Jim, There are four shapes of rollers in the MoMath ride-on exhibit. Three are acorn-like surfaces of revolution and the fourth is a Meissner tetrahedron. One of them is very similar to this very cool commercially available metal set: http://www.grand-illusions.com/acatalog/Solids_of_Constant_Width.html The second has a point at the apex but is differentiable everywhere else, and the third is based on a regular pentagon (extended with radii and rotated to a surface of revolution). (I also wanted to have one sphere in the mix, with a different color, to emphasize that all the others aren't spheres, but that was vetoed...) George http://georgehart.com/ On 1/8/2013 5:35 PM, James Propp wrote:
Does anyone know which sort of rollers the MoMath exhibit "Coaster Rollers" uses?
Jim Propp
On Tue, Jan 8, 2013 at 6:12 AM, Tom Karzes <karzes@sonic.net> wrote:
I wonder if Meissner tetrahedra (true constant width) would work better or worse than Reuleaux tetrahedra (approximate constant width) for this purpose.
Tom
Bill Gosper writes:
MLB>
And what exactly does "smooth" buy us? Let's just ask instead: how would we quadrangulate a rounded tetrahedron? ------ I nearly slid through a stopsign recently. It was on a sharp downgrade, preceded by gravel washed off a hillside. Had the gravel been perfectly spherical, I wouldn't even have slowed down. Except spherical gravel would have rolled away. What about Reuleaux tetrahedra (http://www.youtube.com/watch?v=jK7xPo1YXzY 3:18)? Neil 3D printed a lovely one, ~1.5", and then split for CES w/o photographing it. It's eerie to roll a book over. Why aren't they sold at science museum gift shops? But would one stay put on a hill? Neil claims, with sufficient friction, an amazing 60°! They're much less round than you might think. This has 007esque possibilities, not just for foot chases and booby-traps. Imagine pursuing Bond on a winding road where he releases a few pounds of Reuleaux gravel. You say
http://www.zombiesurvivalwiki.com/thread/3341691/Liquid+Banana+Peel+-+Make+a...
is cheaper? OK, but it leaves a residue. For the perfect crime, use dry ice Reuleaux gravel. --rwg http://gosper.org/reuleauxtet.png _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
--
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun