02/12/2009, 12:10 AM

Gottfried Wrote:The only idea that remains is, to consider the length of the guessed curve of f°0.5(x) in an interval of f°0.5(x) .. f°2.5(x). (but also... I've never dealt with line-integrals). This length should be minimal if the amplitude of the overlaid mod(1)-function is minimal. But this is just crude guess - should be checked on paper first...

Sounds not bad, but here again the length is infinite, and if you chose f(a) for the shortest length in one interval [a,F(a)] - i.e. a straight line - then in the interval [F(a),F(F(a))] the length is longer then for a better choose in the first interval.

So over which and how many intervals do you want to measure the length without being arbitrary?