From: ed pegg <ed@mathpuzzle.com>
I recently did a column on approximations. http://www.maa.org/editorial/mathgames/mathgames_02_14_05.html
I've gotten a lot of results, including an article on class polynomials: http://www.geocities.com/titus_piezas/Approximations.htm
I'm perturbed that multiplication, division, addition, subtraction, and exponentiation aren't considered functions when calculating complexity. Just noodling on the train yesterday, I looked at the CF representations of n^(1/m), n^(Pi/m), and n^(e/m) for n<=9999, m<=9. I was surprised that n^(e/m) showed a noticable paucity of close approximations compared to the other two families. None were particularly impressive though, with no CF term seen over ~1.5e6 (sthg^(Pi/9)). The e family did provide the most fun with its deliberately lengthened (which could be decrease complexity in other languages) (62+101)*(62*101)^(e/4)=61989.99999996... Phil When inserting a CD, hold down shift to stop the AutoRun feature In the Device Manager, disable the SbcpHid device. http://www.cs.princeton.edu/~jhalderm/cd3/ __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com