Pi Day

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Pi Day is March 14, when the world celebrates the mathematical constant of the ratio of the circumference of a circle C to its diameter d: π = C/d. The circumference of a circle is, in turn, equal to 2πr, where r is the circle's radius. The constant is important in many scientific calculations and has long played an important role in engineering.

As a concept, pi has been in use since at least the time of the Babylonians and ancient Egypt: both approximated modern values of pi to within one percent (3.125 and 3.16, respectively). Archimedes is the attested author of the first rigorous definition of pi, which he did by way of geometry, using polygons with ever-greater numbers of sides. By 150 CE, Ptolemy had the value of pi at 3.1416, which he may have done using the Archimedean method.

The first 100 digits of pi are 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679.

Mathematicians have estimated that an approximation of pi to 39 digits will suffice for any cosmological calculation humans might attempt. At that level of precision, which mathematicians achieved in 1630, you can calculate the circumference of the observable universe with an error smaller than the diameter of a single atom of hydrogen.

As of 2023, the world record holder for the most precise calculation of pi is Jordan Ranous of StorageReview. Ranous used y-cruncher, a benchmarking program that uses the Chudnovsky algorithm for main computation, to calculate pi to a precision of one hundred trillion decimal places. The calculation and validation took a few hours shy of two months to complete, using a pair of AMD EPYC 9654 processors that drew on just under 600TB of QLC flash memory and more than 1.5 terabytes of RAM between them.

In 2022, Google Cloud Developer Advocate Emma Haruka Iwao announced that she and her team had calculated the value of pi to a precision of 100 trillion decimal places—a flex on her previous record of 31.4 trillion digits, set in 2019. "We were impressed by the achievement of Emma and the Google Cloud," Ranous wrote, "but we also wondered if we could do it faster, with a lower total cost."

Still, they had to solve one critical problem: How to create a storage volume of sufficient size to hold a text file a hundred trillion digits long. In the end, the team used a RAID 0 array, finishing their calculation in about a third of the compute time it took the team from Google Cloud. ("While RAID 0 might raise some eyebrows," Ranous wrote, "in our defense, the file server storage was carved out of a mirrored Windows Storage Spaces pool, so redundancy was available on the remote host.")

Ranous and his team also published(https://cloud.google.com/blog/products/compute/calculating-100-trillion-digits-of-pi-on-google-cloud) their y-cruncher validation file and the last 100 of those 100 trillion digits—just in case anyone wants to check their work.

So, next one is looking forward to Mole Day, which happens to be October 23.