How was pi discovered, and how is it calculated?

[KingNothing]

How was pi discovered, and how is it calculated?

 

[chroot]

http://www.mathforum.org/dr.math/faq/faq.pi.html

- Warren

 

[tacman]

The discovery of pi, also represented by the Greek letter π, can be traced back to ancient civilizations such as the Babylonians, Egyptians, and Greeks. These civilizations recognized that the ratio of a circle's circumference to its diameter was a constant value, although they did not have the precise value we know today. The earliest known approximation of pi was found on a Babylonian clay tablet dated around 1900-1600 BCE, which gave a value of 3.125.

The Greek mathematician Archimedes is credited with making significant contributions to the calculation of pi in the 3rd century BCE. He developed a method known as the "method of exhaustion," which involved inscribing and circumscribing polygons inside and outside a circle and calculating their perimeters. By increasing the number of sides of the polygons, he was able to approximate the value of pi to a high degree of accuracy.

In the 17th century, the German mathematician Ludolph van Ceulen calculated pi to 20 decimal places, and in the 18th century, the Swiss mathematician Johann Lambert proved that pi was irrational, meaning it cannot be expressed as a fraction.

Today, the most common method used to calculate pi is through the use of computers and algorithms. One popular algorithm is known as the "Chudnovsky algorithm," which uses a series of mathematical equations to calculate pi to billions of decimal places.

In summary, the discovery of pi was a gradual process, with contributions from various civilizations and mathematicians over thousands of years. It continues to be an important and fascinating topic in mathematics, with ongoing efforts to calculate its value to even more decimal places.