Phyllotaxis is the study of the ordered position of leaves on a stem. The leaves on this plant are staggered in a spiral pattern to permit optimum exposure to sunlight. If we apply the Golden Ratio to a circle we can see how it is that this plant exhibits Fibonacci qualities. See picture for more detailed illustration of leaf arrangements.
By dividing a circle into Golden proportions, where the ratio of the arc length is equal to the Golden Ratio, we find the angle of the arcs to be 137.5 degrees. In fact, this is the angle at which adjacent leaves are positioned around the stem. This phenomenon is observed in many types of plants.
In the case of tapered pinecones or pineapples, we see a double set of spirals – one going in a clockwise direction and one in the opposite direction. When these spirals are counted, the two sets are found to be adjacent Fibonacci numbers.
Similarly, sunflowers have a Golden Spiral seed arrangement. This provides a biological advantage because it maximizes the number of seeds that can be packed into a seed head.
Inside the fruit of many plants, we can observe the presence of Fibonacci order.
The banana has 3 sections The apple has 5 sections
As well, many flowers have a Fibonacci number of petals. Some, like this rose, also have Fibonacci, or Golden Spiral, petal arrangements.
Branching plants also exhibit Fibonacci numbers. Again, this design provides the best physical accommodation for the number of branches, while maximizing sun exposure.
Fibonacci Petals
3 petals lily, iris
5 petals buttercup, wild rose, larkspur, columbine
8 petals delphiniums
13 petals ragwort, corn marigold, cineraria
21 petals aster, black-eyed Susan, chicory
34 petals plantain, pyrethrum
55, 89 petals Michaelmas daisies, the Asteraceae family
The occurrence of Fibonacci Numbers in Nature is interesting but the ratio of consecutive Fibonacci Numbers is important.
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