Reflections on Valentin's 2023 Pi day special

[EdS2]

Yes, at some point we get so close to pi that our error calculation might be off. But the original BBC Basic I've been using, on a 6502 (emulator), has 5 byte floats with 32 bits of precision, and that's OK I think for the numbers I give above.

A modern BBC Basic on an Intel-based computer has 10 byte floats with 64 bits of precision, and can give us a few more record-holders:

Code:

    693570     421640  3.14159265
    793985     482685  3.14159265
    981973     596968  3.14159265

(I should have asked it to print more digits for the approximation, of course!)

And yes, I too suspect it should be possible to compute a running approximation somehow. But note that each term of the sum has a multiplier of N inside a floor function - it's not straightforward to factor N out.