Good Math, Bad Math says phi is more fun. After all, "if you write φ as a continued fraction, it's [1;1,1,1,1...]; and if you write it as a continued square root, it's 1 + sqrt(1+sqrt(1+sqrt(1+sqrt(1...))))."
I'm fascinated by how tiny little things affect world history—take the malaria parasite for instance. Forget the Black Death or the Influenza outbreak of 1917, Malaria has had a bigger impact on humanity than any other rampaging pathogen—yet, we still don't completely understand how it works.