Golden Ratio Calculator — Formule
## 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.
### 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.
Exemple Résolu
If the longer segment is 10, find the shorter segment.
- b = a / phi = 10 / 1.61803 ≈ 6.1803
- Total = 10 + 6.1803 = 16.1803
- Check: 16.1803 / 10 ≈ 1.618 = phi
- Check: 10 / 6.1803 ≈ 1.618 = phi