Plants, flowers, pentagonal and their geometry then Fibonacci sequence.

Once I read about something of geometry of flowers. The article said that a key element of it is said to be pentagonal.

Fibonacci sequence, a famous mathematic, is said to be ruling over their geometry.
Anyway, at a first glance, I can’t identify the relation between Fibonacci sequence and the geometry of plants and flowers, nonetheless I can feel they have certain mechanism of forming their shape, mechanism which may possibly be represented and/or modeled by mathematics.

Here is the recurrence relation of Fibonacci Sequence (Numbers).
F₀=0, F₁=1 and F_n=F_n-1+F_n-2 for n>1
So, you see, pasts (term: F_n-1+F_n-2) accumulates in the present (term F_n).
It looks to me of one of mechanisms of growth.

Also, a fact to be noticed is that Fibonacci Sequence has certain relation with Golden Ratio. The ratio is found in something that has beautiful shape.

Unfortunately, it is impossible for me to figure out how that mathematics reaches pentagonal. (There may be certain theories which were proven well by some academics or professional scientists)

Here I took pictures of several flowers which I found in a park nearby to explore a little bit into the geometry of flowers.
You may find some pentagons there.