This article is about the mathematical constant. For the Greek letter, see Pi (letter). For other uses, see Pi (disambiguation). Part of a series of articles on the mathematical constant π Uses Area of a circleCircumferenceUse in other formulae Properties IrrationalityTranscendence Value PeopleThis article is about the mathematical constant. For the Greek letter, see Pi (letter). For other uses, see Pi (disambiguation). Part of a series of articles on the mathematical constant π Uses Area of a circleCircumferenceUse in other formulae Properties IrrationalityTranscendence Value Less than 22/7ApproximationsMadhava's correction termMemorization People ArchimedesLiu HuiZu ChongzhiAryabhataMadhavaJamshīd al-KāshīLudolph van CeulenFrançois VièteSeki TakakazuTakebe KenkoWilliam JonesJohn MachinWilliam ShanksSrinivasa RamanujanJohn WrenchChudnovsky brothersYasumasa Kanada History ChronologyA History of Pi In culture Indiana Pi BillPi Day Related topics Squaring the circleBasel problemSix nines in πOther topics related to π vte The number π (/paɪ/; spelled out as "pi") is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159. The number π appears in many formulae across mathematics and physics. It is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, although fractions such as 22 7 {\displaystyle {\tfrac {22}{7}}} are commonly used to approximate it. Consequently, its decimal representation never ends, nor enters a permanently repeating pattern. It is a transcendental number, meaning that it cannot be a solution of an equation involving only sums, products, powers, and integers. The transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge. The decimal digits of π appear to be randomly distributed,[a] but no proof of this conjecture has been found ArchimedesLiu HuChongzhiAryabhataMadhavaJamshīd al-KāshīLudolph van CeulenFrançois VièteSeki TakakazuTakebe KenkoWilliam JonesJohn MachinWilliam ShanksSrinivasa RamanujanJohn WrenchChudnovskiZu y brothersYasumasa Kanada History ChronologyA History of Pi In culture Indiana Pi BillPi Day Related topics Squaring the circleBasel problemSix nines in πOther topics related to π vte The number π (/paɪ/; spelled out as "pi") is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159. The number π appears in many formulae across mathematics and physics. It is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, although fractions such as 22 7 {\displaystyle {\tfrac {22}{7}}} are commonly used to approximate it. Consequently, its decimal representation never ends, nor enters a permanently repeating pattern. It is a transcendental number, meaning that it cannot be a solution of an equation involving only sums, products, powers, and integers. The transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge. The decimal digits of π appear to be randomly distributed,[a] but no proof of this conjecture has been found
