4 ms·

Pi has the continued fraction expansion: 3; 7, 15, 1, 292, 1, ... That 355/113 is one of the best possible rational approximations to PI, and it occurs right

Pi has the continued fraction expansion: 3; 7, 15, 1, 292, 1, ... That 355/113 is one of the best possible rational approximations to PI, and it occurs right after the 292. In general, a best rational approximation cut off at a very large term in the CF expansion will provide more accuracy than you would think.

walrus 14y ago
355/113 is actually [3,7,15,1]. The reason it's particularly good compared to its length is because it falls right before the 292 term (since 1/292 is a much smaller contribution than 1/1).
- Xcelerate 14y ago
  Ah, indeed you are correct. I had that wrong.
- caf 14y ago
  So, as noted in one of the comments to the original article, the question of why 355/113 is particularly good can be restated as a question of why the 292 term in that expansion is so large.