Pi is exactly 3!

December 20, 2005 2:54 PM

Did we really not know pi to more than 740 decimal places before 1947?

The preamble to the poem Near A Raven claims that "this poem could not have been written prior to 1947, since all the details of the rule it uses were not known before then."

Wikipedia says that "The Iranian mathematician and astronomer, Ghyath ad-din Jamshid Kashani, 1350-1439, computed π to 9 digits in the base of 60, which is equivalent to 16 decimal digits as: 2 π = 6.2831853071795865."

If some guy could calculate pi to 16 decimal places in the 12th or 13th century, why did it take so long to get to 740?

posted by obiwanwasabi to Science & Nature (19 answers total)

Probably because it would be a huge pain in the ass? (not to mention pointless)
posted by delmoi at 3:02 PM on December 20, 2005

because, it's a pointless exercise in arithmetical drudgery, and prior to the invention of machines designed for computation, a real person (who could conceivably spend their time doing something, ya know, beneficial) had to do it with pen and paper and a slide-rule.
posted by sergeant sandwich at 3:03 PM on December 20, 2005

Best answer: Here's a very thorough chronology of the history of calculation of pi. It suggests that the advent of desk calculators enabled Ferguson to calculate to 710 and then 808 places in 1947.
posted by jasper411 at 3:26 PM on December 20, 2005

Note 19 in jasper411's link points out that Van Ceulen spent most of his life in doing that calculation.
posted by vacapinta at 3:34 PM on December 20, 2005

The answer to this question is best understood by trying to calculate pi to 740 digits yourself, without a calculator.
posted by Hildago at 3:35 PM on December 20, 2005

knowing pi out to more than 5 or 6 digits is mostly pretty useless, and you'd have a hard time finding any use at all that required a precision greater than the 16 you mentioned. the only reason one might want to calculate it is to look for patterns in an irrational number in a search for deep insight into the nature of the universe. this is an utterly vain effort that smacks of spooky superstition and numerology, (typically currying the interest of those with a rather superficial knowledge of mathematics), especially when one considers that our base-10 number system is completely arbitrarily chosen.
posted by sergeant sandwich at 3:52 PM on December 20, 2005

Best answer: Moutains of Pi
posted by bendybendy at 4:06 PM on December 20, 2005

Thanks for the link bendybendy! That's a good read.
posted by onalark at 4:41 PM on December 20, 2005

As jasper411's link reveals (if you click on the notes), the calculating had to go hand in hand with advancements in theory, so that they could use methods that were more accurate/converged faster on the true value. It's (very vaguely) like trying to write out '1,000,000' using just tally marks, then roman numerals, then normal numerals, then scientific notation.
posted by fleacircus at 4:50 PM on December 20, 2005

I recall reading somewhere that you only need the first 32 (?) digits of Pi to measure the circumference of our galaxy (solar system? something big.) to half the size of an atom.

Wish I could be more precise, but that statement pretty much defined the uselessness of enumerating any more digits of Pi.
posted by krunk at 5:29 PM on December 20, 2005

Are there any methods that they knew that didn't use series? Because calculating with series by hand sucks. You have to figure out this tiny fraction, which gives 0.00...0012345789, and then you add that to your current value of pi.
posted by smackfu at 6:44 PM on December 20, 2005

There are probably a hundred different ways to calculate Pi. I think if I were doing it by hand I'd want to use an iterative method, such as the one under "An Improved Iteration Formula" in this page. As you can see, that one converges very quickly - it gets you approx. 167 digits after only 3 iterations.
posted by Rhomboid at 8:25 PM on December 20, 2005

Thanks for that link, bendybendy. I remember reading that article in the New Yorker back in 1992, and I think I saved it.

A couple weeks ago I shopped in a bookstore in another city. After the clerk swiped my debit card, I looked at the keypad and noticed that its display didn't have enough spaces to show "ENTER PIN"; instead it read "ENTER PI". I wondered briefly how many digits of pi it needed; I know only 3.14159265, which is probably what my high school calculator showed.
posted by neuron at 9:24 PM on December 20, 2005

Bendybendy,
Mountains of Pi.

Best. New Yorker. Article. Ever. Great link!
posted by Opposite George at 12:20 AM on December 21, 2005

OT, but I like the idea that God or creators of our universe left messages deeply downstream in pi.

This was expressed in Sagan's "Contact" when the Jodie Foster character used her alien seeking smart pattern seeker software to find a pattern in Pi a few thousand digits downstream. I believe it was a circle.

I think this was also expressed in the movie PI where messages were somehow mixed in with the text of the Talmud. That movie taught me the word trepenation. Great movie.

It was also expressed in Magnum PI, when TC got into an argument about it with Higgins. (because I hadn't derailed quiiite enough).
posted by Dag Maggot at 3:01 AM on December 21, 2005

Okay, but this all begs the question.. why did the Iranian work in base 60?
posted by wackybrit at 3:09 AM on December 21, 2005

wackybrit : The sexagesimal system has very ancient roots.
posted by punilux at 4:18 AM on December 21, 2005

And: "Often when told that the Babylonian number system was base 60 people's first reaction is: what a lot of special number symbols they must have had to learn. Now of course this comment is based on knowledge of our own decimal system which is a positional system with nine special symbols and a zero symbol to denote an empty place. However, rather than have to learn 10 symbols as we do to use our decimal numbers, the Babylonians only had to learn two symbols to produce their base 60 positional system."

Also, they had six fingers on each hand.
posted by pracowity at 8:08 AM on December 21, 2005

Here's π to 4493 digits and you can even wear it!
posted by Taken Outtacontext at 1:18 PM on December 21, 2005