Seeds of Helianthus, Fibonacci numbers in Nature

Every spring morning, the flower of the Helianthus plant turns facing eastward towards the sun. Throughout the day it slowly moves west, tracking the sun until nighttime, earning this plant the name sunflower. As amazing as this is, the sunflower also has a fascinating connection with the golden ratio.

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clockwise and counter clockwise patterns can be seen on this sunflower

The seeds at the head of the sunflower form into spirals, the number of spirals going clockwise and the number of spirals going counterclockwise form two adjacent Fibonacci numbers. (Numbers that are part of the Fibonacci sequence 1, 2 3, 5,8 13,…) The ratio of any two adjacent Fibonacci numbers approximate the golden ratio. For example 21/13 = 1.61538 and  43/21 = 1.61905 which are very close to the golden ratio or \phi = \frac{1+\sqrt5}{2} = 1.61803.

This is believed to occur because seeds are formed at the center of the head of the sunflower and migrate outward as new seeds are formed. By approximating the golden spiral pattern the sunflower would maximize the number of seeds for its surface area.

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Pine cones also exhibit the spiral patterns

Sunflowers are not the only plants that exhibit the golden ratio. Pine cones, also have clockwise and counterclockwise patterns that equal two adjacent Fibonacci numbers. The same pattern also exists pine apples. In some plants, their leaves and branches form a spiral pattern which also exhibits the same Fibonacci patterns.

Flowers also generally have a Fibonacci number as the number of petals such as 5 in the case of the cherry blossom, daisies and some sunflowers have 34 petals.

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The Cherry blossom has 5 petals

Sources used