#number-theory

#number-theory

For more than two millennia, mathematicians have produced a growing heap of pi equations in their ongoing search for methods to calculate pi faster and faster. The pile of equations has now grown into the thousands, and algorithms now can generate an infinitude. Each discovery has arrived alone, as a fragment, with no obvious connection to the others. But now, for the first time, centuries of pi formulas have been shown to be part of a unified, formerly hidden structure.

Pi is an infinitely long decimal number that never repeats. How do we know? Well, humans have calculated it to 314 trillion decimal places and didn't reach the end. At that point, I'm inclined to accept it. I mean, NASA uses only the first 15 decimal places for navigating spacecraft, and that's more than enough for earthly applications.

Liam Delap has an interesting party trick that you wouldn't really expect a footballer to pull out of the bag. The Chelsea forward has gone on video a few times showing off his bizarre mathematical ability to quickly calculate the cube roots of large numbers.

Sometimes the reason pi shows up in randomly generated values is obvious—if there are circles or angles involved, pi is your guy. But sometimes the circle is cleverly hidden, and sometimes the reason pi pops up is a mathematical mystery!