PRESENTATION OUTLINE
The number π is a mathematical constant, the ratio of a circle's circumference to its diameter, commonly approximated as 3.14159. It has been represented by the Greek letter "π" since the mid-18th century, though it is also sometimes spelled out as "pi"
Ancient civilizations needed the value of π to be computed accurately for practical reasons. It was calculated to seven digits, using geometrical techniques, in Chinese mathematics and to about five in Indian mathematics in the 5th century AD. The historically first exact formula for π, based on infinite series, was not available until a millennium later, when in the 14th century the Madhava–Leibniz series was discovered in Indian mathematics.
In the 20th and 21st centuries, mathematicians and computer scientists discovered new approaches that, when combined with increasing computational power, extended the decimal representation of π to, as of 2015, over 13.3 trillion (1013) digits. Practically all scientific applications require no more than a few hundred digits of π, and many substantially fewer, so the primary motivation for these computations is the human desire to break records
The best known approximations to π dating before the Common Era were accurate to two decimal places; this was improved upon in Chinese mathematics in particular by the mid first millennium, to an accuracy of seven decimal places. After this, no further progress was made until the late medieval period.
Some Egyptologists have claimed that the ancient Egyptians used an approximation of π as
22
/
7
from as early as the Old Kingdom.This claim has met with skepticism.
