A catalogue of mathematical formulas involving \(\pi\), with analysis

David H. Bailey

doi:10.33993/jnaat502-1259

Authors

David H. Bailey Lawrence Berkeley National Laboratory, USA

DOI:

https://doi.org/10.33993/jnaat502-1259

Keywords:

Pi, computation of pi, history of pi

Abstract views: 325

Abstract

This paper presents a catalogue of mathematical formulas and iterative algorithms for evaluating the mathematical constant \(\pi\), ranging from Archimedes' 2200-year-old iteration to some formulas that were discovered only in the past few decades. Computer implementations and timing results for these formulas and algorithms are also included. In particular, timings are presented for evaluations of various infinite series formulas to approximately 10,000-digit precision, for evaluations of various integral formulas to approximately 4,000-digit precision, and for evaluations of several iterative algorithms to approximately 100,000-digit precision, all based on carefully designed comparative computer runs.

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