Mathematician Reveals Pi Formula That Was Under Their Noses for Centuries
by Ashley Dreiling
If you’re talking numbers, pi is arguably the most popular.
The Greek letter “π” represents the ratio of the circumference of any circle to the diameter of that circle, regardless of the circle’s size. Around 250 BC, Greek mathematician Archimedes created an algorithm to approximate pi, but in 2022, Simon Plouffe quietly published a new manipulation of pi – one that no one noticed for centuries.
The importance of pi cannot be understated, as it’s used as a benchmark for computing power. But pi is hugely popular because it’s an irrational number, and its decimal is both infinite and random (3.14159265359…)
The reason pi is able to capture our imagination like this is that it is an irrational number – in other words, pi’s decimal expansion is never-ending and entirely random. It’s believed that you can find any possible sequence of numbers in pi, and last year Simon Plouffe found a way to calculate any given digit of pi you can dream up.
Plouffe is the “P” in the BBP algorithm he discovered in 1995 that determines the nth digit of the binary expansion of pi. His new formula uses estimates for calculating Euler’s and the Bernoulli numbers, sequences that are time-consuming, labor-intensive, and grow extremely quickly.
For Plouffe, the formula, which he uploaded to the ArXiv preprint server in January 2022, is more about the journey than the destination.
“Not only is the formula true but it is also elegant and simple,” said Plouffe, according to Business News. “It is especially for base 2 that it is a beautiful formula. So, I think we can say that the formula is pretty cool.”
While there are likely no practical uses for this new calculation, its inspirational discovery centuries after the birth of the original algorithm is almost certain to propel the love of pi to new heights. It serves as a reminder to mathematicians and laypeople alike that significant breakthroughs can and do happen at any time and anywhere.