> TLDR: the "(US) survey foot" is 1200/3937 SI meters, and the > "(international) foot" is 0.3048 SI meters, a ratio of about > 1.000002000004000:1 or 1:0.999998.
Fascinating. (1200/3937)/.3048 -> 1.000002000004000008000016000032000064000128000256000512001024002048004096008192016384032768065536131072262144524289048578097156... in which I see a curious string of overlapping powers of two. (1200/3937)/(3048/10000) = (1200 * 10000) / (3937 * 3048) = (2^8 * 3 * 5^6) / (2^3 * 3 * 31 * 127^2) = (2^5 * 5^6) / (31 * 127^2) = 500000 / 499999 which, upon doing long division, makes it obvious what's going on. (And makes it clear that the reciprocal, .999998, is exact.) And there are modifications such as 50000000/49999999; that one produces similar strings of powers of two with more zeros between them. And there are related fractions, such as 100000000/99999997 (which generates powers of three). Obvious once pointed out, but I'd never seen them before. /~\ The ASCII Mouse \ / Ribbon Campaign X Against HTML mo...@rodents-montreal.org / \ Email! 7D C8 61 52 5D E7 2D 39 4E F1 31 3E E8 B3 27 4B
