# Wikipedia talk:WikiProject Mathematics

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WikiProject Mathematics (Rated Project-class)

## "Improper point" listed at Redirects for discussion

The redirect Improper point has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at Wikipedia:Redirects for discussion/Log/2023 February 26 § Improper point until a consensus is reached. —Mx. Granger (talk · contribs) 21:54, 26 February 2023 (UTC)

## "Mode-k flattening" listed at Redirects for discussion

The redirect Mode-k flattening has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at Wikipedia:Redirects for discussion/Log/2023 March 8 § Mode-k flattening until a consensus is reached. -- 65.92.244.151 (talk) 23:25, 9 March 2023 (UTC)

## Merger proposal input requested

Formal request has been received to merge: Hermitian variety into Unital (geometry); dated: February 2023. Proposer's Rationale: If I was more confident in my knowledge of this field and Wikipedia-editing skills, I would just do this myself. Edrudathec. Discuss >>>here<<<. GenQuest "scribble" 20:10, 13 March 2023 (UTC)

## Convergence Solved Leibniz formula for pi

I believe to have solved the convergence issue of the Leibniz formula for pi. [1]https://archive.org/details/improving-the-convergence-of-madhava-gregory-series-and-a-rudimentary-calculation-for. I have updated a couple of pages - Gregory's Series and Leibniz formula for pi. Please can some-one verify this against the published material and find out how to do edits across other places where they say convergence is an issue. Brian (talk) 07:10, 15 March 2023 (UTC)

