This is a list of topics related to
pi (), the fundamental
mathematical constant
A mathematical constant is a number whose value is fixed by an unambiguous definition, often referred to by a special symbol (e.g., an Letter (alphabet), alphabet letter), or by mathematicians' names to facilitate using it across multiple mathem ...
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2 theorem
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Approximations of
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Arithmetic–geometric mean
In mathematics, the arithmetic–geometric mean (AGM or agM) of two positive real numbers and is the mutual limit of a sequence of arithmetic means and a sequence of geometric means. The arithmetic–geometric mean is used in fast algorithms f ...
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Bailey–Borwein–Plouffe formula
The Bailey–Borwein–Plouffe formula (BBP formula) is a formula for . It was discovered in 1995 by Simon Plouffe and is named after the authors of the article in which it was published, David H. Bailey, Peter Borwein, and Plouffe. The formula i ...
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Basel problem
The Basel problem is a problem in mathematical analysis with relevance to number theory, concerning an infinite sum of inverse squares. It was first posed by Pietro Mengoli in 1650 and solved by Leonhard Euler in 1734, and read on 5 December 1735 ...
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Borwein's algorithm
Borwein's algorithm was devised by Jonathan and Peter Borwein to calculate the value of 1 / \pi. This and other algorithms can be found in the book ''Pi and the AGM – A Study in Analytic Number Theory and Computational Complexity''.
Ramanujan†...
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Buffon's needle
In probability theory, Buffon's needle problem is a question first posed in the 18th century by Georges-Louis Leclerc, Comte de Buffon:
:Suppose we have a floor made of parallel strips of wood, each the same width, and we drop a needle onto the ...
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Cadaeic Cadenza
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Chronology of computation of
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Circle
A circle is a shape consisting of all point (geometry), points in a plane (mathematics), plane that are at a given distance from a given point, the Centre (geometry), centre. The distance between any point of the circle and the centre is cal ...
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Euler's identity
In mathematics, Euler's identity (also known as Euler's equation) is the Equality (mathematics), equality
e^ + 1 = 0
where
:e is E (mathematical constant), Euler's number, the base of natural logarithms,
:i is the imaginary unit, which by definit ...
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Six nines in pi
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Gauss–Legendre algorithm
The Gauss–Legendre algorithm is an algorithm to compute the digits of . It is notable for being rapidly convergent, with only 25 iterations producing 45 million correct digits of . However, it has some drawbacks (for example, it is computer ...
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Gaussian function
In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function (mathematics), function of the base form
f(x) = \exp (-x^2)
and with parametric extension
f(x) = a \exp\left( -\frac \right)
for arbitrary real number, rea ...
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History of
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A History of Pi''
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Indiana Pi Bill
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Leibniz formula for pi
Gottfried Wilhelm Leibniz (or Leibnitz; – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Sir Isaac Newton, with the creation of calculus in addition to many ...
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Lindemann–Weierstrass theorem
In transcendental number theory, the Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers. It states the following:
In other words, the extension field \mathbb(e^, \dots, e^) has transc ...
(Proof that is transcendental)
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List of circle topics
A list is a set of discrete items of information collected and set forth in some format for utility, entertainment, or other purposes. A list may be memorialized in any number of ways, including existing only in the mind of the list-maker, bu ...
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List of formulae involving
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Liu Hui's algorithm
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Mathematical constant (sorted by continued fraction representation)
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Mathematical constants and functions
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. For exa ...
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Method of exhaustion
The method of exhaustion () is a method of finding the area of a shape by inscribing inside it a sequence of polygons (one at a time) whose areas converge to the area of the containing shape. If the sequence is correctly constructed, the differ ...
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Milü
''Milü'' (), also known as Zulü (Zu's ratio), is the name given to an approximation of ( pi) found by the Chinese mathematician and astronomer Zu Chongzhi during the 5th century. Using Liu Hui's algorithm, which is based on the areas of reg ...
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Pi
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Pi (art project)
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Pi (letter)
Pi (; Ancient Greek or , uppercase Π, lowercase π, cursive ϖ; ) is the sixteenth letter of the Greek alphabet, representing the voiceless bilabial plosive . In the system of Greek numerals it has a value of 80. It was derived from the Phoeni ...
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Pi Day
Pi Day is an annual celebration of the mathematical constant (pi). Pi Day is observed on March 14 (the 3rd month) since 3, 1, and 4 are the first three significant figures of , and was first celebrated in the United States. It was founded i ...
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PiFast
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PiHex
PiHex was a distributed computing project organized by Colin Percival to calculate specific bits of pi, . 1,246 contributors used idle time slices on almost two thousand computers to make its calculations. The software used for the project made use ...
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Pi in the Sky
''Pi in the Sky'' was an experimental aerial art display where airplanes spelled out pi to decimal 1,000 places in the sky over the San Francisco Bay Area. The display took place on September 12, 2012. It was then displayed again in Austin on M ...
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Pilish
Pilish is a style of constrained writing in which the lengths of consecutive words or sentences match the digits of the number ( pi). The shortest example is any three-letter word, such as "hat", but many longer examples have been constructed, i ...
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Pimania
''Pimania'' is a text-and-graphics adventure game written by Mel Croucher and released by Automata UK in 1982 for the BBC Micro, ZX Spectrum, Dragon 32, and ZX81. It was the first real-life video game Treasure hunt (game), treasure hunt to be rel ...
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Piphilology
Piphilology comprises the creation and use of mnemonic techniques to remember many digits of the mathematical constant . The word is a play on the word "pi" itself and of the linguistic field of philology.
There are many ways to memorize , inclu ...
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Proof that is irrational
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Proof that 22/7 exceeds
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Proof of Wallis product
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Rabbi Nehemiah
Rabbi Nehemiah was a rabbi who lived circa 150 AD (fourth generation of tannaim).
He was one of the great students of Rabbi Akiva, and one of the rabbis who received semicha from R' Judah ben Baba
The Talmud equated R' Nechemiah with Rabbi Ne ...
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Radian
The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. It is defined such that one radian is the angle subtended at ...
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Ramanujan–Sato series
In mathematics, a Ramanujan–Sato series generalizes Ramanujan's pi formulas such as,
:\frac = \frac \sum_^\infty \frac \frac
to the form
:\frac = \sum_^\infty s(k) \frac
by using other well-defined sequences of integers s(k) obeying a certa ...
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Rhind Mathematical Papyrus
The Rhind Mathematical Papyrus (RMP; also designated as papyrus British Museum 10057, pBM 10058, and Brooklyn Museum 37.1784Ea-b) is one of the best known examples of ancient Egyptian mathematics.
It is one of two well-known mathematical papyri ...
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Salamin–Brent algorithm
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Software for calculating
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Squaring the circle
Squaring the circle is a problem in geometry first proposed in Greek mathematics. It is the challenge of constructing a square (geometry), square with the area of a circle, area of a given circle by using only a finite number of steps with a ...
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Turn (geometry)
The turn (symbol tr or pla) is a unit of plane angle measurement that is the measure of a complete angle—the angle subtended by a complete circle at its center. One turn is equal to radians, 360 degrees or 400 gradians. ...
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Viète's formula
In mathematics, Viète's formula is the following infinite product of nested radicals representing twice the Multiplicative inverse, reciprocal of the mathematical constant pi, :
\frac2\pi = \frac2 \cdot \frac2 \cdot \frac2 \cdots
It can also b ...
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