Mathematician:William Shanks

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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 $2^{721}$.




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


  • 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