# Mathematician:Daniel Shanks

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## Mathematician

American mathematician who worked primarily in numerical analysis and number theory.

Best known as the first to compute $\pi$ to $100 \, 000$ decimal places.

Unrelated to William Shanks, who also calculated $\pi$ to a large number of places.

## Nationality

American

## History

- Born: January 17, 1917 in Chicago, Illinois
- Died: September 6, 1996 in Maryland

## Theorems and Definitions

- Newman-Shanks-Williams Prime (with Morris Newman and Hugh Cowie Williams)
- Shanks Transformation
- Shanks' Square Forms Factorization
- Tonelli-Shanks Algorithm (with Alberto Tonelli)

## Publications

- 1959:
*Khintchine's Constant*(*Amer. Math. Monthly***Vol. 66**,*no. 5*: pp. 276 – 279) (with John W. Wrench, Jr.) www.jstor.org/stable/2309633

- 1962:
*Calculation of $\pi$ to 100,000 Decimals*(*Math. Comp.***Vol. 16**: pp. 76 – 99) (with John W. Wrench, Jr.) www.jstor.org/stable/2003813

- 1974:
*Brun's Constant*(*Math. Comp.***Vol. 28**: pp. 293 – 299) (with John W. Wrench, Jr.) www.jstor.org/stable/2005836

## Notable Quotes

*My tardiness in learning of these historical references [to Alberto Tonelli's work on factorization] was because I had lent Volume 1 of Dickson's History to a friend and it was never returned.*

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $10$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $10$