2016-08-20
[public] 319K views, 9.6K likes, 126 dislikes audio only
You probably know that nature is crawling with the Fibonacci numbers 1, 2, 3, 5, 8, 13, 21, etc. But have you ever seen a simple explanation for this phenomenon? This video is the result of my own quest to distill a really accessible explanation from existing research.
Enjoy :)
In the last video on continued fractions I mentioned that part of the explanation involves the golden ratio and the fact that this number is the most irrational number. I'll talk about this in a follow-up video. If you cannot wait check out this website: http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat2.html
Also check out the following video produced as part of research by Douady and Couder about how simple displacement at the center of a plant gives rise to Fibonacci numbers of spirals
The paper itself can be found here https://www.math.ntnu.no/~jarlet/Douady96.pdf
Another very interesting approach by Levitov involves a magnetic cactus, vortices in superconductors and the fabulous Farey numbers: http://www.ams.org/samplings/feature-column/fcarc-phyllotaxis#2
/youtube/video/qhbuKbxJsk8