Pi (π) is a mathematical constant, approximately equal to 3.14159, defined as the ratio of a circle's circumference to its diameter. It appears in many formulas across mathematics and physics, and some of these formulas are used to define it without relying on the definition of the length of a curve. Pi is an irrational and transcendental number, so its decimal digits never end or settle into a repeating pattern, and it cannot be written exactly as a fraction.
Historical calculation
Ancient Egyptians and Babylonians needed fairly accurate approximations of pi for practical work. Around 250 BC, the Greek mathematician Archimedes devised an algorithm that could approximate pi to any desired accuracy. Chinese and Indian mathematicians later produced more precise estimates using geometric methods. The first computational formula based on infinite series appeared about a millennium after Archimedes, and the development of calculus in the 17th century allowed hundreds of digits to be calculated. In the 20th and 21st centuries, computers extended the known digits to hundreds of trillions.
Role in science
Because pi is tied to circles, it appears in trigonometry and geometry, particularly in formulas about circles, ellipses and spheres. It also occurs in fields such as cosmology, thermodynamics, mechanics, electromagnetism, number theory and statistics. Whether its decimal digits are evenly distributed remains an unproven conjecture, and the transcendence of pi shows that squaring the circle with a compass and straightedge is impossible.