[math-fun] Lego orrery design

I'm thinking about the problem of designing gear trains for a lego orrery which I'd like to be fairly accurate. The standard gear sizes are 8, 16, 24, 40, so I have ratios of 1:2:3:5 to work with. I figure that since lg(3) (where lg is log base 2) is irrational, you can get arbitrary accuracy out of a gear train. I think I need a + b lg(3) + c lg(5) ~= lg(period), with a, b, c small. Is LLL the right tool for solving this kind of thing? -- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike http://reperiendi.wordpress.com