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π (sometimes written pi) is a mathematical constant whose value is the ratio of any circle's circumference to its diameter in Euclidean space; this is the same value as the ratio of a circle's area to the square of its radius. It is approximately equal to 3.141593 in the usual decimal notation (see the table for its representation in some other bases). Many formulae from mathematics, science, and engineering involve π, which is one of the most important mathematical and physical constants. π is an irrational number, which means that its value cannot be expressed exactly as a fraction m/n, where m and n are integers. Consequently, its decimal representation never ends or repeats. It is also a transcendental number, which implies, among other things, that no finite sequence of algebraic operations on integers (powers, roots, sums, etc.) can be equal to its value; proving this was a late achievement in mathematical history and a significant result of 19th century German mathematics. Throughout the history of mathematics, there has been much effort to determine π more accurately and to understand its nature; fascination with the number has even carried over into non-mathematical culture. The Greek letter π, often spelled out pi in text, was adopted for the number from the Greek word for perimeter "περίμετρος", first by William Jones in 1707, and popularized by Leonhard Euler in 1737. 3.141592653589793 The name of the Greek letter π is pi, and this spelling is commonly used in typographical contexts when the Greek letter is not available or its usage could be problematic. It is not capitalised (Π) even at the beginning of a sentence. When referring to this constant, the symbol π is always pronounced /ˈpaɪ/, "pie" in English, which is the conventional English pronunciation of the Greek letter. In Greek, the name of this letter is pronounced [pi]. The constant is named "π" because "π" is the first letter of the Greek words περιφέρεια (periphery) and περίμετρος (perimeter), probably referring to its use in the formula to find the circumference, or perimeter, of a circle. π is Unicode character U+03C0 ("Greek small letter pi"). Although practically a physicist needs only 39 digits of Pi to make a circle the size of the observable universe accurate to one atom of hydrogen, the number itself as a mathematical curiosity has created many challenges in different fields. Memorizing digits Main article: Piphilology Recent decades have seen a surge in the record for number of digits memorized. Even long before computers have calculated π, memorizing a record number of digits became an obsession for some people. Memorizing digits Main article: Piphilology Recent decades have seen a surge in the record for number of digits memorized. Even long before computers have calculated π, memorizing a record number of digits became an obsession for some people.Memorizing digits Main article: Piphilology Recent decades have seen a surge in the record for number of digits memorized. It is approximately equal to 3.141593 in the usual decimal notation (see the table for its representation in some other bases). Many formulae from mathematics, science, and engineering involve π, which is one of the most important mathematical and physical constants. π is an irrational number, which means that its value cannot be expressed exactly as a fraction m/n, where m and n are integers. Consequently, its decimal representation never ends or repeats. It is also a transcendental number, which implies, among other things, that no finite sequence of algebraic operations on integers (powers, roots, sums, etc.) can be equal to its value; proving this was a late achievement in mathematical history and a significant result of 19th century German mathematics. Throughout the history of mathematics, there has been much effort to determine π more accurately and to understand its nature; fascination with the number has even carried over into non-mathematical culture. The Greek letter π, often spelled out pi in text, was adopted for the number from the Greek word for perimeter "περίμετρος", first by William Jones in 1707, and popularized by Leonhard Euler in 1737. 3.141592653589793 The name of the Greek letter π is pi, and this spelling is commonly used in typographical contexts when the Greek letter is not available or its usage could be problematic. It is not capitalised (Π) even at the beginning of a sentence. When referring to this constant, the symbol π is always pronounced /ˈpaɪ/, "pie" in English, which is the conventional English pronunciation of the Greek letter. In Greek, the name of this letter is pronounced [pi]. The constant is named "π" because "π" is the first letter of the Greek words περιφέρεια (periphery) and περίμετρος (perimeter), probably referring to its use in the formula to find the circumference, or perimeter, of a circle. π is Unicode character U+03C0 ("Greek small letter pi"). Although practically a physicist needs only 39 digits of Pi to make a circle the size of the observable universe accurate to one atom of hydrogen, the number itself as a mathematical curiosity has created many challenges in different fields. Memorizing digits Main article: Piphilology Recent decades have seen a surge in the record for number of digits memorized. Even long before computers have calculated π, memorizing a record number of digits became an obsession for some people. Memorizing digits Main article: Piphilology Recent decades have seen a surge in the record for number of digits memorized. Even long before computers have calculated π, memorizing a record number of digits became an obsession for some people.Memorizing digits Main article: Piphilology Recent decades have seen a surge in the record for number of digits memorized. Even long before computers have calculated π, memorizing a record number of digits became an obsession for some people. π is ubiquitous in mathematics, appearing even in places that lack an obvious connection to the circles of Euclidean geometry. Although not a physical constant, π appears routinely in equations describing fundamental principles of the Universe, due in no small part to its relationship to the nature of the circle and, correspondingly, spherical coordinate systems. Using units such as Planck units can sometimes eliminate π from formulae.