Question

Does anyone have any insights about e (2.718...)? I'm looking for anything that will help me understand it better or explain a bit about why it shows up in nature so often.

Answer 1

\[\frac{e}{2}=\left ( \frac{2}{1}\right ) ^{1/2}\left ( \frac{2}{3}\frac{4}{3}\right ) ^{1/4}\left ( \frac{4}{5}\frac{6}{5}\frac{6}{7}\frac{8}{7}\right ) ^{1/8}\left ( \frac{8}{9}\frac{10}{9}\frac{10}{11}\frac{12}{11}\frac{12}{13}\frac{14}{13}\frac{14}{15}\frac{16}{17}\right ) ^{1/16}\cdots ~\mathrm{etc.}\]

Answer 2

Thanks, took some contemplation but it's pretty cool to think about.