Math & Statistics · 黄金分割（Golden Ratio） · Updated 2026-10-25
What Is Golden Ratio?
Definition
φ satisfies whole/large = large/small, i.e. x/1=(x+1)/x, giving φ=(1+√5)/2≈1.618 with the clean identity φ²=φ+1 (so 1/φ=φ−1≈0.618). Successive Fibonacci ratios 1,1,2,3,5,8,13… converge to φ (8/13≈0.615). It appears as genuine mathematical structure in the Fibonacci recursion, pentagram geometry and some phyllotaxis (sunflower seeds near 137.5°).
Formula
φ = (1+√5)/2; φ² = φ + 1; 1/φ = φ − 1
Worked Example
Fibonacci ratios 13/21≈0.619, 21/34≈0.6176, 34/55≈0.6182 approach 0.618 from below while 55/34≈1.618 approaches from above.
Common Misconception
"The golden ratio is everywhere; obey it and beauty follows" — claims about the Parthenon, nautilus and Mona Lisa mostly involve cherry-picked rectangles or loose fits (with ±2% measurement error you can always find 1.618). In design it is one usable proportion among many, not an aesthetic axiom.
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