On Jun 2, 2011, at 5:15 PM, Bill Gosper wrote:
Eh? 7 is as symmetrical as you can get. I miscounted: 3 and 7 are the only solutions with all equal radii (I'm not including 2 because the solution is a continuum).
Fourteen appears to be the first instance where all the radii are distinct.
In your aluminum puzzle, two disks are almost indistinguishable, but not
switchable, due to the precise machining. But two others *are*
switchable and apparently indistinguishable. Are you saying they are
mathematically distinct?? By how much? Do you have their actual polynomials?
--Bill The two disks you refer to have very slightly different radius, about 0.013%. That's about 0.1 mil at the scale of the aluminum puzzle -- beyond what can be machined or discerned by hands and eyes. I never worked out the polynomials.
Veit