The number π (/paɪ/; spelled out as "pi") is a mathematical constant, approximately equal to 3.14159. It is defined in Euclidean geometry[a] as the ratio of a circle's circumference to its diameter, and also has various equivalent definitions. It appears in many formulas in all areas of mathematics and physics. The earliest known use of the Greek letter π to represent the ratio of a circle's circumference to its diameter was by the Welsh mathematician William Jones in 1706.[1] It is also referred to as Archimedes's constant.[2][3]
As an irrational number, π cannot be expressed as a common fraction, although fractions such as
22
/
7
are commonly used to approximate it. Equivalently, its decimal representation never ends and never settles into a permanently repeating pattern. Its decimal (or other base) digits appear to be randomly distributed, and are conjectured to satisfy a specific kind of statistical randomness.
It is known that π is a transcendental number:[2] It is not the root of a non-zero polynomial with rational coefficients. The transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge.