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A formula for the nth digit of πœ‹ and πœ‹^n

arxiv.org

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Re: A formula for the nth digit of πœ‹ and πœ‹^n

#11

Post by tyingq Β»

mkl wrote: post #8
tucnak wrote: post #2

So does it mean that these pi-calculating competitions & record are now going to devolve to special olympiads in pointless storage capacity? What will the super computers going to do in view of this discovery? Fascinating times for humans as well as for the machines...

Nothing will change there. There are already much more efficient methods of calculating Ο€. What this lets you do is jump straight to the n th digit without calculating all the ones before it.

Couldn't you "cheat" a bit in a timed competition if you knew exactly how many digits you would reach, and kick this off in parallel to extract a few more to tack to the end? Or would the parallel job be too slow for that? Or the competitions constrain CPU or other resources to a ceiling?

Re: A formula for the nth digit of πœ‹ and πœ‹^n

#12

Post by mojomark Β»

imglorp wrote: post #4
tucnak wrote: post #2

So does it mean that these pi-calculating competitions & record are now going to devolve to special olympiads in pointless storage capacity? What will the super computers going to do in view of this discovery? Fascinating times for humans as well as for the machines...

Ο€fs: Never worry about data again! - https://github.com/philipl/pifs

Any file can be represented as a binary string, and a binary string is just an integer value - which is to say binary strings are simply indexes of files in binary space (i.e. the set of all possible permutations of bits).

Looks to me like nfs is simply transforming a binary space index into a pi-space index. Some files may compress to a smaller value than they are in binary space (if you get lucky), but make no mistake, some files will be much much larger (i.e. the files you're trying to store don't show up in pi until an index value that is a virtually infinite number of digits long).

Re: A formula for the nth digit of πœ‹ and πœ‹^n

#13

Post by _ache_ Β»

_ache_ wrote: post #3

Plouffe ... He used to teach in my university. He is a fantastic man. This is serious, he is crazy about numbers. He is one of the guy behind OEIS (oeis.org). That is not the first formula he found about pi and some of the previous one had been used to break world record about the number of known decimals.

Ok, so the method is real but will not be used to break the next world record. Chudnovsky algorithm is better at that task.

Re: A formula for the nth digit of πœ‹ and πœ‹^n

#14

Post by commandlinefan Β»

The paper seems absolutely brilliant, but the grammar is very strange (there’s even what appears to be a typo in the paper where he says β€œrand n” instead of β€œrank n”). Odd that he wouldn’t have worked with somebody with better written English before publishing.

Re: A formula for the nth digit of πœ‹ and πœ‹^n

#15

Post by scythe Β»

The interesting question, I think, is whether this formula can help address the question of the normality of pi:

http://en.wikipedia.org/wiki/Normal_number

This is particularly exciting because the prevailing opinion had been that we lack the mathematical tools to attack that problem.

Re: A formula for the nth digit of πœ‹ and πœ‹^n

#16

Post by childintime Β»

Chatgpt, please write a function in python for the nth digit of pi.

    Sure, here is a function in Python that calculates the nth digit of Pi using the Chudnovsky algorithm:

    from decimal import *

    def nth_digit_of_pi(n):
        getcontext().prec = n + 1
        C = 426880 * math.sqrt(10005)
        M = 1
        L = 13591409
        X = 1
        K = 6
        S = L
        for i in range(1, n):
            M = (K ** 3 - 16 * K) * M // i ** 3 
            L += 545140134
            X *= -262537412640768000
            S += Decimal(M * L) / X
            K += 12
        return +str(S / C)[n]
Seems off, but I learned something: https://www.wikiwand.com/en/Chudnovsky_algorithm

Re: A formula for the nth digit of πœ‹ and πœ‹^n

#18

Post by anamexis Β»

commandlinefan wrote: post #14

The paper seems absolutely brilliant, but the grammar is very strange (there’s even what appears to be a typo in the paper where he says β€œrand n” instead of β€œrank n”). Odd that he wouldn’t have worked with somebody with better written English before publishing.

It isn't published, it's a pre-print.
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