The Golden Ratio (why it is so irrational) - Numberphile

a mind-rewiring video by numberphile concerning the golden ratio [0] made sense of all the spiral overlay art: yes, plants use it because it is an optimal solution for minimizing overlap when sprouting leaves during growth, maximizing spatial coverage but also, as a number that is least able to be approximated by rational, erm, ratios - it is a pattern that most closely approximates random patterns. So more than any other spiral, a fibonacci spiral has the highest likelihood of overlapping random points in 2D space... (and fibonacci series converges on the golden ratio because they are equivelent expressions of the continued fraction 1+(1/(1+(1/(1+(1/(1+(1/... [0] [this video]

The article attempts to explain this property of phi: > Maybe you have a picture of a flower, and you want to implement “every time the user clicks the mouse, add a petal to the flower.” In that case you want to use the golden ratio: Make the angle from one petal to the next 360/phi and you can loop around the circle forever, adding petals, and the next petal will always fit neatly into the biggest gap and you’ll never loop back to your starting position. And points to a video. I think there's a much clearer explanation which shows how this is because (in some sense) phi is the "most irrational" ratio, stemming from its derivation from continued fractions: [this video] I freely admit I have not a clue how this does or doesn't improve hash algos, but it's a cool video! :)