Gelfond's Constant minus Pi

Theorem

Gelfond's constant minus $\pi$ is very close to $20$:

$e^\pi - \pi \approx 20$

which is nothing more than an amusing coincidence.

Proof

We have:

$e^\pi \approx 23 \cdotp 14069 \, 26327 \, 79269 \ldots$

$\pi \approx 3 \cdotp 14159 \, 26535 \, 89793$

Then:

 23.14069 26327 79269
- 3.14159 26535 89793
---------------------
 19.99909 99791 89486
---------------------

$\blacksquare$

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $23 \cdotp 14069 \, 26327 \, 79269 \, 00572 \, 9086 \ldots$