Flowers (and many if not most things in nature) can be found to have geometric properties that are aligned with the number Φ (Phi). It’s one of those numbers, like Pi, that are endless non-repeating numbers; Phi is, approximately, 1.618034. it really goes on endlessly, though.
The geometry of the pentagon and all related shapes that use the same angles tend to have a natural affinity for both Phi and phi (lowercase) which is equivalent to 1 over Phi, or 1/Φ. this, oddly enough, is equal to Phi-1, or 0.618034.
This is also the number that makes up the “golden ratio”, long known and used for it’s great geometrical qualities.
you can find out more information here, or just do a google search for Phi and the golden ratio.
Here’s a good entry on Phi in plants.
This photo really represents this concept quite well, and it’s something that is so simple for nature but yet so difficult to try and recreate!
I feel there is a lot of undiscovered folding territory in Phi, and I hope to explore this as time goes on.