Golden Ratio Calculator
Calculate golden ratio proportions. Given one length, find the other that creates the golden ratio (1.618...).
B
6.1803
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.
- 01b = a / phi = 10 / 1.61803 ≈ 6.1803
- 02Total = 10 + 6.1803 = 16.1803
- 03Check: 16.1803 / 10 ≈ 1.618 = phi
- 04Check: 10 / 6.1803 ≈ 1.618 = phi
Perguntas Frequentes
What is the golden ratio?
The golden ratio (phi ≈ 1.618) is an irrational number that appears when a line is divided so that the ratio of the whole to the larger part equals the ratio of the larger part to the smaller.
Where does the golden ratio appear in nature?
In spiral shells (nautilus), sunflower seed patterns, pine cones, the arrangement of leaves on stems, and the proportions of the human body.
How is the golden ratio related to Fibonacci numbers?
The ratio of consecutive Fibonacci numbers converges to the golden ratio. F(n+1)/F(n) → phi as n increases.
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