A Guide to Understanding Pi

Pi: An Introduction

Pi is a mathematical constant that measures the ratio of a circle’s diameter – that is, a line that passes through the center of a circle and has both ends on that circle – and its circumference, the entire distance around the circle’s edge. Pi is an irrational number; its value can be calculated to any number of places without ever repeating. It is also transcendental, meaning it will never “end.” Though it can never be understood completely, it is one of the most important constants, since it appears often in many different formulas. The value 3.14 has been known as “pi” – the Greek letter and symbol that now represents it – only about 300 years, but it had already fascinated mathematicians for centuries. The modern name was proposed by William Jones in 1706 and popularized by the mathematician Leonhard Euler when he adopted it around 1737.

A Brief History of Pi

Pi has a very long history. Circles are an integral part of many calculations, including those in subjects like architecture and astronomy, so much so that many great thinkers in the ancient world were attracted to try and calculate pi early on. Archimedes, who lived in the 200s B.C., was the first thinker who came up with a theoretical calculation of pi. As time went on, mathematicians around the world delved into the mystery of pi, including scholars like Ptolemy and Aryabhata. Many Chinese and Arabic mathematicians also estimated pi to differing degrees of accuracy. Even with all these minds at work, it was not until the 18th century that pi was truly better understood. Seekers benefited from Lambert’s discovery in 1761 that pi was irrational, and in 1882 an early version of the Lindemann-Weierstrass theorem was used to prove that pi is transcendental. Nonetheless, less than 1,000 digits of pi were known until the dawn of the computing age. Now, under the leadership of Japanese computer scientist Yasumasa Kanada and his research team, supercomputers have calculated pi as far as 2.5 trillion digits.

The Uses of Pi

From the beginning, pi has been vital in construction and architecture, and it remains so today. Pi was also used heavily in calculations by early astronomers such as Copernicus and Galileo to approximate information like the sizes, distances from Earth, and orbits of various stars and planets. Though we have more precise means of determining these things now, they would not have been possible without pi, which is still valuable in astronomy today. Pi is also essential for calculations in advanced engineering and computing projects dealing with cutting-edge technology at extremely high speeds. It also appears in research in physics, higher math, and other laboratory sciences. Sociologists, statisticians, and demographers use pi in intense quantitative analysis of given populations. Even the “average person” can use pi to determine things like what size pizza is a better deal!


Pi represents one of the enduring challenges of mathematics. It took over four thousand years of constant searching to gain the understanding of pi that humanity has today. No matter how good people become at calculating pi, its complete mystery has yet to unravel. It will always be important in some of the most fundamental applications of math and science. In modern times, pi has inspired its own fan sites and holiday for math enthusiasts, and was even a source of legal controversy! Truly, interest in pi may prove to be as endless as its digits.