The Fibonacci Function Nobody Knows About

There is a π-th Fibonacci number. It equals 2.1170… — and only one function in the universe is allowed to produce it. Infinitely many smooth curves pass through the Fibonacci numbers 1, 1, 2, 3, 5, 8… Every one of them hits every dot. This video is about the three demands that single out THE Fibonacci function, the impostor that almost passes them, the exponent that shatters between the integers, and the detour through the complex plane that repairs it — the same machinery that turned the factorial into the Gamma function. An open problem, for the comments: nobody knows whether F(π) is irrational, let alone transcendental. No current theorem covers numbers built from φ^π. (If Schanuel's conjecture is true, it is transcendental — but that conjecture is far out of reach.) CHAPTERS 00:00 The Number Between the Steps 01:36 The Three Demands 02:55 The Impostor 04:20 The Formula 05:48 The Broken Term 07:16 The Complex Detour 08:47 The Shadow 10:12 Landing on Pi 11:36 Behind Zero 12:57 Demand, Break, Detour Music by Vincent Rubinetti Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/a...