黄金比例计算器 — 公式

Golden Ratio

Definition

phi = (1 + sqrt(5)) / 2 ≈ 1.6180339887...

Two quantities a and b (a > b > 0) are in the golden ratio if:

(a + b) / a = a / b = phi

Properties

  • phi² = phi + 1 ≈ 2.618
  • 1/phi = phi - 1 ≈ 0.618
  • Fibonacci ratio converges to phi

    • In Art and Nature

    The golden ratio appears in the Parthenon, Leonardo da Vinci's works, spiral shells, sunflower seeds, and DNA helices.

    计算示例

    If the longer segment is 10, find the shorter segment.

    1. b = a / phi = 10 / 1.61803 ≈ 6.1803
    2. Total = 10 + 6.1803 = 16.1803
    3. Check: 16.1803 / 10 ≈ 1.618 = phi
    4. Check: 10 / 6.1803 ≈ 1.618 = phi