Are there measurements of pi calculated by meausuring diameter and circumference? How many digits can that pi have?
A formula for the nth digit of π and π^n
121β130 of 143 posts
Re: A formula for the nth digit of π and π^n
#122There is nothing of note here. This paper should be in 'general math', not number theory. You need to know the Bernoulli numbers in order for this to work, which is more computationally difficult than computing pi. So what. Yeah, Plouffe is a famous person in computer science and math, but this does not measure up to the hype. It reminds me of the stuff i tinkered with in high school when i first learned infinite serβ¦
> but not publishable-level, sorry
No one's saying it is, this is arXiv, after all (not a journal). Still a fun little interesting paper, though.
Re: A formula for the nth digit of π and π^n
#123There is nothing of note here. This paper should be in 'general math', not number theory. You need to know the Bernoulli numbers in order for this to work, which is more computationally difficult than computing pi. So what. Yeah, Plouffe is a famous person in computer science and math, but this does not measure up to the hype. It reminds me of the stuff i tinkered with in high school when i first learned infinite serβ¦
I would think the βexplicit expressionβ part is new and enough to make it publishable, and fail to see why not being useful in practice ever should be a factor in determining whether something is number theory.
Now, for the hype, I donβt see any from the authors.
Re: A formula for the nth digit of π and π^n
#124Something like this can be used for "proof of work" in the blockchain world.
That's an interesting point. You could use this to hash values with infinitely scaling difficulty by providing an offset to n where n = difficulty + n. The only issues is collision since the output is always 0-9 but if your POW check is against multiple digits then it might work? Again you could still have potentially infinite repetitions of sequences of digits with different inputs.
Re: A formula for the nth digit of π and π^n
#125Is there a physical limit to how many digits of pi can ever be computed/represented in the universe? For example, letβs say we need one atom for each digit of pi that we want to store, the max limit of digits of pi would be something like the total number of atoms in the universe, minus the atoms required to compute and store the digits. Has that been studied/calculated?
This sounds like a lot of work, when the physical limit of how many decimal places you need in our universe given the Planck length is only 63 or so.
Re: A formula for the nth digit of π and π^n
#126Earlier quoted context omitted.
It isn't.
Look at the first denominator seen in both lines of the equation, the last denominator in the first part of the equation, and the second denominator in the second part of the equation.
The first equations listed in the abstract of the paper are the inequalities used to derive the equation of interest, which is on the second page.
Re: A formula for the nth digit of π and π^n
#127It is all curious, but it seems that procedure that calculates the n-th digit using some other functions that require O(n) calculations (i.e. Bernoulli numbers) is not that exciting, as it's just a speedup comparing to a naive calculation (maybe a big one but still). Although because pi is a transcendental number maybe it is impossible to have an algorithm to return the n-th digit in O(1) operations? Does anyone knowβ¦
The interesting question is: are there real numbers whose N-th digit provably cant be calculated in O(N)?
I don't know of any with practical use, but you can fairly easily define a contrived one:
cmeacham98's constant: a number where the `n`th digit is the `2^n`th digit of pi
Re: A formula for the nth digit of π and π^n
#128[deleted]
Re: A formula for the nth digit of π and π^n
#129Earlier quoted context omitted.
Ok, so the method is real but will not be used to break the next world record. Chudnovsky algorithm is better at that task.
Not this one, but algorithms that can calculate the specific digit positions but nothing else are indeed used for world records, mainly for the verification. If two radically different algorithms converge into the same digits at something like the trillionth position then you will have a high confidence for the rest of digits.
Also wouldnt this be highly parallelizable?
Re: A formula for the nth digit of π and π^n
#130Earlier quoted context omitted.
You have no idea how atrocious the English is in papers that I see as a reviewer. And depending on journal I don't even get to reject it for that as long as the science is sound.
Can you insist the writing be improved for publication?
I can list that in the feedback to the authors or recommend that in the confidential remarks to the editor. If they will listen (and force the authors if necessary) depends on the journal.