# Leibniz's Formula for Pi/Historical Note

## Historical Note on Leibniz's Formula for Pi

Leibniz discovered his formula for $\pi$ in $1673$.

He took great pleasure and pride in this discovery.

*It's as if, by this expansion, the veil which hung over that strange number had been drawn aside.*

Simple as it is, Leibniz's Formula for Pi is inefficient, in that it needs hundreds of terms in order to calculate a few decimal places.

Some sources ascribe this formula to James Gregory.

## Sources

- 1937: Eric Temple Bell:
*Men of Mathematics*... (previous) ... (next): Chapter $\text{VII}$: Master of All Trades - 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $3 \cdotp 14159 \, 26535 \, 89793 \, 23846 \, 26433 \, 83279 \, 50288 \, 41972 \ldots$ - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.19$: Leibniz ($1646$ – $1716$) - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {B}.13$: How Leibniz Discovered his Formula $\pi / 4 = 1 - \frac 1 3 + \frac 1 5 - \frac 1 7 + \cdots$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $3 \cdotp 14159 \, 26535 \, 89793 \, 23846 \, 26433 \, 83279 \, 50288 \, 41971 \ldots$