[math-fun] NYTimes: Dodecahedral salt
FYI -- December 10, 2006 Salt That DoesnÂt Stick By CLIVE THOMPSON Everyone knows the havoc that humidity wreaks on salt. You pick up a saltshaker, tip it upside down and  nothing. The problem is molecular. Salt grains are cube shaped, so it doesnÂt take much to get them to stack together like Legos. Salt producers have created nonsticking salt before by adding chemicals to prevent binding. But this year, in the July issue of Crystal Growth and Design, a team of Indian scientists announced that they had discovered a better way to attack the problem: they produced salt that is round. To accomplish this, they added the amino acid glycine to a pan of brine and then let the salty liquid evaporate. The resulting crystals were shaped like dodecahedrons: 12-sided grains. In this nearly spherical form, the grains no longer stacked like bricks but like oranges in a sack. The researchers put some of the round salt into a container, left it for a year and found that it still poured freely. The glycine has a side effect: it makes the salt slightly sweeter. Pushpito K. Ghosh, one of the lead scientists on the project, claims he canÂt detect it  ÂAnd IÂve eaten a lot of it!  but he suspects that chefs might.
Must not have been rhombic dodecahedra :-) Jim On 12/10/06, Henry Baker <hbaker1@pipeline.com> wrote:
FYI --
December 10, 2006
Salt That Doesn't Stick
By CLIVE THOMPSON
Everyone knows the havoc that humidity wreaks on salt. You pick up a saltshaker, tip it upside down and nothing.
The problem is molecular. Salt grains are cube shaped, so it doesn't take much to get them to stack together like Legos. Salt producers have created nonsticking salt before by adding chemicals to prevent binding. But this year, in the July issue of Crystal Growth and Design, a team of Indian scientists announced that they had discovered a better way to attack the problem: they produced salt that is round.
To accomplish this, they added the amino acid glycine to a pan of brine and then let the salty liquid evaporate. The resulting crystals were shaped like dodecahedrons: 12-sided grains. In this nearly spherical form, the grains no longer stacked like bricks but like oranges in a sack. The researchers put some of the round salt into a container, left it for a year and found that it still poured freely.
The glycine has a side effect: it makes the salt slightly sweeter. Pushpito K. Ghosh, one of the lead scientists on the project, claims he can't detect it "And I've eaten a lot of it!" but he suspects that chefs might.
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A nifty circular table based on dissections is available. With a spin, it becomes a table twice as large as before. The mechanism is beautiful. Fletcher Capstan Tables http://www.dbfletcher.com/capstan/ --Ed Pegg Jr
Very cool, but not strictly circular. At 07:58 PM 12/10/2006, Ed Pegg Jr wrote:
A nifty circular table based on dissections is available. With a spin, it becomes a table twice as large as before. The mechanism is beautiful.
Fletcher Capstan Tables http://www.dbfletcher.com/capstan/
--Ed Pegg Jr
Mon, 11 Dec 2006 07:32:25 -0800 Henry Baker <hbaker1@pipeline.com> Very cool, but not strictly circular. Why not? Doesn't the ring that encircles the table when it is in compressed mode make it strictly circular? (The outside of the ring appears to be a circle with the 6-person radius. The inside of the ring could be an inscribed "hexagon" with arcs (with the 12-person radius) instead of lines. When the table is expanded, the outer edges of the inner pie-wedges/segments join to form a circle.) At 07:58 PM 12/10/2006, Ed Pegg Jr wrote:
A nifty circular table based on dissections is available. With a spin, it becomes a table twice as large as before. The mechanism is beautiful.
Fletcher Capstan Tables http://www.dbfletcher.com/capstan/
--Ed Pegg Jr
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
I suppose that it could be strictly circular if the band around the smaller table isn't of fixed thickness, so that it can hide the larger radius pieces within itself. If the smaller circular band is of constant thickness, then there will be gaps in the table top where the radii don't match. I single-stepped the movies to try to see the smaller circular band better, but the movie appears to jump discontinuously at just the right moment -- perhaps to hide the shape of the smaller circular band from potential copiers. At 07:43 AM 12/11/2006, greenwald@cis.upenn.edu wrote:
Mon, 11 Dec 2006 07:32:25 -0800 Henry Baker <hbaker1@pipeline.com>
Very cool, but not strictly circular.
Why not? Doesn't the ring that encircles the table when it is in compressed mode make it strictly circular? (The outside of the ring appears to be a circle with the 6-person radius. The inside of the ring could be an inscribed "hexagon" with arcs (with the 12-person radius) instead of lines. When the table is expanded, the outer edges of the inner pie-wedges/segments join to form a circle.)
At 07:58 PM 12/10/2006, Ed Pegg Jr wrote:
A nifty circular table based on dissections is available. With a spin, it becomes a table twice as large as before. The mechanism is beautiful.
