Reflections on Valentin's 2023 Pi day special

[Valentin Albillo]

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Hi, EdS2,

(03-22-2023 09:11 AM)EdS2 Wrote:  Once again Valentin has posed an interesting programming challenge based on an interesting mathematical finding.

You should work on diversifying your adjectives.

Quote:The link to Pi this time is in the counting of square-free integers (I've a feeling we called them quadratfrei in my day

No need to use a German term in an English-language forum when there's an exact English equivalent.

Quote:I did a little investigating of this, in BBC Basic, one of my preferred languages, and of course this is outside Valentin's rules of engagement.

Not so. Quoting my rules:

"Note: No hard rules so no need for a parallel thread, post here whatever you want as long as it's on topic and NO CODE PANELS, but I'd appreciate it if you'd use vintage HP calcs (physical/virtual), [...]"

and "I'd appreciate it if" is not the same as "I mandate that" so you could've posted your BBC BASIC code in the main thread. That is, if you actually wrote a solution.

Quote:What's different in my case, then, is having none of the augmented 71B's augmentations [...]

You should really work on diversifying your vocabulary.

Quote:My related challenges, then, would be
- to respond to Valentin's challenge using an unaugmented 71B, or a similarly ordinary Basic

Right now I'm going to have dinner but once it's over I'll concoct and post some code for you.

Quote:- to find values of N which incidentally deliver unfairly close values of Pi

Please define "unfairly close". Too vague as it stands.

Quote:In particular, I'd like to see (or write) a program which does the accurate counting by inclusion-exclusion, rather than trial division by prime squares.

It's fairly clear to me that you don't realize that this is exactly what the Möbius function accomplishes: it provides the required minus sign for the terms to be excluded, and the plus sign for the terms to be included. In other words, what both my solutions currently compute, so there you are.

Quote:I'd also quite like to port V's small-memory solution to an unaugmented Basic.

By "unaugmented Basic" you mean a non-expandable BASIC ? Please do. My code just about to be posted might be of help.

Thanks for your interest.
V.