Is there a relationship between nature and Math????? That is the question.
 
Draw a vertical line on your paper about two inches long. This is going to be the stem of a plant. You are now going to draw branches sprouting from this stalk. Where are you going to draw these branches? Are they symmetrical, asymmetrical , are they uniformly spaced, are they same distance apart?  On the same sheet of paper draw a circle, this represents the same stem as before except it  is from a different viewpoint, you are looking from above the plant straight down the shaft. Where do you place the branches on the stem? Are they evenly symmetrically spaced  around the shaft, how many degrees apart are the branches?

What is/are the most important factor(s) for leaf placement.

A flower  populates itself with by making  seeds.  The more seeds that the flower makes the better chance for survival.  The flower is limited in the number of seeds, it is limited in the area it has to develop seed.  How does the flower to make the most seeds with a limited amount of space?  Is it better to have seeds in straight rows and columns ?  Why?  Is it better to have rectangle shape?  Why?  Is it better to have a curve shape?  Why?
 
 
Here is a site that may shed  some light. When you are finished with this site return to this site by pressing the "Back" Key.  The sections that you need to read  are "Fibonacci Numbers and Branching Plants";   "Petals on flowers";  "Pine Cones"; " leaf arrangement" ;
 
 
 Now that you have read this section do a new drawing showing two viewpoints  a side view and a view from overhead indicating where the leaves would grow from the plant. Indicate the angle between the branches. In the "Pine Cones"  explore the highlighted  names of plants to see if the Fibonacci numbers appear.
 

Why does the Golden section and Fibonacci
sequence appear in Nature?

Before you go to the 'Why' what you need to know is how to determine the value of the
Golden section and you need to determine the ratio of Fibonacci sequence 

Here are the questions that you must answer.
What amount per turn in one direction are the leaves  placed?
What is this value?
Why is this value better then the value .5 or .48 or .6.
Is a rational number value better than  an irrational value for plant leaf placement? Explain your answer.
 
Read the following sections:
Why do the Golden section and Fibonacci numbers appear in nature?
Why is the Golden section the "best" number?
Why is the Golden section the "best" number?
Why exact fractions are fruitless!
The rational answer is the irrationals!
 

 Why does the Golden section and Fibonacci
sequence appear in Nature?