The Fibonacci sequence is one of those math marvels that even elementary students can appreciate. Like the discovery of the √2, it possesses this element of mystery that makes Pythagoras‘ harmonic series look like a rubber-band shoe-box next to a concert grand. Pythagoras famously drowned the fellow who discovered that √2 was neither even nor odd. It went against his religion. Fortunately for Gödel, the Pythagoreans did not control peer review when he demonstrated that unprovability was a whole lot worse than irrational numbers, but all math was “incomplete” and unable to exclude ambiguous theorems. But if we don’t demand that math obey our ideas of God, we can sit back an enjoy it. Here’s a YouTube video marvelling at the ubiquity of Fibonacci, calling it the fingerprint of God.
It is a well-worn metaphor, which other mathematicians might reserve for the Mandelbrot set. Physicists, on the other hand, prefer to see this in things like cosmology. Which raises the question, is the Fibonacci series merely a mathematician’s trick, or is there something hiding in the physics? Do the sunflower whorls contain a physical necessity, or merely an aesthetic necessity to match Fibonacci? And if so, then what about the spirals of galaxies? Surely we can say more about Fibonacci than mathematical aesthetics!