For thousands of years, mathematicians have attempted to extend their understanding of π , sometimes by computing its value to a high degree of accuracy. Ancient civilizations, including the Egyptians and Babylonians , required fairly accurate approximations of π for practical computations. Around 250 BC, the Greek mathematician Archimedes created an algorithm to approximate π with arbitrary accuracy. In the 5th century AD, Chinese mathematicians approximated π to seven digits, while Indian mathematicians
The invention of calculus soon led to the calculation of hundreds of digits of π , enough for all practical scientific computations. Nevertheless, in the 20th and 21st centuries, mathematicians and computer scientists have pursued new approaches that, when combined with increasing computational power, extended the decimal representation of π to many trillions of digits. [4] [5] These computations are motivated by the development of efficient algorithms to calculate numeric series, as well as the human quest
Because its definition relates to the circle, π is found in many formulae in trigonometry and geometry , especially those concerning circles, ellipses and spheres. It is also found in formulae from other topics in science, such as cosmology , fractals , thermodynamics , mechanics , and electromagnetism . In modern mathematical analysis , it is often instead defined without any reference to geometry; therefore, it also appears in areas having little to do with geometry, such as number theory and statistics .