# Brouncker's Formula

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## Theorem

- $\dfrac 4 \pi = 1 + \cfrac {1^2} {2 + \cfrac {3^2} {2 + \cfrac {5^2} {2 + \cfrac {7^2} {2 + \cfrac {9^2} {2 + \cdots} } } } }$

## Proof

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## Also presented as

This can also be presented as:

- $\dfrac \pi 4 = \dfrac 1 {1 + \cfrac {1^2} {2 + \cfrac {3^2} {2 + \cfrac {5^2} {2 + \cfrac {7^2} {2 + \cfrac {9^2} {2 + \cdots} } } } } }$

## Source of Name

This entry was named for William Brouncker.

## Sources

- 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.21$: Euler ($\text {1707}$ – $\text {1783}$) - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {B}.12$: Wallis's Product: Footnote $1$