# Approximate Relations between Pi and Euler's Number/Fanelli's Approximation

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## Approximate Relation between $\pi$ (pi) and Euler's number $e$

This approximation to $\pi$ is accurate to $5$ decimal places:

- $\sqrt [9] {10 e^8} = 3 \cdotp 14159 \, 828 \ldots$

This sequence is A057466 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

## Source of Name

This entry was named for Michele Fanelli.

## Historical Note

Fanelli's approximation is the name coined by $\mathsf{Pr} \infty \mathsf{fWiki}$ to the approximation $\sqrt [9] {10 e^8} = 3 \cdotp 14159 \, 828 \ldots$.

Michele Fanelli abandoned further work on establishing similar correspondences, and in more recent times has contributed towards the literature on the Riemann Hypothesis.

## Sources

- 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $2 \cdotp 71828 \, 18284 \, 59045 \, 23536 \, 02874 \, 71352 \, 66249 \, 77572 \, 47093 \, 69995 \ \ldots$