Wikipedia is not the place to publish or publicize your original research. Nor is it the place to ask editors to find your mistakes. Nor is putting something on archive.org the same thing as publishing it in a peer-reviewed publication. —David Eppstein (talk) 07:13, 15 March 2023 (UTC)
I didn’t try to read your paper, but you should try asking for help on some other forum (reddit? stack exchange?). The only vaguely appropriate venue here is Wikipedia:Reference desk/Mathematics. But you might want to start by researching the large, large amount of past work that has been done on this problem. If you have a good idea about a practical way to compute π, it is pretty likely that other people have had very similar ideas already. –jacobolus (t) 15:12, 15 March 2023 (UTC)
Okay I read your paper. Your idea is essentially the same as Archimedes's Measurement of a Circle from about 250 BC (except you switch over to using Gregory's series at some point instead of continuing with polygon division). (Also see Pi § Polygon approximation era and Viète's formula.) I can guarantee you someone has tried this before somewhere and written about it, and I imagine you could find a reference if you hunted for it. –jacobolus (t) 17:33, 15 March 2023 (UTC)
Thanks! - I know the issue is the word 'Discovery'. When you look at the solution it is quite obvious this is not new.
May be you meant - Liu Hui's method or Viète's formula, not about Archimedes is it?
There was an anomaly I came across in trigonometry - deep in the derivations - surprised it was there in basic math. Looking for an answer, I came across this page - and I couldn't beleive what I was reading. A little effort and you can see the solution right in front of you - you don't need extensive derivations and experimentation, to get to this formula - a 13year old can come up with it.
And yet all over wikipedia is plastred a notion that this series is not useful.
In my document and talks I have mentioned this frustration.
People (not well read mathematicians) looking for ideas end up on this platform. There is a good reason why I put this there - we'll know in time.
A little inkling that solutions exist could be in those sentences.
Hope you know how many places people vouch by this link of Leibniz and Gregory's formula.
Currently my only beef is with the sentence that the series does not converge quickly. That sentence (and many others pages) sitting in wikipedia haave misled so many I believe. May be I wrote it on the page a bit too strongly.
Mathematicians are not in error but the ones the maintain the record because it looks like information is withheld.
Nevertheless - I respect the way you guard these pages. And I will take your point and leave it at that.
Thanks for taking the effort to read the paper - I see you are better than others on this forum that interact personally. Brian (talk) 19:10, 15 March 2023 (UTC)
Archimedes repeatedly applied the identity
${\displaystyle \cot {\tfrac {1}{2}}\theta =\cot \theta +{\sqrt {\cot ^{2}\theta +1}},\qquad 0<\theta <\pi }$
except expressed as a geometric construction, in the style of his time and context. (Desmos plot)–jacobolus (t) 20:37, 15 March 2023 (UTC)
You can read about this in Miel, George (1983). "Of calculations past and present: the Archimedean algorithm" (PDF). American Mathematical Monthly. 90 (1): 17–35.jacobolus (t) 20:55, 15 March 2023 (UTC)
You are right - all of them in history have been repeatedly been dividing angles. It is not uncommon - each method is a discovery - even if it is related. Isn't it? That's what wikipedia shows again and again - isn't it? But the real proof of all these is the limit identity of tan isn't it?
But the problem the paper address is not the limit identity isn't it? It merely says its an extra and attributes it to the limit identity doesn't it?
However the paper addresses the ignorance of the convergence doesn't it? Brian (talk) 21:25, 15 March 2023 (UTC)
Here is one example of a paper adopting more or less the same approach you suggest, but with a lot more work put into the explanation and experiments. I am sure the idea is older than this though. Fernández Guasti, M. (2005). "Blending two major techniques in order to compute π". International Journal of Mathematical Education in Science and Technology. 36 (1): 85–92. doi:10.1080/002073904123313.. –jacobolus (t) 18:31, 15 March 2023 (UTC)
Thanks, I am not a mathematician. I believe you are. If so even you, will come up with it in just a few minutes. I mean no details, experiments required. In one of my videos I say just this. Brian (talk) 19:16, 15 March 2023 (UTC)
For Wikipedia's purpose what matters is whether you can find reliable sources which make particular claims. It would e.g. be conceivably possible to mention this M. Fernández Guasti paper because it was published in a peer-reviewed journal, even if the journal is sort of obscure and low-impact. Though I would recommend against including more than a sentence or two at most, since it is not an especially novel, effective, or historically important method of improving the convergence calculations of π. On the other hand, adding a section based on e.g. a YouTube video or a PDF self-published to the internet archive by an amateur does not meet Wikipedia guidelines. –jacobolus (t) 21:24, 15 March 2023 (UTC)
Yes this is right. I shouldn't be adding items that aren't peer reviewed. At least history of this document will be a testament that I tried to tell wikipedians that a sentence in there was incorrect and misleading to many. Brian (talk) 21:28, 15 March 2023 (UTC)
And Jacob, your arguments are quite fine. But you are missing the point - I feel burried in formation in the papers is not wikipedia spirit. TLDR is! so then people can look the burried stuff Brian (talk) 21:31, 15 March 2023 (UTC)
Oh and this is a very very good example..your answers mentions so may papers but they don't mention the tan limit identity though which is the root... because that is not connected in wikipedia! Brian (talk) 21:42, 15 March 2023 (UTC)
Your "tan limit identity" is not in any fundamental way different from the method of Archimedes (also Liu Hui, Aryabhata, Jamshīd al-Kāshī, François Viète, Adriaan van Roomen, Ludolph van Ceulen, and Willebrord Snellius), except for being a self-published paper from 2023 instead of a historically famous work from centuries ago. (I'm not trying to sound harsh or dismissive here: this is a true and meaningful insight which is why it has come up and been used repeatedly by mathematicians and amateurs over the past 2+ millennia. There's nothing wrong with rediscovering previously known ideas for oneself.) –jacobolus (t) 22:01, 15 March 2023 (UTC)
it is not fundamentally different - it is fundamental Brian (talk) 05:23, 16 March 2023 (UTC)
Dave, I believe you haven't checked math.stackexchange either? :), Its ok - I see no point in any discussion here. Brian (talk) 19:20, 15 March 2023 (UTC)
You might have gotten our replies mixed up. I mentioned you could start a conversation at e.g. reddit or stack exchange if you want feedback on your paper. David only said that Wikipedia is not a good venue for original research. –jacobolus (t) 21:39, 15 March 2023 (UTC)
Yes, that is what I meant when I made that sarcastic comment. I had already suggested it on stackexchange - [2]. That's where I was pursuing it. Wikipedia was a sideline attempt to get attention so I could correct a mistake in laymans view of pi calculation. Brian (talk) 21:47, 15 March 2023 (UTC)
Can you explain what the "mistake" is?
That this series converges incredibly slowly for ${\displaystyle x=1}$ is a straight-forward factual statement. It takes about 5 billion terms to get 10 digits! Note that this is an entirely different claim from anything about the convergence near ${\displaystyle x=\tan \left(2^{-n}\arctan 1\right).}$jacobolus (t) 21:49, 15 March 2023 (UTC)
Thanks- Just correct this part.
"Finding ways to get around this slow convergence has been a subject of great mathematical interest." - you can change it to something like "Quite a lot of methods are available for improving this convergnce" (you may make a better sentence) ... then add a few references to the paper you mentioned to me and any other peer reviewed information will be better. Also many places in wikipedia this type of line exists.. that undermines the Leibniz formula... I don't believe I am the right person for this kind of job because I am not an accomplished mathematician. But there are people who can correct this misleading so, when people like me show up we know to dig further. Thanks for getting to the point. Brian (talk) 21:59, 15 March 2023 (UTC)
I will indeed add material there, but it is a nontrivial undertaking which requires actually doing the research and writing. –jacobolus (t) 22:03, 15 March 2023 (UTC)
Yes now you understand, where I am coming from. I wish, I wish... wikipedia had pointed to the tan limit identity with respect to this convergence - because they are closely related - I was a pain for me to figure it out - something so simple and already known - just not connected. We need a right person for this job. Brian (talk) 22:12, 15 March 2023 (UTC)
Here's what the "Gregory's series" article looked like a month ago. In the future I intend to add some more figures showing how convergence is much (much!) faster closer to 0, discussing Madhava's correction term, evaluation for ${\displaystyle x=1/{\sqrt {3}}}$, Machin-like formulas, Euler transform (originally due to Newton), and so on. –jacobolus (t) 22:32, 15 March 2023 (UTC)
Thanks! Brian (talk) 22:34, 15 March 2023 (UTC)
Oh and there appears to be a serious anomaly inside trigonometry related to this formula. Hope you can find references to that as well,or a soution to that then all will be perfect. Thanks again. Brian (talk) 23:10, 15 March 2023 (UTC)
I don't understand what you mean. –jacobolus (t) 23:19, 15 March 2023 (UTC)
Ok don't bother about it for now. I'll show it to you when I get it all verified. Then we can find the references. Brian (talk) 23:21, 15 March 2023 (UTC)

## "Mode-k flattening"

FYI has been nominated for renaming to some title to be determined. Some of the suggestions are "mode-m flattening", "mode-n flattening", "mode flattening", "flattening", etc. For the discussion, see the talk page. -- 65.92.244.151 (talk) 21:32, 21 March 2023 (UTC)

65.92.244.151 (talk) 21:32, 21 March 2023 (UTC)