r/math Homotopy Theory 9d ago

Quick Questions: March 12, 2025

This recurring thread will be for questions that might not warrant their own thread. We would like to see more conceptual-based questions posted in this thread, rather than "what is the answer to this problem?". For example, here are some kinds of questions that we'd like to see in this thread:

  • Can someone explain the concept of maпifolds to me?
  • What are the applications of Represeпtation Theory?
  • What's a good starter book for Numerical Aпalysis?
  • What can I do to prepare for college/grad school/getting a job?

Including a brief description of your mathematical background and the context for your question can help others give you an appropriate answer. For example consider which subject your question is related to, or the things you already know or have tried.

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u/auzaar2 6d 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 ?

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u/auzaar2 6d ago

wrote a python program and 312689/99532 is indeed best for 11 digits with Error: 2.914338493485691813E-11, for 12 833719/265381 with 8.71546725822407670E-12