People across the world are eating pies and celebrating the circle this Saturday — and this year's Pi Day is particularly special. The full date, 3/14/15, is pi to the first four places. At 9:26 a.m. and 53 seconds, you can even celebrate pi to nine places: 3.141592653.
NPR's Math Guy, Keith Devlin of Stanford University, joined Weekend Edition Saturday host Scott Simon to share a few facts about the number behind the celebrations. First, he reminds us that it's equal to a circle's circumference divided by its diameter. Then he shares some more esoteric facts:
It took millennia to prove that pi is irrational
Pi first was discovered by ancient mathematicians, but it took until the 18th century for scientists to finally prove that pi is irrational. That means it can't be expressed exactly in decimals — if you try to calculate it, you get an infinite series of digits that are random, not predictable.
The 18th-century proof, Devlin says, was related to a problem posed by the ancient Greeks: whether it was possible to draw a square with the same area as a given circle.
"The answer is no," Devlin says, "and it has to do with the degree to which the digits in the decimal expansion of pi are random."
Pi has been calculated to more than a trillion digits...
Ages ago, Babylonian, Egyptian, Greek, Indian and Chinese mathematicians calculated pi to the first three or four places, and also used fractional approximations, including 22/7 and 355/113.
"In the 16th century, a German who presumably had a lot of time on his hands spent most of his life computing pi to 35 places," Devlin says.
A 19th-century Englishman made it to 707 places ... but only the first 527 were correct.
We've come a long way since then. Computers have been used to compute pi to well over a trillion places.
... but for most purposes, you don't need many digits at all.
Pi to just 9 places, for instance, allows you to calculate the circumference of the Earth and be accurate to within 1/4 of an inch.
Pi can be calculated from an endless addition problem
A series known as Gregory's series consists of all the reciprocals of the odd numbers, summed up with alternating signs.
It might make more sense to see it. The endless sum begins: 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + 1/13 ... and continues infinitely.
"Since this sum goes on forever, you can't actually add it up," says Devlin, "but you can use mathematical techniques to determine the answer a different way. And that answer is pi/4."
The symbol π is short for "perimeter."
"Pi is the circumference of a circle whose diameter is 1," says Devlin. A circumference is the perimeter of a circle — "and pi is the first letter of the Greek word perimeter."
And while pi may be ancient, that shorthand is not: the use of the symbol π to represent the value only dates back to the 18th century.
9(MDE1MTIxMDg0MDE0MDQ3NTY3MzkzMzY1NA001))
Transcript
SCOTT SIMON, HOST:
Today is March 14, a day of the year when mathematicians around the world celebrate Pi Day. That mathematical constant denoted by the Greek letter pi, the number you get when you divide the circumference of a circle by its diameter. Back in 1988 on March 14, a physicist called Larry Shaw organized the first Pi Day celebration. It was at the Exploratorium in San Francisco, and youngsters marched around one of their circular rooms there and wound up eating fruit pies. Ever since, March 14 has been Pi Day. Celebratory events are organized across the United States and other parts of the world. But why March 14? Our own math guy Keith Devlin of Stanford University joins us. Keith, thanks so much for being with us.
KEITH DEVLIN: Thanks for having me on, Scott, and happy Pi Day to you.
SIMON: Happy Pi Day to you. Why March 14?
DEVLIN: OK, so it goes from the - when you take pi and you try to write it down as a decimal, the first thing to notice is you can't actually do that. If you start to enumerate the decimals of pi, it starts out 3.1415926 yada, yada, yada, and actually goes on forever without repeating or settling into some sort of nice pattern. So it's what mathematicians call an irrational number. But if you take the first two decimal places, you get 3.14. If you're American and you give dates in this crazy fashion that we do on this side of the Atlantic, as the month before the day, then you get 3/14 for 3.14. So that's March the 14. In fact, this year is a really, really special Pi Day...
SIMON: Yeah.
DEVLIN: ...Because it's 2015. So you actually have 3/14/15, so today is a very unusual Pi Day in that it gives us the year as well.
SIMON: Oh, mercy. What is a - what does a guy like you, a distinguished, erudite mathematician do on Pi Day?
DEVLIN: (Laughter) Well, what I do is I talk to my friend Scott Simon about Pi Day...
SIMON: Oh, right.
DEVLIN: ...And pi (laughter).
SIMON: Other than our conversation, what...
DEVLIN: The reality is, I share this sort of - the sensible reason why Larry Shaw did this. It's getting kids to sort of look at mathematics and think about mathematics. And as soon as you start talking about pi, that actually connects to almost all of mathematics and all of science and engineering because pi...
SIMON: Or radio, radio.
DEVLIN: Yeah, we couldn't be speaking on the radio if it wasn't for pi. We wouldn't be able to speak on a mobile phone or smartphone if it wasn't for pi. We wouldn't have computers. Celebrating Pi Day is a really good way to get kids aware of the role mathematics plays in today's world.
SIMON: Keith, here's a question that I haven't had a chance to ask you through the movie awards season, yeah. Who do you want to play you, Benedict Cumberbatch or Eddie Redmayne?
DEVLIN: Oh, that's an interesting one. They were both awesome...
SIMON: Now that mathematicians are so, you know...
DEVLIN: Oh, wow. I'll go for Benedict Cumberbatch.
SIMON: Oh, all right. Let me just - let me just check in the control room...
DEVLIN: (Laughter) Let's contact his agent.
SIMON: There's a feeling in the control room that that's begging credulity, but..,
DEVLIN: OK, I'll go for the other for the other guy then. I thought both performances were superb.
SIMON: Well, and because mathematicians are the most interesting people, aren't they?
DEVLIN: Well, I think so.
SIMON: Keith Devlin, executive director of the H-STAR Institute at Stanford University, our math guy and a fascinating man. Thanks so much for being with us.
DEVLIN: My pleasure, Scott. And once again, happy Pi Day to you and all our listeners.
(SOUNDBITE OF SONG, "LEIBNIZ'S SERIES FOR PI")
ZAMBRA: (Singing) 3.14159265358...
SIMON: And you can read more about Pi Day if you haven't had your fill of it with our own Keith Devlin. He's featured in The New York Times' Wordplay blog. We have a link to it on our Facebook page and these wonderful voices. This is Zambra. They're a choral group based in Santa Cruz, Calif.
(SOUNDBITE OF SONG, "LEIBNIZ'S SERIES FOR PI")
ZAMBRA: (Singing) ...7950 - 3.14159 - 197 - 3.1415... Transcript provided by NPR, Copyright NPR.
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