The number pi is one of the most famous numbers in mathematics. It describes the relationship between the circumference of a circle and its diameter. Today we know trillions of digits of pi, but the journey to understand it began thousands of years ago with practical problems in building, farming, and astronomy.
Some of the earliest known approximations come from ancient Babylon around 2000 BCE, where mathematicians used a value of about 3.125. This was accurate enough for measuring land and constructing circular structures. In ancient Egypt, around 1650 BCE, the Rhind Papyrus shows an even better estimate of about 3.1605. These early values were not theoretical discoveries. They were tools used to solve everyday engineering challenges.
A major breakthrough came around 250 BCE with the Greek mathematician Archimedes. Instead of guessing a value, he developed a systematic method. By drawing polygons inside and outside a circle, he was able to prove that pi must lie between 3.1408 and 3.1429. This idea of improving accuracy step by step using geometry was one of the first examples of rigorous mathematical reasoning.
In China, similar geometric thinking developed independently. Around the third century CE, the mathematician Liu Hui refined polygon methods by repeatedly doubling the number of sides. Starting from a hexagon, he worked up to a 96 sided polygon and obtained an approximation of about 3.1416. His reasoning showed a deep understanding of how increasing the number of sides makes the polygon follow the curve of the circle more closely.
Chinese mathematics reached an extraordinary level of precision around 480 CE with Zu Chongzhi. He proved that pi lies between 3.1415926 and 3.1415927, and he proposed the remarkably accurate fraction 355 divided by 113. This remained the best known value in the world for nearly a thousand years. Although his original text has been lost, historians believe he used extremely large polygons to achieve this level of accuracy.
A new direction emerged in India around 1400 CE, when Madhava of Sangamagrama developed infinite series for calculating pi. Instead of relying purely on geometry, he used ideas that would later become part of calculus. These methods allowed mathematicians to compute pi more efficiently and laid the foundations for modern mathematical analysis.
European mathematicians continued this progress. In 1593, Francois Viete discovered an infinite product formula for pi. In 1706, William Jones introduced the symbol pi, taken from the Greek word for perimeter. A few decades later, Leonhard Euler popularised this notation, and it became standard in mathematics worldwide.
In 1777, the French scientist Buffon introduced a surprising new connection. By dropping needles onto a floor marked with parallel lines, he showed that probability could be used to estimate pi. This experiment linked geometry with randomness and can be seen as an early form of the Monte Carlo simulation techniques widely used in modern science and computing.
The twentieth century brought the power of machines into the story. In 1949, the ENIAC computer calculated 2037 digits of pi, an achievement that would have been impossible by hand. As computing technology advanced, records increased rapidly. By 1989, computers had reached over one billion digits. In 2019, a Google supercomputer calculated 31.4 trillion digits.
Today, more than one hundred trillion digits of pi are known. Yet in practical science and engineering, such extreme precision is rarely needed. About fifteen decimal places are sufficient to navigate spacecraft across the solar system. This shows that while pi has become a symbol of mathematical curiosity and computational power, its real importance lies in the fundamental role it plays in understanding shapes, motion, waves, and the structure of the universe.
One striking fact captures this perfectly. If pi were known to thirty nine decimal places, it would be possible to calculate the circumference of the observable universe with an error smaller than the width of a hydrogen atom. From ancient builders estimating circles to modern scientists exploring space, the story of pi is a powerful example of how human curiosity drives mathematical discovery.
Pi Day is celebrated each year on 14 March (3-14) because the date matches the first three digits of pi, 3.14. It is a fun way to promote interest in mathematics and science through activities such as solving puzzles, reciting digits of pi, coding simulations, and even eating circular foods like pies. Many schools and universities use the day to explore the history of mathematics, real world applications of numbers, and the role of precision and approximation in science and engineering.
There are lots more interactive activities to try on our mini site: https://jamesabela.github.io/piday/index.html
