The number π (/paɪ/ ; spelled out as pi) is a mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to its The number π ( ; spelled out as pi) is a mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to its diameter. It appears in many formulae across mathematics and physics, and some of these formulae are commonly used for defining π, to avoid relying on the definition of the length of a curve. The number π is an irrational number, meaning that it canno Perhaps because of the simplicity of its definition and its ubiquitous presence in formulae, π has been represented in popular culture more than other mathematical constructs. In the Palais de la Découverte (a science museum in Paris) there is a circular room known as the pi room. On its wall are inscribed 707 digits of π. The digits are large wooden characters attached to the dome-like ceiling. The digits were based on an 1873 calculation by English mathematician William Shanks, which included an error beginning at the 528th digit. The error was detected in 1946 and corrected in 1949. In Carl Sagan's 1985 novel Contact, it is suggested that the creator of the universe buried a message deep within the digits of π. This part of the story was omitted from the film adaptation of the novel. In the 1967 Star Trek episode "Wolf in the Fold", a computer possessed by a demonic entity is contained by being instructed to "Compute to the last digit the value of π". In the United States, Pi Day falls on 14 March (written 3/14 in the US date format), and is popular among students. π and its digital representation are often used by self-described "math geeks" for inside jokes among mathematically and technologically minded groups. A college cheer variously attributed to the Massachusetts Institute of Technology or the Rensselaer Polytechnic Institute includes "3.14159". Pi Day in 2015 was particularly significant because the date and The number π ( ; spelled out as pi) is a mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to its diameter. It appears in many formulae across mathematics and physics, and some of these formulae are commonly used for defining π, to avoid relying on the definition of the length of a curve. The number π is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, although fractions such as ⁠22/7⁠ are commonly used to approximate it. Consequently, its decimal representation never ends, nor does it enter a permanently repeating pattern. It is a transcendental number, meaning that it cannot be a solution of an algebraic equation involving only finite sums, products, powers, and integers. The transcendence of π implies that it is impossible to solve the ancient problem of squaring the circle with a compass and straightedge. The decimal digits of π appear to be evenly distributed, but no proof of this conjecture has been found. Mathematicians have attempted to extend their understanding of π, sometimes by computing its value to a high degree of accuracy. Ancient civilizations, including the Egyptians and Babylonians, required fairly accurate approximations of π for practical computations. Around 250 BC, the Greek mathematician Archimedes created an algorithm to approximate π with arbitrary accuracy. In the 5th century AD, Chinese mathematicians approximated π to seven digits, while Indian mathematicians made a five-digit Perhaps because of the simplicity of its definition and its ubiquitous presence in formulae, π has been represented in popular culture more than other mathematical constructs. In the Palais de la Découverte (a science museum in Paris) there is a circular room known as the pi room. On its wall are inscribed 707 digits of π. The digits are large wooden characters attached to the dome-like ceiling. The digits were based on an 1873 calculation by English mathematician William Shanks, which included an error beginning at the 528th digit. The error was detected in 1946 and corrected in 1949. In Carl Sagan's 1985 novel Contact, it is suggested that the creator of the universe buried a message deep within the digits of π. This part of the story was omitted from the film adaptation of the novel. In the 1967 Star Trek episode "Wolf in the Fold", a computer possessed by a demonic entity is contained by being instructed to "Compute to the last digit the value of π". In the United States, Pi Day falls on 14 March (written 3/14 in the US date format), and is popular among students. π and its digital representation are often used by self-described "math geeks" for inside jokes among mathematically and technologically minded groups. A college cheer variously attributed to the Massachusetts Institute of Technology or the Rensselaer Polytechnic Institute includes "3.14159". Pi Day in 2015 was particularly significant because the date and time 3/14/15 9:26:53 reflected many more digits of pi. In parts of the world where dates are commonly noted in day/month/year format, 22 July represents "Pi Approximation Day", as 22/7 ≈ 3.142857. Some have proposed replacing π by τ = 2π, arguing that τ, as the number of radians in one turn or the ratio of a circle's circumference to its radius, is more natural than π and simplifies many formulae. This use of τ has not made its way into mainstream mathematics, but since 2010 this has led to people celebrating Two Pi Day or Tau Day on June 28. In 1897, an amateur mathematician attempted to persuade the Indiana legislature to pass the Indiana Pi Bill, which described a method to square the circle and contained text that implied various incorrect values for π, including 3.2. The bill is notorious as an attempt to establish a value of mathematical constant by legislative fiat. While the bill was passed by the Indiana House of Representatives, it was rejected by the Indiana Senate, and thus did not become a law.