If leaves are space a rational number divisor a/b of 360 degrees around a trunk, then after b turns, leaves will directly shadow each other. To avoid this you need the amount of turn between leaves to be as difficult as possible to approximate by a rational number.
Using continued fractions we can see that the most difficult rational to approximate is
1 + 1/(1 + 1/(1 + 1/(...)))
which is (1+sqrt(5))/2 which is the Golden Ratio.
You can also get better packings by using the Fibonacci Spiral, which again gives the Golden Ratio:
If leaves are space a rational number divisor a/b of 360 degrees around a trunk, then after b turns, leaves will directly shadow each other. To avoid this you need the amount of turn between leaves to be as difficult as possible to approximate by a rational number.
Using continued fractions we can see that the most difficult rational to approximate is
1 + 1/(1 + 1/(1 + 1/(...)))
which is (1+sqrt(5))/2 which is the Golden Ratio.
You can also get better packings by using the Fibonacci Spiral, which again gives the Golden Ratio:
http://en.wikipedia.org/wiki/Fibonacci_sequence#In_nature
You can look these things up if you're interested.