The golden ratio is equal to
φ =
a/
b given the conditions above. Let
ƒ be the fraction of the circumference subtended by the golden angle, or equivalently, the golden angle divided by the angular measurement of the circle. : f = \frac{b}{a+b} = \frac{1}{1+\varphi}. But since : {1+\varphi} = \varphi^2, it follows that : f = \frac{1}{\varphi^2} This is equivalent to saying that
φ 2 golden angles can fit in a circle. The fraction of a circle occupied by the golden angle is therefore :f \approx 0.381966. \, The golden angle
g can therefore be numerically approximated in
degrees as: :g \approx 360 \times 0.381966 \approx 137.508^\circ,\, or in radians as : : g \approx 2\pi \times 0.381966 \approx 2.39996. \, == Golden angle in nature ==