A catalogue of mathematical formulas involving \(\pi\), with analysis
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 f...
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| Format: | Article |
| Language: | English |
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Publishing House of the Romanian Academy
2021-12-01
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| Series: | Journal of Numerical Analysis and Approximation Theory |
| Subjects: | |
| Online Access: | https://www.ictp.acad.ro/jnaat/journal/article/view/1259 |
| _version_ | 1811296717935476736 |
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| author | David H. Bailey |
| author_facet | David H. Bailey |
| author_sort | David H. Bailey |
| collection | DOAJ |
| description |
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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| first_indexed | 2024-04-13T05:53:25Z |
| format | Article |
| id | doaj.art-cf0f3b5ea4484993856c01bb421bdacf |
| institution | Directory Open Access Journal |
| issn | 2457-6794 2501-059X |
| language | English |
| last_indexed | 2024-04-13T05:53:25Z |
| publishDate | 2021-12-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Journal of Numerical Analysis and Approximation Theory |
| spelling | doaj.art-cf0f3b5ea4484993856c01bb421bdacf2022-12-22T02:59:42ZengPublishing House of the Romanian AcademyJournal of Numerical Analysis and Approximation Theory2457-67942501-059X2021-12-01502A catalogue of mathematical formulas involving \(\pi\), with analysisDavid H. Bailey0Lawrence Berkeley National Laboratory 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. https://www.ictp.acad.ro/jnaat/journal/article/view/1259Picomputation of pihistory of pi |
| spellingShingle | David H. Bailey A catalogue of mathematical formulas involving \(\pi\), with analysis Journal of Numerical Analysis and Approximation Theory Pi computation of pi history of pi |
| title | A catalogue of mathematical formulas involving \(\pi\), with analysis |
| title_full | A catalogue of mathematical formulas involving \(\pi\), with analysis |
| title_fullStr | A catalogue of mathematical formulas involving \(\pi\), with analysis |
| title_full_unstemmed | A catalogue of mathematical formulas involving \(\pi\), with analysis |
| title_short | A catalogue of mathematical formulas involving \(\pi\), with analysis |
| title_sort | catalogue of mathematical formulas involving pi with analysis |
| topic | Pi computation of pi history of pi |
| url | https://www.ictp.acad.ro/jnaat/journal/article/view/1259 |
| work_keys_str_mv | AT davidhbailey acatalogueofmathematicalformulasinvolvingpiwithanalysis AT davidhbailey catalogueofmathematicalformulasinvolvingpiwithanalysis |