Re: [math-fun] Exhibit for MoMath?
(Sorry about RoundCube(?) losing the indentation below.) GH>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 (Gaa, now it won't UNindent!) Well, an advantage of several similar mechanisms side by side is that multiple kids can experiment. Pursuing this, repeat the several triangles with their surrounding squares replaced by semicircles and again by regular pentagons, say. A theorem this important deserves multiple coverage. And to balance squishy with crunchy, some mechanization of http://gosper.org/perigal.htm . Which raises the possibility of other dissections when the three bounding figures are other than squares. --rwg
Neil just made http://gosper.org/perigal.gif , after failing to find a decent precedent on the Web. --rwg On Mon, Dec 17, 2012 at 12:42 PM, Bill Gosper <billgosper@gmail.com> wrote:
(Sorry about RoundCube(?) losing the indentation below.)
GH>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
(Gaa, now it won't UNindent!) Well, an advantage of several similar mechanisms side by side is that multiple kids can experiment. Pursuing this, repeat the several triangles with their surrounding squares replaced by semicircles and again by regular pentagons, say. A theorem this important deserves multiple coverage. And to balance squishy with crunchy, some mechanization of http://gosper.org/perigal.htm . Which raises the possibility of other dissections when the three bounding figures are other than squares. --rwg
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Bill Gosper