Reflections on Valentin's 2023 Pi day special

[EdS2]

(03-22-2023 09:11 AM)EdS2 Wrote:  My related challenges, then, would be
- to respond to Valentin's challenge using an unaugmented 71B, or a similarly ordinary Basic
- to find values of N which incidentally deliver unfairly close values of Pi

Having managed to produce a BBC Basic program - not by writing one, more by porting and augmenting solutions posted - here are some findings from my second challenge-to-self. I think it should be clear what I'm after, so here are some cherry-picked examples:

Code:

        28         17  3.14362099
       426        259  3.14145283
      1186        721  3.14159601
      5374       3267  3.14159277
     25684      15614  3.14159262
     89440      54373  3.14159265

(And in case it isn't clear, I keep a track of what the error in the estimate in Pi is, and look for a best-so-far lowest error, for each value of N. The above is a subset of the list of record-breakers. The final value listed above is rather close to pi: 3.1415926532...)

I used a fast BBC Basic engine for this - I simply ran the original program for successive values of N. Perhaps there's a cheaper way, as this does seem to be highly redundant.