Golden Angle

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.,

=137.507... degrees

(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).

Another angle related to the golden ratio is the angle

 theta=cot^(-1)phi approx 31.7 degrees

or twice this angle

 2theta=tan^(-1)2 approx 63.4 degrees,

the later of which is the smaller interior angle in the golden rhombus.

See also

Golden Gnomon, Golden Ratio, Golden Rectangle, Golden Triangle, Phyllotaxis

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Livio, M. The Golden Ratio: The Story of Phi, the World's Most Astonishing Number. New York: Broadway Books, 2002.Sloane, N. J. A. Sequence A096627 and A131988 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Golden Angle

Cite this as:

Weisstein, Eric W. "Golden Angle." From MathWorld--A Wolfram Web Resource.

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