Brouncker's Formula

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

Brouncker's Formula 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 $1$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Brouncker, William, Viscount (1620-85)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Brouncker, William, Viscount (1620-85)