[VA] SRC #009 - Pi Day 2021 Special

[Valentin Albillo]

      
Hi all:

Thanks to J-F Garnier, Gerson W. Barbosa. Albert Chan, PeterP and robve for your interesting posts, much appreciated. This isn't my final results and comments yet but a few intermediate comments to things you say in your posts, read on ...

J-F Garnier Wrote:For point (c), well ... it's a nice identity

If you say so ... this means you think that  2 + 2 = 4   is a "nice identity" too ?

J-F Garnier Wrote:I don't think we can say that the equation e^(i π) + 1 = 0 can be used to get π from e. If you try to get π from this expression, you will just end with π = acos(-1).

Well, you can isolate \(\pi\) in the equation and you get   \(\pi\) = log_e(-1) / i, which apart from constants -1 and i features a logarithm base e as a fundamental part of it, and which your Emu71+Math ROM readily evaluates as:

      >LOG((-1,0))/(0,1)

            (3.14159265359, 0),     i.e.: \(\pi\)

and I see no cosine in that evaluation.

J-F Garnier Wrote:I don't know -and don't think there is - any relation that can be used to get π from e.

Paraphrasing Hamlet:

      "There are more things in heaven and earth, Jean-François, than are dreamt of in your philosophy"

In other words, you bet there are.

Gerson W. Barbosa Wrote:A nice multi-purpose identity, I would say.

Thanks for your appreciation of the expression (not identity, unless like J-F you consider 2 + 2 = 4 an identity).

PeterP Wrote:This is astounding I have to say and now I want to go out and publish papers very Sunday as well. Has academic publishing really come to this?

Some of it, regrettably yes. See robve comments immediately below and my comments on it.

robve Wrote:Predatory journals like these aim to make money by publishing pretty much anything as long as you pay. Predatory and hijacked journals are popping up like bad mushrooms:

This blog entry explains it all in great detail and also includes a long list of such journals.

      Science Spammers

The list includes many IOSR journals like the two featuring the four papers I cited.

robve Wrote:No data is reported on "IOSR Journal of Mathematics". It is doubtful that these papers are peer reviewed by academics.

It isn't "doubtful" at all: they aren't, period. It's quite impossible that any paper claiming that \(\pi\) is actually a simple algebraic value would pass any kind of peer review by real academics, it would be immediately thrown to the garbage bin to keep company with papers solving the quadrature of the circle and other such nonsense.

robve Wrote:The improper integral can be evaluated [...] using a vintage HP or SHARP BASIC calculator using Romberg with midpoint quadrature

I seem to remember that in some other post in another thread you said something along the lines of "every programmer should write their own integration procedure".

Well, I could agree in principle with that statement, writing quadrature programs is fun, but I've never bothered to write Romberg-based ones, as they are extremely inefficient in my not-so-humble opinion. Said procedures were OK for very limited HP calcs of old such as the slow, RAM-starved HP-34C, but for powerful models such as the HP-71B, say, there are much, much better, faster alternatives, some of which I've programmed in the far past, with excellent results.

I don't know why the Math ROM creators used Romberg in the ROM instead of a better, faster method but then again, they made many questionable decisions and glaring omissions as well (J-F has remedied some of that in his awesome Math Pac 2 and he's not done with it yet.)


My final results/comments in a few days. Let me remind all interested people that point d hasn't been addressed by anyone yet. As it's my long-standing policy, if it finally goes utterly unaddressed I won't comment on it either.

Best regards.
V.