I just spent the last 3 hours figuring out why this is cool. I’ve never considered spirals so intensely in my entire life. You should have been there; it was spectacular, especially when my head exploded. By the way, I was doing these derivations and proofs on paper at 2AM so it could all be entirely inaccurate.
The ratios of the numbers in the Fibonacci Sequence oscillate around and converge on the Golden Ratio, phi=1.61803399, which can be derived by solving phi=a/b or phi=(a+b)/a, where a=(b/2)(1+sqrt(5)) (which can be demonstrated geometrically quite nicely apparently [1:25-1:40]), which yields phi=(1+sqrt(5))/2).
The Golden Ratio does not describe spirals, but specifically the spiral where roughly the effective diameter of the last 180* becomes the effective radius of the next 90*.
I suspect that The Fibonacci Sequence and The Golden Ratio in relation to “spirals occurring in nature” are applied too generously and abused across the internet. In any case, the strange obsession with The Golden Ratio has never sat well with me so I spent several hours mapping out my arguments against it, but then in attempting to prove my own theories I kept proving why the Golden Ratio is awesome. I only have a few more issues and I was half way through trying to determine the angular frequency (or range) pattern which sunflower seeds (or pine cone leaves or pineapple spirals) must follow to give over-excited Fibonnacci and Golden Ratio fans the ability to claim complementary spirals both occurring at rates that correspond to numbers in the Fibonnacci sequence but that’s when my head exploded.
What is the scientific name for a pine cone leaf?
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