101β110 of 143 posts
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.
Proof: the first digit of pi is 3, not zero.
See also Plouffe's earlier (1995) formula to extract hexadecimal digits of pi: https://en.m.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80...
const nDigitOfPi = (n) => (22/7).toString()[n+1]
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Yes, it looks like you're right. But I don't understand the reasoning - is he actually saying you can use this formula to compute pi^n to n decimal places? So it doesn't produce arbitrary digits on their own, but excellent approximations to pi^n? And this was by taking 4 terms of the zeta function infinite product expansion. 2xn digits would presumably be given by taking more terms (but quite a few, one for every priβ¦
Yeah, my sense is that the author knows this is more of a neat trick than a "practical" way of calculating pi. There's a bit on page 5 about how the Chudnovsky method totally blows this approach out of the water.
See also Plouffe's earlier (1995) formula to extract hexadecimal digits of pi: https://en.m.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80...
We should also have decimal/binary/hex digits of Tau to complete the set.
See also Plouffe's earlier (1995) formula to extract hexadecimal digits of pi: https://en.m.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80...
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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.
"Published" in this context is short for "published to a journal" or more completely for this thread "gone through the full edit cycle you would expect from a paper published to a journal". 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)β¦
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.
The only possible "last digit" it could not have is zero: if the last digit were to be a zero, that digit would be superfluous and could be discarded, making the digit before that the real "last digit". Proof: the first digit of pi is 3, not zero.
That aside, the apparent "empty space" on the either side of a number is in reality consisting of infinite zeroes.
Just because we typically choose to "display" most numbers without those zeroes, it doesn't mean they aren't there in a very real, practical and important sense.
They are there, because if they aren't there, then something else might be, and then all our numbers would have to be assumed to be wrong or incomplete... so instead, we assume the zeroes.
The terrible reality is the zeroes extend off infinitely in either direction, and we use empty space as shorthand for this so we don't have to spend longer than the age of the universe to write a single number with full accuracy.
Earlier quoted context omitted.
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.
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.
Earlier quoted context omitted.
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.
"Published" in this context is short for "published to a journal" or more completely for this thread "gone through the full edit cycle you would expect from a paper published to a journal". 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)β¦