Being off by 0.3 degrees is enough to ruin it. Scatter seeds around a centre, turning each one by exactly the golden angle of 137.507 degrees, and they interlock without gaps while the visible crossing spirals always count out as consecutive Fibonacci numbers; set the angle to 137.2 degrees and the seeds snap into radial spokes with wasted gaps between them. The reason is that φ = 1.618… is the irrational number hardest to approximate by fractions, so multiples of the golden angle never fall periodically on top of one another. Claims that φ governs beauty in painting or human proportion, by contrast, are mostly overstated.
Being off by 0.3 degrees is enough to ruin it. Scatter seeds around a centre, turning each one by exactly the golden angle of 137.507 degrees, and they interlock without gaps while the visible crossing spirals always count out as consecutive Fibonacci numbers; set the angle to 137.2 degrees and the seeds snap into radial spokes with wasted gaps between them. The reason is that φ = 1.618… is the irrational number hardest to approximate by fractions, so multiples of the golden angle never fall periodically on top of one another. Claims that φ governs beauty in painting or human proportion, by contrast, are mostly overstated.
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