# Mathematician:William Shanks

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## Mathematician

English amateur mathematician famous for using Machin's Formula for Pi to calculate $\pi$ (pi) to $707$ places in $1873$, a result which was correct only up to the $527$th place.

The error was highlighted in $1945$ (or $1946$) by D.F. Ferguson, using a mechanical calculator.

Shanks' approximation was the longest expansion of $\pi$ until the advent of the electronic digital computer about one century later.

Shanks also calculated Euler's number $e$ and the Euler-Mascheroni constant $\gamma$ to many decimal places.

Also published a table of primes up to $60 \, 000$ and found the natural logarithms of $2$, $3$, $5$ and $10$ to $137$ places.

Also calculated the exact powers of $2$ up to $2^{721}$.

## Nationality

English

## History

- Born: 25 January 1812 in Corsenside (8 km NE of Bellingham), Northumberland, England
- Died: June 1882 in Houghton-le-Spring, Durham, England

## Publications

- 1853:
*Contributions to Mathematics, comprising chiefly the Rectification of the Circle*

## Critical View

*These tremendous stretches of calculation ... prove more than the capacity of this or that computer for labor and accuracy; they show that there is in the community an increase in skill and courage ...*- -- a Victorian commentator

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): A List of Mathematicians in Chronological Sequence - 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $3 \cdotp 14159 \, 26535 \, 89793 \, 23846 \, 26433 \, 83279 \, 50288 \, 41972 \ldots$ - 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $1,111,111,111,111,111,111$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): A List of Mathematicians in Chronological Sequence - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $3 \cdotp 14159 \, 26535 \, 89793 \, 23846 \, 26433 \, 83279 \, 50288 \, 41971 \ldots$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $1,111,111,111,111,111,111$ - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**Shanks, William**(1812-82)