Fletcher Capstan Tables http://www.dbfletcher.com/capstan/
--Ed Pegg Jr
Mon, 11 Dec 2006 07:56:12 -0800 Henry Baker <hbaker1@pipeline.com> I suppose that it could be strictly circular if the band around the smaller table isn't of fixed thickness, so that it can hide the larger radius pieces within itself. If the smaller circular band is of constant thickness, then there will be gaps in the table top where the radii don't match. I single-stepped the movies to try to see the smaller circular band better, but the movie appears to jump discontinuously at just the right moment -- perhaps to hide the shape of the smaller circular band from potential copiers. I assumed it was not constant width/thickness --- that's what I meant by an inscribed, rounded, "hexagon". I, too, couldn't see the detail in the movie. I doubt, though, that the discontinuity was intended to hide anything. First, this seems like one logical way to construct such a table, but once you see the table itself, surely you can think up a couple of different ways of implementing it. Second, a potential copier could simply look at a real example of such a table. (The tricky part, I'd guess, would be the alignment of the vertices of the inner "hexagon" and the outer ring --- wouldn't they have to be pretty accurate in order to avoid gaps in the smaller table? Although, I suppose you could build it with a bit of give --- so that they get nudged into place as the table compacts. I'm sure furniture builders have many ways of getting around this problem, though, so my guesses as to what's hard and what's easy are probably worthless.) In any case, I found the table and mechanism extremely pretty. At 07:43 AM 12/11/2006, greenwald@cis.upenn.edu wrote:
Mon, 11 Dec 2006 07:32:25 -0800 Henry Baker <hbaker1@pipeline.com>
Very cool, but not strictly circular.
Why not? Doesn't the ring that encircles the table when it is in compressed mode make it strictly circular? (The outside of the ring appears to be a circle with the 6-person radius. The inside of the ring could be an inscribed "hexagon" with arcs (with the 12-person radius) instead of lines. When the table is expanded, the outer edges of the inner pie-wedges/segments join to form a circle.)
At 07:58 PM 12/10/2006, Ed Pegg Jr wrote:
A nifty circular table based on dissections is available. With a spin, it becomes a table twice as large as before. The mechanism is beautiful.
Fletcher Capstan Tables http://www.dbfletcher.com/capstan/
--Ed Pegg Jr
Copying wouldn't be legal--the web site says its patented, although it doesn't say where. The following US patents might be relevant: 6009814, 6994032. --ms greenwald@cis.upenn.edu wrote:
Mon, 11 Dec 2006 07:56:12 -0800 Henry Baker <hbaker1@pipeline.com>
I suppose that it could be strictly circular if the band around the smaller table isn't of fixed thickness, so that it can hide the larger radius pieces within itself.
If the smaller circular band is of constant thickness, then there will be gaps in the table top where the radii don't match.
I single-stepped the movies to try to see the smaller circular band better, but the movie appears to jump discontinuously at just the right moment -- perhaps to hide the shape of the smaller circular band from potential copiers.
I assumed it was not constant width/thickness --- that's what I meant by an inscribed, rounded, "hexagon".
I, too, couldn't see the detail in the movie. I doubt, though, that the discontinuity was intended to hide anything. First, this seems like one logical way to construct such a table, but once you see the table itself, surely you can think up a couple of different ways of implementing it. Second, a potential copier could simply look at a real example of such a table.
(The tricky part, I'd guess, would be the alignment of the vertices of the inner "hexagon" and the outer ring --- wouldn't they have to be pretty accurate in order to avoid gaps in the smaller table? Although, I suppose you could build it with a bit of give --- so that they get nudged into place as the table compacts. I'm sure furniture builders have many ways of getting around this problem, though, so my guesses as to what's hard and what's easy are probably worthless.)
In any case, I found the table and mechanism extremely pretty.
At 07:43 AM 12/11/2006, greenwald@cis.upenn.edu wrote:
Mon, 11 Dec 2006 07:32:25 -0800 Henry Baker <hbaker1@pipeline.com>
Very cool, but not strictly circular.
Why not? Doesn't the ring that encircles the table when it is in compressed mode make it strictly circular? (The outside of the ring appears to be a circle with the 6-person radius. The inside of the ring could be an inscribed "hexagon" with arcs (with the 12-person radius) instead of lines. When the table is expanded, the outer edges of the inner pie-wedges/segments join to form a circle.)
At 07:58 PM 12/10/2006, Ed Pegg Jr wrote:
A nifty circular table based on dissections is available. With a spin, it becomes a table twice as large as before. The mechanism is beautiful.
Fletcher Capstan Tables http://www.dbfletcher.com/capstan/
--Ed Pegg Jr
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
The ring which makes the small configuration truly circular is clearly not of uniform width. I can see this and know that it's absolutely necessary. This table idea would generalize to area ratios > 2 with considerable added complexity, including having more than two layers when in the small configuration. (I'm not contending that this would be practical.) The way they achieve very small gaps is simply to size and shape all pieces extremely accurately. Modern large production woodworking machinery makes this a bit easier but great craftsmanship is still needed, especially since wood expands and contracts nonisotropically with varying moisture in the air. I've done a fair amount of woodworking but I'd never attempt this. Steve Gray Ed Pegg Jr wrote:
A nifty circular table based on dissections is available. With a spin, it becomes a table twice as large as before. The mechanism is beautiful.
Fletcher Capstan Tables http://www.dbfletcher.com/capstan/
--Ed Pegg Jr
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participants (6)
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Ed Pegg Jr -
greenwald＠cis.upenn.edu -
Henry Baker -
James Buddenhagen -
Mike Speciner -
Steve, stevebg