The number p 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 "p" since the mid-18th century, though it is also sometimes spelled out as "pi" ( / p a? / ).

The number p 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 "p" since the mid-18th century, though it is also sometimes spelled out as " pi " ( / p a? / ).

Being an irrational number , p cannot be expressed exactly as a common fraction , although fractions such as 22/7 and other rational numbers are commonly used to approximate p. Consequently its decimal representation never ends and never settles into a permanent repeating pattern . The digits appear to be randomly distributed; however, to date, no proof of this has been discovered. Also, p is a transcendental number  – a number that is not the root of any non-zero polynomial having rational coefficients . This transcendence of p implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge .