The Fibonacci Spiral

This pattern is built from squares whose side lengths follow the Fibonacci sequence — 1, 1, 2, 3, 5, 8, 13… Drawing a quarter-circle inside each square creates the familiar Fibonacci spiral.

As the sequence grows, the ratio of neighbouring Fibonacci numbers approaches the golden ratio, $\phi \approx 1.618$. The Fibonacci spiral therefore closely approximates a golden spiral, although the two are not mathematically identical.