Let me try that again. Let me ask a simpler and straightforward version of the question: ----------------------------------------- Let A = { p in R^2 : 1 < ||p|| <= 2 }. PUZZLE: Prove there is no C^2 homeomorphism H : S^1 x (1,2] -> A such that if L(r) denotes the length of the curve H(S^1, r) in A, then L(r) is independent of r. ----------------------------------------- (The important difference between the e-mail I sent a few minutes ago is changing a <= sign to a < sign, and changing [1,2] to (1,2].) Sorry about that. --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele