Pi, or π, is a mathematical constant. It is defined as the ratio of a circle’s circumference to its diameter, and it also has various equivalent definitions.
So let’s find out some trivia and facts about this mathematical constant.
- The number π, Pi, is a mathematical constant
- It is defined as the ratio of a circle’s circumference to its diameter
- It also has various equivalent definitions
- It appears in many formulas in all areas of mathematics and physics
- It is approximately equal to 3.14159
- It has been represented by the Greek letter “π” since the mid-18th century
- It is also spelled out as “pi”
- It is also called Archimedes’ constant
- Being an irrational number, π cannot be expressed as a common fraction
- Equivalently, its decimal representation never ends and never settles into a permanently repeating pattern
- Still, fractions such as 22/7 and other rational numbers are commonly used to approximate π
- The digits appear to be randomly distributed
- In particular, the digit sequence of π is conjectured to satisfy a specific kind of statistical randomness, but to date, no proof of this has been discovered
- Also, π is a transcendental number
- That is, it is not the root of any polynomial having rational coefficients
- This transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge
- Ancient civilizations required fairly accurate computed values to approximate π for practical reasons, including the Egyptians and Babylonians
- Around 250 BC the Greek mathematician Archimedes created an algorithm for calculating it
- In the 5th century AD Chinese mathematics approximated π to seven digits
- While Indian mathematics made a five-digit approximation
- Both using geometrical techniques
- The historically first exact formula for π, based on infinite series, was not available until a millennium later
- When in the 14th century the Madhava–Leibniz series was discovered in Indian mathematics
- In the 20th and 21st centuries, mathematicians and computer scientists discovered new approaches that, when combined with increasing computational power, extended the decimal representation of π to many trillions of digits after the decimal point
- Practically all scientific applications require no more than a few hundred digits of π, and many substantially fewer
- So the primary motivation for these computations is the quest to find more efficient algorithms for calculating lengthy numeric series, as well as the desire to break records
- The extensive calculations involved have also been used to test supercomputers and high-precision multiplication algorithms
- Because its most elementary definition relates to the circle, π is found in many formulae in trigonometry and geometry
- Especially those concerning circles, ellipses, and spheres
- In more modern mathematical analysis, the number is instead defined using the spectral properties of the real number system, as an eigenvalue or a period, without any reference to geometry
- It appears therefore in areas of mathematics and the sciences having little to do with the geometry of circles
- Such as number theory and statistics, as well as in almost all areas of physics
- The ubiquity of π makes it one of the most widely known mathematical constants both inside and outside the scientific community
- Several books devoted to π have been published
- Record-setting calculations of the digits of π often result in news headlines
- Attempts to memorize the value of π with increasing precision have led to records of over 70,000 digits
- 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 2008 Open University and BBC documentary co-production, The Story of Maths, aired in October 2008 on BBC Four
- In this British mathematician Marcus du Sautoy shows a visualization of the, historically first exact, formula for calculating π when visiting India and exploring its contributions to trigonometry
- 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 1853 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 novel Contact it is suggested that the creator of the universe buried a message deep within the digits of π
- The digits of π have also been incorporated into the lyrics of the song “Pi” from the album Aerial by Kate Bush
- In the United States, Pi Day falls on 14 March (written 3/14 in the US style), 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
- Several college cheers at the Massachusetts Institute of Technology include “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, July 22 represents “Pi Approximation Day,” as 22/7 = 3.142857
- During the 2011 auction for Nortel’s portfolio of valuable technology patents, Google made a series of unusually specific bids based on mathematical and scientific constants, including π
- In 1958 Albert Eagle proposed replacing π by τ (tau), where τ = π/2, to simplify formulas
- However, no other authors are known to use τ in this way
- Some people use a different value, τ = 2π = 6.28318…, arguing that τ, as the number of radians in one turn, or as the ratio of a circle’s circumference to its radius rather than its diameter
- It is more natural than π and simplifies many formulas
- Celebrations of this number, because it approximately equals 6.28, by making 28 June “Tau Day” and eating “twice the pie”, have been reported in the media
- However, this use of τ has not made its way into mainstream mathematics
- 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 scientific constant by legislative fiat
- The bill was passed by the Indiana House of Representatives, but rejected by the Senate, meaning it did not become a law
- In contemporary internet culture, individuals and organizations frequently pay homage to the number π
- For instance, the computer scientist Donald Knuth let the version numbers of his program TeX approach π
- The versions are 3, 3.1, 3.14, and so forth
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