Journey into PI 
Computing \(\pi\) over time
The following tables present some results computed for the value of \(\pi\) throughout the ages.
| Source/Author | Date | Approximation | Value |
| Babylon | 2000 B.C. | \(3+\frac{1}{8}\) | \(3.125\) |
| Egypt Ahmes papyrus |
1650 B.C. | \((\frac{16}{9})^{2}\) | \(3.1605\) |
| Archimedes | 250 B.C. | \(3\frac{10}{71}<\pi<3\frac{1}{7}\) | \(3.14185\) |
| Ptolomeu | 150 A.D. | \(\frac{377}{120}\) | \(3.14166\) |
| Tsu Chung Chih | 480 | \(\frac{355}{113}\) | \(3.141592\) |
| Simon Duchesne | 1583 | \((\frac{39}{22})^{2}\) | \(3.14256\) |
| Source/Author | Date | Approximation or Method Used |
Number of Correct Decimals | Computing time |
| Ludolph Van Ceulen | 1609 | Archimedes Method | \(34\) | |
| Sharp | 1705 | \(72\) | ||
| Machin | 1706 | Machin Formula | \(100\) | |
| De Lagny | 1719 | \(127\) | ||
| Euler | 1755 | \(\frac{\pi}{4}=5\arctan\left(\frac{1}{7}\right)+\) \(\hspace{3ex}2\arctan\left(\frac{3}{79}\right)\) | \(20\) | \(<\) 1 hour |
| Shanks | 1874 | \(\arctan\) Formulas | \(527\) | 707 hours |
| Ferguson | 1945 | \(\arctan\) Formulas | \(620\) | |
| Wrench & Levi | 1948 | \(\arctan\) Formulas | \(808\) | |
| Smith & Wrench | 1949 | \(\arctan\) Formulas | \(1\,120\) | |
| Reitweisner ENIAC computer |
1949 | Machin Formula | \(2\,037\) | \(\approx\) 70 hours |
| Nicholson & Jeenel | 1954 | \(\arctan\) Formulas | \(3\,092\) | |
| PEGUSUS computer | 1957 | \(10\,021\) | \(\approx\) 33 hour | |
| IBM 704 computer | 1959 | \(10\,000\) | 1h40m | |
| Shanks & Wrench IBM 7090 computer |
1961 | \(100\,265\) | 8 hours | |
| Guilloud & Dichampt CDC 6600 computer |
1967 | \(500\,000\) | 44h 45m | |
| Guilloud & Bouyer CDC 7600 computer |
1973 | \(1 \,001 \,250\) | 23h 18m | |
| Miyoshi & Nakayana FACOM M-200 computer |
1981 | \(2 \,000 \,038\) | ||
| Kanada, Yoshino & Tamura HITACHI S-810 computer |
1982 | \(16 \,777 \,206\) | ||
| Chudnovsky brothers IBM 3090 computer |
1984 | \(1 \,011 \,196 \,691\) | ||
| Chudnovsky brothers | 1994 | Ramanujam Series | \(4 \,044 \,000 \,000\) | |
| Takahashi-Kanada | 1997 | 2th and 4th order Borwein Algorithms |
\(51 \,539 \,600 \,000\) | |
| Takahashi-Kanada | 1999 | Bren/Salamin Algorithm 4th order Borwein Algorithm |
\(206 \,158 \,430 \,000\) | (1) |
(1) Record for the largest extension of digits of \(\pi\) in 2000
