Golden angle

In geometry, the golden angle is the angle created by dividing the circumference c of a circle into a section a and a smaller section b such that

$c=a+b \,$

and

$\frac{c}{a}=\frac{a}{b}$

and taking the angle of arc subtended by the length of circumference equal to b as the golden angle. There are φ² golden angles in a circle, where φ is the golden number. Therefore a golden angle is $\frac {360^{\circ}}{\phi^2} \approx 137.51^{\circ}$ . Since $\frac{1}{\phi^2} = 2-\phi$ , this is also ${360^{\circ}}({2- \phi}) \approx 137.51^{\circ}$ , or in radians ${2 \pi}({2- \phi}) \approx 2.4000 \mbox{ rad}$ .

Golden angle

See also

See also: Golden angle, Angle, Arc, Circle, Geometry, Golden ratio, Phyllotaxis, Radian