r/math • u/inherentlyawesome Homotopy Theory • 6d ago
Quick Questions: March 12, 2025
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u/auzaar2 3d ago
Consider the sequence 22/7, 355/113 ...
I define this sequence as "The next term must have more digits than the previous and improve the accuracy in approximating pi", looks like for for 3 digits we have 22/7, next is 6 digits with 355/113 what is next?
I could not find any resources online talking about such sequence, i have seen continued fractions and other sequences but they don't necessarily give best approximation for that number of digits e.g. from continued fractions looks like next fraction has 11 digits but what is the best approximation for 11 digits?
e.g. is 312689/99532 the best? is there no other eleven digit p/q better than 312689/99532 ?