Henry's question suggests the following math problem in the context of polishing a (large) BB: Suppose you are given a continuous curve A: [0,L] —> S^2 parametrized by arclength for some L > 0, where S^2 is the unit sphere. Let D(r, p) denote the closed disk of radius r about the point p of S^2, where r is measured along S^2. Then define gap_L(A) = sup{ r > 0 | For some p in S^2, D(r, p) does not intersect A([0,L])} For any L > 0, define mingap(L) = inf { gap(A) | A: [0,L] —> S^2 is parametrized by arclength }. Then what can be said about the values of mingap(L) ? What is its asymptotic behavior as L —> oo ??? —Dan Henry Baker wrote: ----- It's the year 1500, and some wealthy patron wants a transparent glass and/or rock crystal sphere perhaps 6-8" in diameter. How would you fabricate it? ... ... -----