The golden ratio spiral: visual infinite descent

NEW (Christmas 2019). Two ways to support Mathologer Mathologer Patreon: https://www.patreon.com/mathologer Mathologer PayPal: paypal.me/mathologer (see the Patreon page for details) 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!