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Golden Angle

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The golden angle is the angle that divides a full angle in a golden ratio (but measured in the opposite direction so that it measures less than 180 degrees), i.e.,

GA=2pi(1-1/phi)
(1)
=2pi/(1+phi)
(2)
=2pi(2-phi)
(3)
=(2pi)/(phi^2)
(4)
=pi(3-sqrt(5))
(5)
=2.399963...
(6)
=137.507... degrees
(7)

(OEIS A131988 and A096627; Livio 2002, p. 112).

It is implemented in the Wolfram Language as GoldenAngle.

van Iterson showed in 1907 that points separated by 137.5 degrees on a tightly bound spiral tends to produce interlocked spirals winding in opposite directions, and that the number of spirals in these two families tend to be consecutive Fibonacci numbers (Livio 2002, p. 112).

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