Calculadora da Proporção Áurea — Formula

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.

    Exemplo Resolvido

    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