#3 Pi

The number pi is the ratio between the circumference of a circle and its diameter. It's approximately equal to 3.14159265, although the digits go on forever.

Some mathematicians are obsessed with computing pi to more and more digits. In the year 1610, a German mathematician computed pi to 35 digits. In 1789, a Slovene mathematician computed pi to 140 digits. This was all done by hand, in poorly heated houses.

An English amateur mathematician spent 20 years calculating pi to 707 digits, finishing in 1873. 71 years later, it was discovered that he had made a mistake at the 528th digit, and all the digits following it were wrong.

In 2002, frantic Japanese mathematicians used a supercomputer to accurately compute pi to 1,241,100,000,000 digits.

Based on all this effort, you might assume that it'd be useful to know a trillion digits of pi. However, if you had a circle the size of the observable universe, and you wanted to compute its circumference with an accuracy equal to the size of a proton, the number of digits of pi that you'd need is only 43.

Either mathematicians are totally crazy, or they're planning ahead for a time when the survival of humanity will depend on the ability to construct extremely large, accurate circles.

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