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  2. Bailey–Borwein–Plouffe formula - Wikipedia

    en.wikipedia.org/wiki/Bailey–Borwein–Plouffe...

    This does not compute the nth decimal digit of π (i.e., in base 10). [3] But another formula discovered by Plouffe in 2022 allows extracting the nth digit of π in decimal. [4] BBP and BBP-inspired algorithms have been used in projects such as PiHex [5] for calculating many digits of π using distributed computing. The existence of this ...

  3. Bellard's formula - Wikipedia

    en.wikipedia.org/wiki/Bellard's_formula

    Bellard's formula is used to calculate the nth digit of π in base 16. Bellard's formula was discovered by Fabrice Bellard in 1997. It is about 43% faster than the Bailey–Borwein–Plouffe formula (discovered in 1995). [1] [2] It has been used in PiHex, the now-completed distributed computing project.

  4. Approximations of π - Wikipedia

    en.wikipedia.org/wiki/Approximations_of_π

    This formula permits one to fairly readily compute the kth binary or hexadecimal digit of π, without having to compute the preceding k − 1 digits. Bailey's website [97] contains the derivation as well as implementations in various programming languages.

  5. A New Formula for Pi Is Here. And It’s Pushing Scientific ...

    www.aol.com/formula-pi-pushing-scientific...

    The digits of pi extend into infinity, and pi is itself an irrational number, meaning it can’t be truly represented by an integer fraction (the one we often learn in school, 22/7, is not very ...

  6. Leibniz formula for π - Wikipedia

    en.wikipedia.org/wiki/Leibniz_formula_for_π

    The formula is a special case of the Euler–Boole summation formula for alternating series, providing yet another example of a convergence acceleration technique that can be applied to the Leibniz series. In 1992, Jonathan Borwein and Mark Limber used the first thousand Euler numbers to calculate π to 5,263 decimal places with the Leibniz ...

  7. Chudnovsky algorithm - Wikipedia

    en.wikipedia.org/wiki/Chudnovsky_algorithm

    ) + / A detailed proof of this formula can be found here: [14] This identity is similar to some of Ramanujan 's formulas involving π , [ 13 ] and is an example of a Ramanujan–Sato series . The time complexity of the algorithm is O ( n ( log ⁡ n ) 3 ) {\displaystyle O\left(n(\log n)^{3}\right)} .

  8. List of formulae involving π - Wikipedia

    en.wikipedia.org/wiki/List_of_formulae_involving_π

    where C is the circumference of a circle, d is the diameter, and r is the radius.More generally, = where L and w are, respectively, the perimeter and the width of any curve of constant width.

  9. Pi - Wikipedia

    en.wikipedia.org/wiki/Pi

    The number π (/ p aɪ /; spelled out as "pi") is a mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to its diameter.It appears in many formulae across mathematics and physics, and some of these formulae are commonly used for defining π, to avoid relying on the definition of the length of a curve.