# Blog

## International Day of Mathematics (Pi Day)

by Ana Clarke 14/03/2022

In 1988, the physicist Larry Shaw, known as the "Prince of Pi", proposed to establish March 14 as Pi Day. Using the English notation and accepting 3.14 as an approximation of pi, we have: 3-14.

Pi is a constant that establishes the relationship between a circumference and its diameter, regardless of which circumference or diameter it is. The constant of this relationship is the same for a wheel, a coin or even the rings of Saturn.

The number Pi is one of the most fascinating and famous numbers in mathematics. The interest that Pi unleashes among mathematicians and non-mathematicians goes beyond all limits. Let’s review some of the milestones behind Pi number’s fame.

Who discovered the number pi?

Establishing who was the first to deduce the value of Pi is not easy. 2,000 years before Christ, the Babylonians had calculated it at 3.125. Around the same time, the Egyptians said it was 3.16049. Even the Bible provides its version of the number Pi with an approximation to 3.

In the third century B.C., Archimedes of Syracuse approximated the number Pi using polygons inside and outside a circle. He ended up with a 96-sided polygon and his final approximation was 3.14163. Archimedes also introduced the Greek letter π to refer to this constant, as it was the first letter of the Greek words: περιφέρεια and περίμετρος, which mean periphery and perimeter.

A century later, Claudius Ptolemy used a 720-sided polygon to arrive at another approximation of Pi: 3.141666. Liu Hui, in the third century after Christ, worked with polygons up to 3092 sides to get an approximate value of 3.14159. Zu Chongzhi added two decimal places in the 5th century: 3.1415929. At the same time in India, Persia and Italy with Fibonacci, similar results were reached.

In 1615, Ludolph van Ceulen accurately found the first 35 digits of pi. It was such a milestone in the history of pi that Van Ceulen had these digits engraved on his own grave.

William Shanks dedicated 20 years of his life to the study of the number pi. In 1872 he described the first 707 of pi number decimals. As a tribute to Shanks’s discovery, his number pi with the 707 decimal places was written under the dome of the Palais de la Découverte in Paris.

This was the last milestone achieved by the calculation mathematicians in the time when there were no calculators. Once computers took over, the challenge was to deduce the most Pi decimal point numbers in a certain amount of time.

Interesting assets of Pi number

In the 1760s, Johann Heinrich Lambert was the first to prove that the number pi is irrational. This means that Pi cannot be expressed as the ratio of two integers. Pi has an infinite decimal expansion with no repeats and no patterns. Pi decimal numbers go on and on.

Pi number is also a transcendental number. It is an exciting property proved by Ferdinand von Lindemann in 1882. This means that the number pi is not the root of any polynomial with integer coefficients. Because of this, it is known that pi cannot be written as any finite combination of integers and/or their roots.

Transformed by Pi

The number pi has fascinated so many people that:

When a survey was conducted among subway passengers in my home city of Buenos Aires to find out what number they remember most, Pi came in the first place. So 31416 was setup as the emergency number in the subway.

There is a Pi Bar in San Francisco, USA.

Pi fans have tattooed the Greek letter and several of its decimals.

People have entered into the Guinness Book of Records for remembering by heart thousands of the decimals of the number pi.

There are mnemonic rules for remembering the first decimal numbers of pi.

The cinema has also echoed the fame of the number Pi with films like Pi - Faith in Chaos.

The number Pi is not only a mathematically interesting number. It is applied in many functions in our lives. In NASA, for example, Pi number has an essential role in the day-to-day job of its scientists. They use Pi number to measure craters as well as determine the size of the planets that orbit suns other than our own (exoplanets).

Pi number is also behind the Internet, mobile phones, GPS signals and the radio because these waves have circular motion.