The Golden Ratio (why it is so irrational)
Additional information
Check out Brilliant (and get 20% off) by clicking https://brilliant.org/numberphile
More Golden Ratio stuff: http://bit.ly/Golden_Ratio
More Ben Sparks Numberphile videos: http://bit.ly/Sparks_Playlist
Ben's Twitter: https://twitter.com/SparksMaths
Ben's website: www.bensparks.co.uk
Geogebra file Ben used: https://www.geogebra.org/m/YThycjQK#material/T8eKzDu5
Note on this video: Ben uses "one over a number" quite often during the video to make a fraction of a turn between 0 and 1, but the same effects apply if you turn more than a complete turn (e.g. sqrt(2) = approximately 1.414... of a turn, i.e. 1 whole turn and 0.414... of a further turn).