The golden ratio spiral: visual infinite descent

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So you all know the golden (ratio) spiral. But did you know that not only the golden ratio but really every number has such a spiral associated with it? And that this spiral provides key insights into the nature of a number. Featuring more proofs by contradiction by infinite descent (my current obsession), infinite continued fractions, etc.

Here are some articles that debunk a lot of the golden spiral in nature nonsense:
Clement Falbo
http://web.sonoma.edu/Math/faculty/falbo/cmj123-134

George Hart
http://www.georgehart.com/rp/replicator/replicator.html
https://www.youtube.com/channel/UCTl0dASnxto6j2wlVs5Bs2Q

Keith Devlin
http://devlinsangle.blogspot.com.au/2017/04/fibonacci-and-golden-ratio-madness.html

Here is a very good website devoted to everything to do with the golden ratio and Fibonacci
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fib.html

Thank you very much to Michael (editing), Marty (nitpicking) and Danil (translating).

Enjoy!

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