l****a
发帖数: 366 | 1 I take some time to type the following passage from a book
called "Concrete Mathematics: A foundation for Computer
Scienence"
written by three geniuses: Graham, Knuth, and Patashnik.
"A remakrable theorem was discovered independently by three
mathematicians - Bohl, Sierpinski, and Weyl - at about the
same time in 1909: if \alpha is irrational then the
fractional
parts {n\alpha} are very uniformly distributed between 0
and 1, as n \rightarrow \infty. One way to state this is
that:
\[ \lim_{n \ri | H****h
发帖数: 1037 | 2 If a is irrational, E=1/2+o(1), V=1/12+o(1).
If a=p/q, (p,q)=1, E=1/2-1/(2*q)+O(1/n), V=1/12-1/(12*q^2)+O(1/n). |
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