I think it should be called "Pi and the rise of pay-for publication" or perhaps "Predatory journals and miscomputing pi". If a predatory 'journal' is more interested in taking submissions' money than presenting science, then the thought of peer review doesn't enter into the picture.
The journals that are mentioned are present on Beal's list of predatory journals [1], and so are even widely acknowledged to be crap journals.
https://en.wikipedia.org/wiki/Predatory_open_access_publishi...
It looks like the best place to verify reputable open access journals is through the Directory of Open Access Journals: https://doaj.org/oainfo. I don't see any of the journals mentioned in the article listed.
It used to be "if you have to pay, then it's not worth publishing in it", but plos requires $1500 so that rules out of the window.
My favorite wrong value for pi is 355/113, as it is surprisingly accurate for its simplicity.
As a side note:
> and by the third century Chinese mathematician Liu Hui and the fifth century Indian mathematician Aryabhata, both of whom found pi to at least four digit accuracy.
Zu Chongzhi should also be mentioned:
https://en.wikipedia.org/wiki/Zu_Chongzhi
The simple fraction 355/113, or Milü:
https://en.wikipedia.org/wiki/Milü
which is very easy to rememember (the first three odd numbers repeated twice) and gives in its simplicity an excellent approximation.
On Windows Calc:
355/113-pi=2,6676418906242231236893288649633e-7
The article links to 11 papers, but they have only two authors: one claming π = 17 – 8√3, and another one claming π = (14 – √2)/4.
Reading his little paper, I was amazed at how many formula there are for calculating pi. Math is fun.
Well, The thing about "the collapse of peer review" (or the rise of predatory journals) is that it involves something like the collapse of the "scientific community". For a device like peer review to work, you need to have a pool of individuals who are trustworthy - who care more about the truth more than they care about one or another sources of immediate benefit.
The institution of tenure is intended to facilitate this - the ideal is a professor receives tenure and then can pursue their ideals rather than constantly looking over their shoulder wondering if they are going to survive.
Of course, tenure is subject to abuse and tenure isn't the only way to get a pool of people who are significantly interested in "what is true" rather than "will this benefit me". But elimination of tenure and the reworking of the university on a "neo-liberal" basis of pay-for-immediate-performance does seems to be gradually destroying the community part of the scientific community (if a given authority just wants money, why shouldn't any of their peer reviews be up for the highest bid or why should they endorse predatory journal or etc). That's not as much of a problem with technical fields where it's known that truth can be nearly mechanically verified (math is approaching that level but sociology seems unlikely to get there soon, for example).
We may get to a point where our society has immense technical know-how but has abandoned science as such. Goes along with "post-truth" I suppose.