Reflections on Valentin's 2023 Pi day special

[EdS2]

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Reflecting on how I might myself present a similar challenge, for example in a BBC Basic forum, it feels to me that the design problem is to bring to the attention of the reader a certain interesting property of integers, and then - surprise - to link it to pi. And then the challenge itself is to find ways of writing programs to explore this property.

In the case of the challenge on these forums, there's an additional aspect, which is to be able to make use of the marvellous augmentations to the 71B's Basic, the various ROMs. And as noted, they make a great deal of difference because of the relative slowness of interpreted language.

To keep with the topic of reflecting on Valentin's challenge, indeed in the HP Calculators subforum which is where we find this thread, I might wonder what can we do with the 15C, or the 42S, or perhaps the 41, on this problem. The 15C is of course not augmented - it knows nothing of primes or factorisations - whereas it's possible the 42S knows more, and surely there are excellent ROMs for the 41 which could help.

It is possible to augment BBC Basic with a ROM, but it wasn't very commonly done. I think it involves trapping a syntax error and re-parsing the failing statement. More common, perhaps, is to add some machine code (perhaps using the built-in assembler) and then CALL or USR that code, for some expensive inner function.

As to the unfairly accurate estimates of Pi which might come up from this counting challenge, it's clear to me that we won't find the best examples at round numbers. We might even find, like Buffon, that we can advantageously and unfairly batch up our results. (If indeed he did... ah, no, it was Lazzarini.)