Manifestations and the Evolutionary Background of the Fibonacci Sequence and the Golden Ratio in Plants

Overview

My thesis examines the occurrence of certain mathematical phenomena in the phyllotaxis and seed formations of certain plants. I begin by presenting the mathematical background behind the Fibonacci sequence, a series of numbers, starting with the integer pair 0 and 1, where the value of each element is calculated as the sum of the two preceding it. The second chapter analyses the mathematical nature of the golden ratio. I derive the value of the golden ratio by processing the fractions of certain geometrical line segments. From there I will present the mathematical correlation between the Fibonacci numbers and the golden ratio. This correlation is presented by Binet’s formula, the limit of the ratio of two consequent Fibonacci numbers. I will be inspecting the mathematical theorems in the growth of plants. I begin by addressing a phenomenon known as phyllotaxis, the arrangement of leaves or other parts of the plant on a plant stem. The third chapter analyses phyllotaxy by applying the golden ratio into the divergence angle, an angle between successively growing leaves, seedpods or florets. I will be presenting five specimens of the Fibonacci sequence and golden ratio in plants. I will be displaying the Fibonacci sequence in each specimen by highlighting the parastichies on each plant. In addition, I will derive the golden ratio arithmetically from the number of spirals on each plant. I will end my thesis by concluding the mathematical nature behind phyllotaxy and plant growth patterns. I will also present some further insights into the manifestations of the Fibonacci sequence and golden ratio, for example their occurrence in anatomy and architecture.

Competition history

• ISEF 2021 Plant Sciences · Entry PLNT052

Resources

• ISEF abstract page ↗

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