VE> 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.

That's amazing! Especially since they seem to lie diametrically opposed.

I never worked out the polynomials.

Veit All we need are a few hundred digits and FindIntegerNullVector . (And a bit of shamelessness.) --rwg