## Calculating Pi Less Terribly

Back on “Pi Day” I shared a terrible way of calculating the digits of π. It’s neat in principle, yes. Drop a needle randomly on a uniformly lined surface. Keep track of how often the needle crosses over a line. From this you can work out the numerical value of π. But it’s a terrible method. To be sure that π is about 3.14, rather than 3.12 or 3.38, you can expect to need to do over three and a third million needle-drops. So I described this as a terrible way to calculate π.

A friend on Twitter asked if it was worse than adding up 4 * (1 – 1/3 + 1/5 – 1/7 + … ). It’s a good question. The answer is yes, it’s far worse than that. But I want to talk about working π out that way.

(More …)

## Matthew Wright 9:30 pm

onSunday, 17 May, 2015 Permalink |I tried memorising pi once, but for some reason I couldn’t finish. It wasn’t very rational of me. I sort of had to say that. (Actually, I probably didn’t…)

LikeLike

## Joseph Nebus 5:27 pm

onWednesday, 20 May, 2015 Permalink |Aw, not to fear. I don’t think worse of you for saying it. It is the kind of joke people have to say, after all.

LikeLike

## abyssbrain 3:40 am

onMonday, 18 May, 2015 Permalink |It’s really difficult to manually calculate pi using a series. William Shanks claimed to have calculated pi manually up to more than 700 digits using the Machin’s formula,

but he erred on the 528th digit, I think. It was a very amazing achievement nonetheless.

LikeLike

## Joseph Nebus 5:31 pm

onWednesday, 20 May, 2015 Permalink |Shanks’s case is interesting, not just because of his great work and tragic error. There is also that museum rotunda that tries to honor him by displaying the digits of pi; it was built before his error was found.

So the question is: keep the digits he calculated which are wrong, or replace them with the digits he would have calculated had he done the work right? Bearing in mind the purpose is to honor Shanks’s work, and

nobodyis going to get the digits of pi from reading what is essentially a piece of memorial art.LikeLiked by 1 person

## Chow Kim Wan 1:47 am

onWednesday, 3 June, 2015 Permalink |From what I know, the Gregory-Leibniz series, while theoretically correct, converges very slowly to the desired value. I tried it once, up to around eight hundred terms. It was nightmare trying to get the figure to converge to a reasonably good number of decimal places. Some other formulas are more useful for this purpose. This series remains one of theoretical interest and mathematical beauty.

LikeLike

## Joseph Nebus 10:40 pm

onFriday, 5 June, 2015 Permalink |Oh, there’s no need to disparage the series as ‘theoretically’ correct; it’s right, no question about that. It’s just a matter of how much work is required to get what you want out of it. As series approximations for pi go, it’s not very efficient. It takes a lot of work to get a few meager decimal places right. But at least it’s very easy to understand.

If you were stranded on a desert island and needed to calculate the digits of pi for some reason, you could remember this formula well enough and work out its terms well enough. Other formulas would get you more decimal places with fewer terms being calculated, but you have to remember and apply the formulas, and that’s a pain.

Interestingly, it’s possible to calculate an arbitrary

binarydigit of pi without working out all the binary digits that come before it. There’s no way to do that for the decimal digits of pi; I forget whether there’s merely no known way to do that, or if it’s known to be impossible to do that. But the result is if you wanted to know just the (say) 2,038 trillionth binary digit of pi, you could work that out without knowing anything about the 2,037,999,999,999,999 digits that came before it.LikeLiked by 1 person