The Golden Ratio

Divide any Fibonacci number by the one before it, and the ratio converges toward 1.618... — the golden ratio, symbolized by the Greek letter phi (φ). This irrational number is often claimed to shape the proportions of the Parthenon and Renaissance paintings, though historians dispute those examples as cherry-picked. Where it genuinely appears is in deliberate modern design — layout grids and framework proportions that designers choose on purpose.

The golden ratio creates a rectangle where cutting off a square leaves a smaller rectangle with the same proportions — infinitely. This self-similar property connects Fibonacci to fractals, spirals, and the deep mathematical structure underlying growth patterns across biology and art.