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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}.

See also

Science Fair Project Encyclopedia Contents Page
10-26-2009 08:16:03
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