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In "nβth digit of π and π^n" are both n the same? In other words, for say π^50 does the formula only give me the 50th digit, or does it give me any arbitrary digit I want?
Yes.
> In other words, for say π^50 does the formula only give me the 50th digit
Yes.
> or does it give me any arbitrary digit I want?
It gives you the n-th digit of \pi^n. Here n is arbitrary.
The paper seems absolutely brilliant, but the grammar is very strange (thereβs even what appears to be a typo in the paper where he says βrand nβ instead of βrank nβ). Odd that he wouldnβt have worked with somebody with better written English before publishing.
It isn't published, it's a pre-print.
Earlier quoted context omitted.
It isn't published, it's a pre-print.
If you can download it from arxiv, it is published. Researchers donβt really care whether the paper went through formal peer review and publication process in some journal, because that process is of little value: they can figure out that the author meant rank instead of rand etc.
For example, https://arxiv.org/help/jref says:
> When a article is published, the author may wish to indicate this in the abstract listing for the article. For this reason, the journal reference and DOI (Digital Object Identifier) fields are provided for articles.
This can only make sense if "public abstract on arxiv" is not the same as "published" in the way you mean.
Earlier quoted context omitted.
That would make it a rational number, so we can rule that out
Exactly, the only possible "last digit" it could have (in keeping with the silly premise that it has one), is zero.
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 += Decimalβ¦
since this is Python, `nth_digit_of_pi(-1)` should give us the last number of Pi.
Finally, we can find the last digit of pi
In "nβth digit of π and π^n" are both n the same? In other words, for say π^50 does the formula only give me the 50th digit, or does it give me any arbitrary digit I want?
Earlier quoted context omitted.
Exactly, the only possible "last digit" it could have (in keeping with the silly premise that it has one), is zero.
I don't think that would be true seeing 1/3 = 0.3333.. , or am I reading this wrong?
0 recurring represents the end of a quantity, and the absence of any further quantity, forever.
Eg: 0.012500000000000...
The significant portion is 0.0125 - the recurring zeroes serve a mathematical role akin to that of a full-stop in a sentence. Hence zero being (jokingly, but in a sense truthfully) always the "last digit".