The Golden Angle is the angle where the ratio of the two arc lengths (𝑎 & 𝑏) that make up a circle is given by the Golden Ratio φpic.twitter.com/xbpZbpUL76
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The Golden Angle (~137.51°) is the angle by which certain flowers (e.g.
) pack their successive seeds--this is because it happens to be an optimal "packing angle"
A little bit over or under the Golden Angle and the packing quickly becomes less efficientpic.twitter.com/0Z23wYHb4l
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Golden angle ~ 1/(Fine-structure constant) ;-)
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But that’s just a matter of units
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What instinct tells them this angle?
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Over millions of years of evolution, cells have ended up laying down just the right amount of stuff in just the right place so the final result is most efficient
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Where do we measure the angle exactly on that diagram? Is it the direction of offset between successive layers of seeds?
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Let θ=2πkn≡2π{kn}, r²=n, then k=φ makes θ a equidistributed sequence on [0, 2π]. φ seems to be the number that makes (θ, r²) the most uniformly distributed because the continued fraction of φ has the beautiful form [1;1,1,1,...]. http://mathworld.wolfram.com/EquidistributedSequence.html …
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