Birth, growth and computation of pi to ten trillion digits

DOI10.1186/1687-1847-2013-100zbMath1380.01012OpenAlexW2102036391WikidataQ56853496 ScholiaQ56853496MaRDI QIDQ1693543

Hans Agarwal, Syamal K. Sen, Ravi P. Agarwal

Publication date: 31 January 2018

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1687-1847-2013-100

zbMATH Keywords

circleMatlabrandom sequenceerror-freehistory of pistability of a computertrillion digits

Mathematics Subject Classification ID

General histories, source books (01A05)

Related Items

Inequalities and asymptotic expansions associated with the Wallis sequence ⋮ Sharp inequalities and asymptotic expansion associated with the Wallis sequence ⋮ Some properties of the remainders in certain series representations for the constant \(\pi\) ⋮ Asymptotic expansions for the Wallis sequence and some new mathematical constants associated with the Glaisher-Kinkelin and Choi-Srivastava constants ⋮ On the asymptotic expansions of products related to the Wallis, Weierstrass, and Wilf formulas ⋮ A `lost' chapter in the calculation of \(\pi\): Baron Zach and MS Bodleian 949 ⋮ A new form of the Machin-like formula for pi by iteration with increasing integers

Uses Software

• hfloat

Cites Work

• The Chronology of PI
• A Problem on Arc Tangent Relations
• A simple proof that 𝜋 is irrational
• On 22/7
• Value of π
• Is mathematics ``out there?
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Further refinements of Gurland's formula for \({\pi}\)
• Refinements of Gurland's formula for pi
• Hypergeometric analogues of the arithmetic-geometric mean iteration
• The legal values of pi
• A very rapidly convergent product expansion for pi
• Une histoire chinoise du ``nombre \(\pi\). (A Chinese history of the ``number \(\pi\))
• Best \(k\)-digit rational approximation of irrational numbers: pre-computer versus computer era
• Golden ratio versus pi as random sequence sources for Monte Carlo integration
• Is \(\pi\) normal ?
• The arithmetic-geometric mean of Gauss
• Circle measurements in ancient China
• Explicit Ramanujan-type approximations to pi of higher order
• John Ward's method for the calculation of pi
• Dihedral quartic approximations and series for \(\pi\)
• John Machin and Robert Simson on inverse-tangent series for \(\pi\)
• Quadrature of the circle in ancient Egypt
• Approximating \(\pi\) with Ramanujan's modular equations
• The quest for pi
• Zhao Youqin and his calculation of \(\pi\)
• Class number three Ramanujan type series for \(1/\pi\)
• An explicit cubic iteration for \(\pi\)
• Van Ceulen's tombstone
• Improvement in the irrationality measures of \(\pi\) and \(\pi^ 2\)
• Best \(k\)-digit rational bounds for irrational numbers: pre- and super-computer era
• An Elegant Continued Fraction for &#960
• On the rapid computation of various polylogarithmic constants
• The Arithmetic-Geometric Mean and Fast Computation of Elementary Functions
• Some Comments on a NORC Computation of &#960
• On Wallis' Formula
• Calculation of π to 100,000 Decimals
• On a Sequence Arising in Series for &#960
• The Discovery of the Series Formula for π by Leibniz, Gregory and Nilakantha
• A Faster Product for $\pi$ and a New Integral for ln $\frac{\pi}{2}$
• Pi, Euler Numbers, and Asymptotic Expansions
• On the irrationality measure of $ \pi$
• Cubic and Higher Order Algorithms for π
• Of Calculations Past and Present: The Archimedean Algorithm
• More Quadratically Converging Algorithms for &#960
• The Computation of π to 29,360,000 Decimal Digits Using Borweins' Quartically Convergent Algorithm
• Numerical results on the transcendence of constants involving 𝜋,𝑒, and Euler’s constant
• The Ubiquitous π
• The Ubiquitous π
• [https://portal.mardi4nfdi.de/wiki/Publication:3807144 New Indian Values of ? from the M?nava S�lba S?tra]
• Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi
• Fast Multiple-Precision Evaluation of Elementary Functions
• Computation of π Using Arithmetic-Geometric Mean
• Lazzarini's Lucky Approximation of π
• Many Correct Digits of π, Revisited
• On Lambert's Proof of the Irrationality of &#960
• A Simple Formula for &#960
• Rational approximations to π and some other numbers
• The computation of classical constants
• A Spigot Algorithm for the Digits of &#960
• The Calculation of π
• Complementary Two-Way Algorithms for Negative Radix Conversions
• Algorithms Involving Arithmetic and Geometric Means
• Rational Approximations to &#960
• On Huygens' Approximation to π
• Recalculation and Extension of the Modulus and of the Logarithms of 2, 3, 5, 7 and 17