π (or pi) is a mathematical constant that is the ratio of a circle's circumference to its diameter. It is approximately equal to 3.14159. π is an irrational number, which means that it cannot be expressed exactly as a ratio of two integers, although it is roughly approximated by 22/7. It is a transcendental number – a number that cannot be produced with a finite sequence of algebraic operations (sums, products, powers, and roots). The transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge. The digits in the decimal representation of π appear to be random. Because its definition relates to the circle, π is found in many formulae in trigonometry and geometry, such as Euler's identity, eiπ + 1 = 0. It is also found in formulae from other branches of science, such as cosmology, number theory, statistics, fractals, thermodynamics, mechanics, and electromagnetism. (more...)
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