PHI · The Golden Ratio & Fibonacci Spiral

construction · — subdivisions ratio a : b = φ

The Divine Proportion

φ =1

where a : b = a+b : a = φ

A rectangle whose sides are in ratio φ can be split into a square and a smaller rectangle that is itself golden — rotated, and scaled by 1/φ. Repeating the subdivision forever produces a self-similar cascade, and quarter-circle arcs through each square trace the logarithmic Fibonacci spiral.

Each step scales the rectangle by 1/φ ≈ 0.6180 and turns it a right angle.
The spiral keeps a constant ~137.5° angle — the golden angle.
The vertex converges to a single fixed point, the eye of the spiral.

subdivisions 0 · phase idle