Golden ratio is (√5+1)/2.
This number is special because it’s the most irrational number that exists.
A rational number could be expressed as p/q an irrational number could also be expressed as p/q to some degree of accuracy (take π and 22/7). Where p and q are relatively small.
However (√5+1)/2 cannot be easily expressed as small p/q.
I cannot easily type this but (√5+1)/2 is expressed at a continued fraction of 1+1/(1+1/(1+1/(1+1/…….)))). That corresponds to the smallest real number where the variability in the next term is extremely high.
TL;DR Watch this brilliant [Numberphile video](https://youtu.be/sj8Sg8qnjOg)
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