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Science & Environment

The 'Math Guy' Presents 5 Facts About 3.14

A man stands in front of a blackboard illustrating the pi number.

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 nineplaces: 3.141592653.

NPR's Math Guy, Keith Devlin of Stanford University, joined Weekend Edition Saturdayhost 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.

Copyright 2020 NPR. To see more, visit https://www.npr.org.