles case, in case anyone thinks it only works for 3-4-5, and the equilateral and obtuse cases, with just enough liquid for the "largest" square, failing dissimilarly. --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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what's wrong with wonderful exhibits that do happen to be elsewhere? the kids who visit moma probably won't see exhibits that are in, say, chicago. i remember two great exhibits from the museum of science and industry in chicago from the 1960's: a) drop a bunch of pingpong balls through a lattice of obstructions into bins at the bottom and watch the bell curve form; b) soap films! bob baillie --- George Hart wrote:
Bill,
That's a fairly common exhibit that I've seen at many science museums. As you point out, one of its limitations is that it only demonstrates the theorem for a single triangle. For MoMath, I wanted to create all new exhibits, not found anywhere else. So I came up with a variation in which the triangle was adjustable. The C^2 is always the same, but the right angle moves along a semicircle, so the legs can vary and sliding components change the leg squares appropriately. We engineered a way where it was feasible, not with a fluid (which would leak), but with a fixed volume of small beads. In the end it didn't make the final cut of exhibits. However, it's possible it may show up as a replacement exhibit at some time in the future.
George http://georgehart.com/
On 12/17/2012 1:03 AM, Bill Gosper wrote:
Doug Hofstadter found this nice YouTube: http://www.youtube.com/watch?v=CAkMUdeB06o&sns=em Regardless of its rigor, it makes the statement of the theorem unmistakable and unforgettable. Perhaps adjacent could be the isosceles case, in case anyone thinks it only works for 3-4-5, and the equilateral and obtuse cases, with just enough liquid for the "largest" square, failing dissimilarly. --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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Bob, That would have been the Mathematica exhibit, by Charles and Ray Eames. I remember seeing it as a kid at the NY World's Fair, and I'm sure it had a positive effect on my interest in math. There's a restored copy on display now at the NY Hall of Science in Queens. http://en.wikipedia.org/wiki/Mathematica:_A_World_of_Numbers..._and_Beyond I agree it is fine to replicate exhibits from elsewhere, but I wanted to create novel ones for MoMath while I had the opportunity and budget. If MoMath creates enough interest, there will be math museums in cities all across the country and the best math exhibits should be replicated widely. George http://georgehart.com/ On 12/17/2012 11:07 AM, Robert Baillie wrote:
what's wrong with wonderful exhibits that do happen to be elsewhere? the kids who visit moma probably won't see exhibits that are in, say, chicago.
i remember two great exhibits from the museum of science and industry in chicago from the 1960's: a) drop a bunch of pingpong balls through a lattice of obstructions into bins at the bottom and watch the bell curve form; b) soap films!
bob baillie ---
George Hart wrote:
Bill,
That's a fairly common exhibit that I've seen at many science museums. As you point out, one of its limitations is that it only demonstrates the theorem for a single triangle. For MoMath, I wanted to create all new exhibits, not found anywhere else. So I came up with a variation in which the triangle was adjustable. The C^2 is always the same, but the right angle moves along a semicircle, so the legs can vary and sliding components change the leg squares appropriately. We engineered a way where it was feasible, not with a fluid (which would leak), but with a fixed volume of small beads. In the end it didn't make the final cut of exhibits. However, it's possible it may show up as a replacement exhibit at some time in the future.
George http://georgehart.com/
On 12/17/2012 1:03 AM, Bill Gosper wrote:
Doug Hofstadter found this nice YouTube: http://www.youtube.com/watch?v=CAkMUdeB06o&sns=em Regardless of its rigor, it makes the statement of the theorem unmistakable and unforgettable. Perhaps adjacent could be the isosceles case, in case anyone thinks it only works for 3-4-5, and the equilateral and obtuse cases, with just enough liquid for the "largest" square, failing dissimilarly. --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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participants (4)
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Bill Gosper -
Fred lunnon -
George Hart -
Robert Baillie