The golden mean, golden ratio or golden proportion is essentially "phi." One way to see the ratio is from the division of a rectangle such that a square is formed. The golden ratio is formed when the proportion of the smaller part to the remainder is the same as the smaller to the whole. This proportion can be found in the human arm: The ratio of the forearm to the hand is identical to the ratio of the hand to the whole arm from the elbow down. This ratio is nature's efficiency scale and is at the foundation of all life.
The Golden Numbers in Plants
Plants offer a striking formation of the golden ratio. The golden ratio is derived in this case from the Fibonacci series of numbers, which forms, over repeated intervals, the golden ratio. The Fibonacci series is simple: Starting with 0 or 1, create a set of numbers where the next number of the series is the sum of the previous two. As organic life develops and grows, it grows according to this pattern. From it, the densely packed petals of a rose flower or a head of cabbage makes mathematical sense.
The Fibonacci Series
The Fibonacci series and the golden ratio from which it derives, is at the basis of all life. It is proof of order and regularity in the universe and, as such, has religious significance, especially to Muslims. The petals of a rose growing out of the stem manifest this ratio. Its purpose is purely natural: to maximize the efficient use of light at each level of growth.
Phi and Rose Petals
As the petals of the rose develop, the Fibonacci series can be seen. Its natural basis is that each new set of petals grows in the spaces between the previous set. This makes sense since the upper leaves will not take all the light from the lower. This is an efficient arrangement where the light from the sun is evenly arranged through all levels of the plant's development. Over time, the average arc of the circle that these petals use in their growth is 137.5 degrees. There are some variations, but this figure comes up the most as the most efficient mode of development given the amount of sunlight available.
Roses and Rationality
The wild rose has five petals arranged horizontally. It is not a vertical arrangement like the leaves on a tree, but this does not affect the mathematics --- the numbers still apply. The basic aesthetic point here is that nothing can grow or develop unless it derives specifically from that which immediately precedes it. The Fibonacci numbers on a rose simply show that each petal is dependent on the others preceding it precisely in the Fibonacci series: Each new one is the sum of the two that came before. If you take the mathematical relationships of any two adjacent rose petals and divide them, they will always come out as Phi, or 1.618.