A Brief History of Pi  Summary and Q&A
TL;DR
Pi has been studied for thousands of years and its value has been estimated by various civilizations with increasing accuracy using methods like the method of exhaustion and infinite series.
Questions & Answers
Q: How did ancient civilizations estimate the value of Pi?
Ancient civilizations used various methods, such as comparing circles to squares, pentagons, hexagons, and other polygons, to estimate the value of Pi. These estimates became more accurate as the number of sides on the polygon increased.
Q: How did the introduction of decimal notation and algebra impact the calculation of Pi?
Decimal notation, developed in India, and algebra, developed in Persia, revolutionized the calculation of Pi. Decimal notation simplified arithmetic, while algebra allowed mathematicians to manipulate equations and solve complex problems, including those related to Pi.
Q: How did European mathematicians calculate Pi after a thousand years of stagnation?
European mathematicians, inspired by the Scientific Revolution and the Age of Enlightenment, adopted new rational and theoretical approaches to calculating Pi. They used infinite series, first used in India, to estimate Pi with increasing accuracy.
Q: Why do people continue to calculate more digits of Pi?
People continue to calculate more digits of Pi for various reasons. It serves as a test for the accuracy and efficiency of new computers, a source of random numbers, and a symbol of human curiosity and desire to understand the world.
Summary & Key Takeaways

Pi, the ratio of a circle's circumference to its diameter, is an important mathematical constant that has been studied for thousands of years.

The ancient civilizations of Egypt and Babylon estimated Pi to be 3.16 and 3.125 respectively, with surprising accuracy considering the limited tools and knowledge of the time.

Greek mathematician Archimedes used the method of exhaustion, calculating the perimeter of polygons inscribed in and circumscribed around a circle, to estimate Pi to two decimal places.