03/11/2016

How Many Digits of Pi Do We Really Need?

2:20 minutes

Mathematician James Grime of the YouTube channel Numberphile has determined that 39 digits of pi—3.14159265358979323846264338327950288420—would suffice to calculate the circumference of the known universe to the width of a hydrogen atom. (That number is rounded, for those of you keeping track.)

*If you listened to this segment live, please note that the antepenultimate digit in the 39 digits of pi mentioned was misstated. The guest accidentally said “1…2…0,” when in reality he meant to say “4…2…0.” The transcript has also been updated. Thanks to Twitter fan @openMindedSkep for pointing this out. We have amended the audio file on this page. 

Segment Guests

James Grime

James Grime is known to many as the mathematician from the YouTube Channel Numberphile. He’s based in
Cambridge, England.

Segment Transcript

IRA FLATOW: Now, you know today is March 11th or 3.11, just three days away from one of our favorite days, 3.14, which you all know as– that’s right, pi day. We celebrate it every year and this year is no exception. So we called up the mathematician, James Grime of the YouTube channel Numberphile, that’s phile spelled with a ph. Anyway we called up James because we wanted to know, well, how many digits of pi do we actually need and he didn’t disappoint us.

JAMES GRIME: So as everyone knows from school, pi is used to calculate the circumference of a circle. The formula for the circumference of a circle is pi times the diameter of the circle. Now, if you wanted to calculate something very large, let’s say we wanted to calculate the circumference of the known universe, which is going to be a huge thing. Now, the diameter of the observable universe is about 1 trillion trillion kilometers, so it’s a massive thing. We want to know the circumference of that universe.

Now we’re going to use pi for that, so we take pi, we multiply it by the diameter and we can get the circumference. No problem. But pi, something that goes on forever, it’s an infinite decimal. It will go on forever. So where do we stop?

Now, it turns out that we only need to use 38 decimal places to calculate the circumference of the universe to within the diameter of one hydrogen atom. So by 38 decimal places, I mean it will be a 3.14159265358979323846264338327950288420.

IRA FLATOW: Wait a minute. Go back. He’s gone. I missed a number there, sequence of 39 digits of pi. That was mathematician James Grime of the YouTube series a Numberphile on why we only need 39 digits of–

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