The Golden Ratio: Phi, 1.618

Fibonacci Numbers and Spirals in Plants

Plants illustrate the Fibonacci series in the numbers and arrangements of petals, leaves, sections and seeds.

Fibonacci numbers in plant spirals

Plants that are formed in spirals, such as pinecones, pineapples and sunflowers, illustrate Fibonacci numbers.  Many plants produce new branches in quantities that are based on Fibonacci numbers.

Fibonacci numbers in plant branching

Here a sunflower seed illustrates this principle as the number of clockwise spirals is 55 (marked in red, with every tenth one in white) and the number of counterclockwise spirals is 89 (marked in green, with every tenth one in white.)

Here a plant illustrates that each successive level of branches is often based on a progression through the Fibonacci series.

Fibonacci numbers in plant sections

You might expect symmetry in plants, but if you cut a fruit or vegetable you will often find that the number of sections is a Fibonacci number:

Bananas have 3

Apples have 5

Fibonacci numbers in flower petals

Many flowers have petals that total a number in, or very close to, the Fibonacci series:

3 Lilies
5 Buttercups, Roses
8 Delphinium
13 Marigolds
21 Black-eyed susans
34 Pyrethrum
55/89 Daisies
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