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A formula for the nth digit of ๐œ‹ and ๐œ‹^n

arxiv.org

81โ€“90 of 143 posts

Re: A formula for the nth digit of ๐œ‹ and ๐œ‹^n

#81
post #4

Earlier quoted context omitted.

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

this is a great motivating example for the definition of Kolmogorov complexity.

It is my favorite fake-counter example.

Re: A formula for the nth digit of ๐œ‹ and ๐œ‹^n

#82
post #78

But... pi is in the formula. If you already know it, then why bother?

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.

Re: A formula for the nth digit of ๐œ‹ and ๐œ‹^n

#83

But... pi is in the formula. If you already know it, then why bother?

Not sure where you're seeing that. Did you misread a formula?

The very first denominator seen is (2ฯ€)^2n, the last denominator on that line is the same, the first denominator of the second line is ฯ€^2n+1 and the second denominator in the second line is the same. Are you not seeing that?

Re: A formula for the nth digit of ๐œ‹ and ๐œ‹^n

#84

The paper seems absolutely brilliant, but the grammar is very strange (thereโ€™s even what appears to be a typo in the paper where he says โ€œrand nโ€ instead of โ€œrank nโ€). Odd that he wouldnโ€™t have worked with somebody with better written English before publishing.

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.

Re: A formula for the nth digit of ๐œ‹ and ๐œ‹^n

#85

๐œ‹ in the title is a character I haven't seen before, [Mathematical Italic Small Pi]( https://unicode-table.com/en/1D70B/ ).

Yes, and there's also bold (๐›‘), bold italic (๐…), sans-serif bold (๐ฟ), and sans-serif bold italic (๐žน), all distinct from the run-of-the-mill Greek Small Letter Pi (ฯ€) which is often rendered quite differently from the "standard mathematical pi" in addition to, of course, being semantically different. There's a lot of fun stuff in the Mathematical Alphanumeric Symbols block (https://unicode-table.com/en/blocks/mathematical-alphanumeri...)

Re: A formula for the nth digit of ๐œ‹ and ๐œ‹^n

#86
post #69

Earlier quoted context omitted.

But why?

For me, it stimulates a mental shift that could be good exercise elsewhere: instead of storing the string, you find the string somewhere and store its index. It also stimulate the imagination: what other transcendental numbers might this work with? How long do you have to search in the digits to find your string? What can you say about the size of the index (how far you searched) vs your string length? Etc. It's pattโ€ฆ

It doesnโ€™t even work with pi.

Re: A formula for the nth digit of ๐œ‹ and ๐œ‹^n

#88
post #52

Earlier quoted context omitted.

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

If you can download it from arxiv, it is published. Researchers donโ€™t 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.

There is definitely a difference between "public(ly available on arxiv)" and "published (in a peer-reviewed journal)". Depending what I want to do I may prefer on or the other for my work as a researcher.

Re: A formula for the nth digit of ๐œ‹ and ๐œ‹^n

#89

The paper seems absolutely brilliant, but the grammar is very strange (thereโ€™s even what appears to be a typo in the paper where he says โ€œrand nโ€ instead of โ€œrank nโ€). Odd that he wouldnโ€™t have worked with somebody with better written English before publishing.

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.

> And depending on journal I don't even get to reject it for that as long as the science is sound.

and you shouldn't. As long as it is somewhat legible, forcing people who are not native English speakers to conform to another language 100 % in order for their science to be published is horrendous.

There was a time 300 years ago, where great thinkers who did not speak French or German could not publish their thoughts and answers, and to us now it seems atrocius. Let us not go a head and redo that with English

Re: A formula for the nth digit of ๐œ‹ and ๐œ‹^n

#90

Earlier 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.

> And depending on journal I don't even get to reject it for that as long as the science is sound. and you shouldn't. As long as it is somewhat legible, forcing people who are not native English speakers to conform to another language 100 % in order for their science to be published is horrendous. There was a time 300 years ago, where great thinkers who did not speak French or German could not publish their thoughtsโ€ฆ

The problem is that "somewhat legible" is not a given and you don't know if the version that comes out of language editing (if it is still done, a lot of journals skip it to save money) is still scientifically correct.

Edit: A possible solution would be to have "good idea, please language edit and send back for further review" as an option along with "reject" / "needs major revisions" / "needs minor revisions" / "accept".

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