Is pi an infinite number? What is the 31 trillionth digit of pi?

In Aug 2021,The University of Applied Sciences of the Grisons calculated π to 62,831,853,071,796 digits, adding 12.8 trillion new digits to the previous record. They used a high-performance computer with one terabyte of RAM and 510 terabytes of disk space. The calculation took 108 days and 9 hours to complete.

In March 2019 Iwao Emma Haruka from Google cloud computing calculated the value of π to 31,415,926,535,897 digits using a program called y-cruncher. She then set the world record in 2022 by calculating up to 100 trillion digits of π.

The history of the computation of π is a long and fascinating one, dating back to ancient times. π is the ratio of the circumference of a circle to its diameter, and it is an irrational number, meaning that it cannot be expressed as a fraction of two integers. It is also a transcendental number, meaning that it cannot be the solution of any polynomial equation with rational coefficients. Some of the earliest approximations of π were made by the ancient Babylonians, Egyptians, Sumerians, and Chinese, who used various methods to estimate the area or circumference of a circle. They obtained values ranging from 3 to 3.16. The first rigorous calculation of pi was done by Archimedes of Syracuse (287–212 BC), one of the greatest mathematicians of the ancient world. He used a method called exhaustion, which involved inscribing and circumscribing regular polygons around a circle and calculating their perimeters.

Many other mathematicians and scientists contributed to the computation of π over the centuries, using different techniques such as infinite series, continued fractions, arithmetic-geometric means, and Monte Carlo methods.
Some notable names include Zu Chongzhi (429–501), who calculated pi to seven decimal places; François Viète (1540–1603), who derived an infinite product formula for pi; John Machin (1680–1751), who computed pi to 100 decimal places; Srinivasa Ramanujan (1887–1920), who discovered many rapidly converging series for pi; and John Wrench (1913–1990), who computed pi to one million decimal places using a desk calculator. Today, computers have enabled the computation of π to trillions of digits, using algorithms such as the Chudnovsky algorithm, the Bailey–Borwein–Plouffe formula, and the y-cruncher program. These calculations are mainly done for testing the performance and reliability of computers, as well as for setting world records.

However, for most practical purposes, only a few digits of π are sufficient. 😊