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

Journal of Numerical Analysis and Approximation Theory

David H. Bailey¹ 

[1] Lawrence Berkeley National Laboratory;

关键词: Pi;    computation of pi;    history of pi;   

DOI  :  

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown