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

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): $2 \cdotp 71828 \, 18284 \, 59045 \, 23536 \, 02874 \, 71352 \, 66249 \, 77572 \, 47093 \, 69995 \ \ldots$