Definition:Pi/Historical Note/Modern Developments
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Historical Note on $\pi$ (Pi)
Since the middle of the $20$th century, considerable advances in the known digits of $\pi$ (pi) have been made using computers.
In $1945$ (or $1946$ -- sources are contradictory), D.F. Ferguson calculated $\pi$ to $610$ digits using a desk calculator, in the meantime discovering that the hitherto record-breaking $707$-digit work of William Shanks was incorrect from the $528$th place onwards.
During the course of $1947$, Ferguson extended his work to $710$ and $808$ digits.
In $1949$, working with John Wrench, this was once again extended to $1120$ digits.
By $1949$, electronic computers were being used.
Some of the record-breaking calculations are given in the following table:
| Date | Contributor(s) | Computer | Time taken | Number of Digits |
|---|---|---|---|---|
| $1949$ | John Wrench, L.R. Smith and others | ENIAC | $70$ hours | $2037$ |
| $1954$ | S.C. Nicholson and J. Jeenel | NORC | $13$ minutes | $3093$ |
| $1958$ | George E. Felton | Ferranti Pegasus | $33$ hours | $10 \, 021$ |
| $1961$ | Daniel Shanks and John Wrench | IBM 7090 | $8.7$ hours | $100 \, 265$ |
| $1967$ | Jean Guilloud and M. Dichampt | CDC 6600 | $28$ hours | $500 \, 000$ |
| $1983$ | Yasumasa Kanada, Sayaka Yoshino and Yoshiaki Tamura | HITAC M-280H | $33$ hours | $16 \, 777 \, 206$ (that is, $2^{24}$) |
| $29$ April $2009$ | Daisuke Takahashi and others | T2K Open Supercomputer | $29 \cdotp 09$ hours | $2 \, 576 \, 980 \, 377 \, 524$ |
| $11$ November $2016$ | Peter Trueb, using software by Alexander Yee | $4 \times$ Xeon E7-8890 v3 @ 2.50 GHz | $105$ days | $22 \, 459 \, 157 \, 718 \, 361$ |
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Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $3 \cdotp 14159 \, 26535 \, 89793 \, 23846 \, 26433 \, 83279 \, 50288 \, 41972 \ldots$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $3 \cdotp 14159 \, 26535 \, 89793 \, 23846 \, 26433 \, 83279 \, 50288 \, 41971 \ldots$