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Is there a method to find the value of the $n$-th decimal place of $\pi$ which is more efficient than having to compute all decimal places before as well?

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    $\begingroup$ You might look up to look up the Bailey-Borwein-Plouffe results about the hexadecimal representation of $\pi.$ $\endgroup$
    – Geoff Robinson
    Commented Jul 25, 2014 at 21:28
  • $\begingroup$ These are called spigot algorithms. $\endgroup$
    – Douglas Zare
    Commented Jul 26, 2014 at 19:03

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Yes, there are such algorithms. -- See e.g. Xavier Gourdon: Computation of the $n$-th decimal digit of $\pi$ with low memory. There also is the Bailey-Borwein-Plouffe formula already mentioned by Geoff Robinson in a comment -- see https://www.math.hmc.edu/funfacts/ffiles/20010.5.shtml.

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