Howdy ho. No reason for a welcome around here, it's not about me it's about the Mathematical Anti-Telharsic Harfatum Septomin, eh!? (I hope at least one of ya are familiar with that guy) Nonetheless, I've become obsessed with the transcendental property, and thusly therein my familiarization, I've come to ask this. Pi is transcendental, we got that, however, just being transcendental doesn't mean it is only defined by series or summations or integrals or anything above basic arithmetic. So, why hasn't there been more attempts to define Pi as a definite arithmetic progression? I've been having some fun exploring Pi in correlation to Phi and a truncated icosahedron, but haven't had much time as of late to finish it. Again, nonetheless, what are some of the more famous failures attempting to describe the exact nature of Pi other than a series, summation, integral or etc.?