You have probably been told that a single number, roughly 1.618, governs everything from galaxies to seashells to the proportions of your face. This episode sorts the provable mathematics of the golden ratio from the romanticized fiction that has grown around it. We start with the real thing: the positive solution to x squared minus x minus one equals zero, its status as the most irrational number because its continued fraction is made entirely of ones, the way Fibonacci ratios swing back and forth around it without ever landing, and its exact appearance in the diagonals of a regular pentagon and the faces of a dodecahedron.

Then we trace the history of the obsession, from Euclid's dry extreme and mean ratio and the crisis it caused among the Pythagoreans, to Luca Pacioli's 1509 book The Divine Proportion illustrated by Leonardo da Vinci, t ...