Jan 23, 2023

There’s A Formula To Calculate Any Digit Of Pi, And Nobody Noticed For Centuries

Posted by in categories: computing, mathematics

What’s your favorite number? There are literally infinite options, and yet only a few which seem to stand out as more popular than others: there’s seven, obviously; 13 or 666 for the badasses among us; and √2 for anyone who just likes annoying Pythagoreans.

But there’s really only one number out there that can claim to be World Champion: pi. What other mathematical constant is literally used as a benchmark for computing power, or forms the basis for a never-ending worldwide grudge match over who can list the most random digits in the correct order (current record: 111,700)?

The reason pi is able to capture our imagination like this is because it is an irrational number – in other words, its decimal expansion is never-ending and entirely random. It’s thought that any sequence of numbers you can possibly think of can be found somewhere in the expansion of pi, and yet knowing any particular sequence somewhere in the expansion tells you no information about which digit comes next.

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