History of Pi in Timeline
Pi (π) is a fundamental mathematical constant, representing the ratio of a circle's circumference to its diameter, approximately 3.14159. It is a transcendental number, meaning it is not the root of any non-zero polynomial equation with rational coefficients. Pi appears extensively in mathematics, physics, and engineering. While often defined geometrically, it can also be defined using various formulae to avoid reliance on the length of a curve. Its ubiquity stems from its deep connection to circles and trigonometric functions, making it indispensable in diverse calculations.
1900: Babylonian Approximation of Pi
Around 1900 BC, a clay tablet in Babylon implied an approximation of π as 25/8 = 3.125, within one percent of the true value.
1914: Ramanujan's Formulae
In 1914, Srinivasa Ramanujan published innovative new formulae for π, known for their elegance and rapid convergence.
1929: Reprint of William Jones' Work
In 1929, David Eugene Smith reprinted "William Jones: The First Use of π for the Circle Ratio" in A Source Book in Mathematics.
1946: Ferguson's Approximation
In 1946, Daniel Ferguson achieved a 620-digit approximation of π, the best approximation achieved without a calculating device.
1946: Error Detection in Pi Room Digits
In 1946, an error was detected in the 528th digit of π inscribed in the Palais de la Découverte's pi room, based on William Shanks' 1873 calculation.
1949: First Computer Calculation of Pi
In 1949, John Wrench and Levi Smith reached 1,120 digits using a desk calculator. Also in 1949, a team led by George Reitwiesner and John von Neumann achieved 2,037 digits using the ENIAC computer.
1949: Correction of Pi Room Digits
In 1949, the error in the digits of π inscribed in the Palais de la Découverte's pi room was corrected.
1955: Record Broken: 3,089 Digits of Pi
In 1955, the record for calculating digits of π was broken again, reaching 3,089 digits using an arctan series.
1957: New Record: 7,480 Digits of Pi
In 1957, the record for calculating digits of π was broken, reaching 7,480 digits.
1958: 10,000 Digits of Pi Calculated
In 1958, the calculation of π reached 10,000 digits.
1961: 100,000 Digits of Pi Reached
In 1961, the calculation of π reached 100,000 digits.
1971: Publication of Newton's Mathematical Papers
In 1971, Derek Thomas Whiteside edited and published The Mathematical Papers of Isaac Newton, Vol. 4, 1674–1684.
1973: One Million Digits of Pi Reached
In 1973, the calculation of π reached 1 million digits.
1975: Iterative Algorithms for Computing Pi
In 1975, Eugene Salamin independently published iterative algorithms for computing π that avoid reliance on infinite series.
1976: Iterative Algorithms for Computing Pi
In 1976, Richard Brent independently published iterative algorithms for computing π that avoid reliance on infinite series.
1980: Widespread Use of Iterative Algorithms
After 1980, iterative algorithms became widely used for computing π because they are faster than infinite series algorithms.
1980: Accelerated Pi Computation
Around 1980, new iterative algorithms and fast multiplication algorithms accelerated the computation of π.
1980: Howe's Fourier Analysis Reduction
In 1980, Howe stated that establishing the fundamental theorems of Fourier analysis reduces to the Gaussian integral, highlighting pi's importance in normal distributions and probability.
1984: Borwein Algorithm
In 1984, John and Peter Borwein produced an iterative algorithm that quadruples the number of digits in each step.
1985: Gosper Uses Ramanujan's Formula
In 1985, Bill Gosper used Ramanujan's formula to set a record of 17 million digits for calculation of Pi.
1985: Pi in Carl Sagan's Contact
In Carl Sagan's 1985 novel Contact, the creator of the universe is suggested to have buried a message within the digits of π.
1987: Borwein Algorithm Increases Digit Calculation
In 1987, John and Peter Borwein developed an iterative algorithm that increases the number of digits five times in each step when calculating Pi.
1987: Chudnovsky Formula Developed
In 1987, the Chudnovsky formula was developed for calculating Pi.
1989: Chudnovsky Brothers Calculate Pi
In 1989, the Chudnovsky brothers surpassed 1 billion digits in Pi calculation.
1991: Discovery of π in the Mandelbrot Set
In 1991, David Boll discovered an occurrence of π in the Mandelbrot set, observing its appearance when examining the behavior near the "neck" at (−0.75, 0).
1995: Kanada Sets Records
Between 1995 and 2002, Japanese mathematician Yasumasa Kanada set several records for computing π using iterative methods.
1995: Simple Spigot Algorithm
In 1995, Stan Wagon and Stanley Rabinowitz produced a simple spigot algorithm.
1995: BBP Digit Extraction Algorithm
In 1995, the BBP digit extraction algorithm was discovered by Simon Plouffe for calculating Pi.
1998: PiHex Project Begins
Between 1998 and 2000, the PiHex project started using Bellard's formula (a modification of the BBP algorithm) to compute digits of Pi.
2000: PiHex Project Concludes
Between 1998 and 2000, the PiHex project concluded using Bellard's formula (a modification of the BBP algorithm) to compute digits of Pi.
2002: Kanada Sets Records
Between 1995 and 2002, Japanese mathematician Yasumasa Kanada set several records for computing π using iterative methods.
2004: Observations on Arctangent Method
In 2004, Hwang Chien-Lih published "Some Observations on the Method of Arctangents for the Calculation of π" in Mathematical Gazette.
2005: Elementary Derivation of Euler's Series
In 2005, Hwang Chien-Lih published "An elementary derivation of Euler's series for the arctangent function" in Mathematical Gazette.
2005: Pi in Kate Bush's Aerial
In 2005, the digits of π were incorporated into the lyrics of the song "Pi" from the album Aerial by Kate Bush.
2006: Akira Haraguchi's Unverified Claim
In 2006, Akira Haraguchi, a retired Japanese engineer, claimed to have recited 100,000 decimal places of Pi; however, the claim was not verified by Guinness World Records.
2006: Plouffe Generates New Formulae for Pi
In 2006, Simon Plouffe used the PSLQ integer relation algorithm to generate several new formulae for π.
September 2010: Yahoo! Computes Bits of Pi
In September 2010, a Yahoo! employee used Hadoop to compute 256 bits of π at the two-quadrillionth bit.
2010: Celebration of Tau Day
Since 2010, people have celebrated Two Pi Day or Tau Day on June 28, following proposals to replace π by τ = 2π.
2011: Yee and Kondo Calculate Pi
In 2011, Alexander Yee and Shigeru Kondo calculated 10 trillion digits of Pi.
2012: Differential Calculus Precedes Integral Calculus
In 2012, Remmert explained that differential calculus typically precedes integral calculus in the university curriculum. Therefore, definitions of π should not rely on integral calculus.
March 2015: Rajveer Meena's Pi Memorization Record
In March 2015, Rajveer Meena in India recited 70,000 digits of π in 9 hours and 27 minutes, certified by Guinness World Records.
2015: Significant Pi Day
Pi Day in 2015 (3/14/15) was particularly significant because the date and time 3/14/15 9:26:53 reflected many more digits of pi.
May 2019: Vacuum Permeability Constant Definition
Before May 2019, the vacuum permeability constant μ0, appearing in Maxwell's equations, was defined as exactly 4π × 10−7 H/m.
2022: Iwao Calculates 100 Trillion Digits of Pi
In 2022, Emma Haruka Iwao calculated 100 trillion digits of π.
2022: Plouffe Founds Base-10 Algorithm
In 2022, Plouffe found a base-10 algorithm for calculating digits of Pi.
