3 ms·
> So you absorb 3 to generate 3/1, then you absorb 7 to generate (3×7+1)/(7×1+0)=22/7, then you absorb 15 to generate (15×22 + 3)/(15×7 + 1) = 333/106 The OP d
by Someone 4y ago
> So you absorb 3 to generate 3/1, then you absorb 7 to generate (3×7+1)/(7×1+0)=22/7, then you absorb 15 to generate (15×22 + 3)/(15×7 + 1) = 333/106
The OP did not have the sequence of best rational approximations derived from the continued fraction, but
3/1 = 3.0
22/7 = 3.142857142857143
311/99 = 3.1414141414141414
355/113 = 3.1415929203539825
That is decimal-based, picking, for any number of digits, the best (according to some criterion) approximation of pi using that number of decimal digits.
They skipped 333/106, for example, because the better approximation 355/113 uses the same number of decimal digits, and included 311/99 because it happens to (just) need 5 decimal digits.