Fibonacci Numbers, The Golden Ratio, And Their Effect On Phyllotaxis In Nature

Molly Irvin
Kouba
Math 16A
Exam ID #16
Do Plants Understand Math?: Fibonacci Numbers, The Golden Ratio, and Their Effect on Phyllotaxis in Nature The Fibonacci sequence, Lucas Numbers, and the Golden Ratio are commonly found in nature as patterns that many plants and animals follow for optimal growth and development. They explain many phenomena such as whorled phyllotaxis in plants or human proportions as well as many weather patterns and possibly other occurrences. As a plant sciences major, I found these rules to be particularly fascinating in plants and tried to explore the relation to my studies so far at UC Davis. The Fibonacci sequence refers to a sequence of numbers “Fn = Fn-1 + Fn-2 where Fn equals the term number, Fn-1 equals
This number leads to the phenomenon known as The Golden Ratio or “The Golden Angle,” which is approximately 137.5 degrees (Rehmeyer, 2007). The Golden ratio and Phi were thought to be named by Phidias, an ancient Greek sculptor, born in 490 BC, who used the ratios in his pieces (Hom, 2013). There are many examples of The Golden Ratio and Phi being discovered and used in history. They were held in high regard to Ancient Egyptians and were considered sacred as it was thought to be used to construct temples. As a result, they referred to it as the “Sacred Ratio” They were also thought to be developed by Pythagoras, who used ratio to discover his Pythagorean theorem (Holloway, 2013). Aldolf Zeising, a German psychologist, described this relationship by saying “The Golden Ratio is a universal law in which is contained the ground-principle of all formative striving for beauty and completeness in the realms of both nature and art, and which permeates, as a paramount spiritual ideal” (World
So why are these sequences important to a plant sciences major? Plants are probably the most common example of Fibonacci numbers and the Golden Ratio in nature. Some examples of these are flower petals, fruit, pinecones, tree branches, and leaf arrangement on a stem. The reason for this growing pattern is quite fascinating and practical. Most plants grow new parts in angles measuring 137.5 degrees using natural hormones called auxins. This phenomenon is known in botany as “Whorled Phyllotaxis,” (whorled arrangement) which allows for the optimal amount of sunlight and room to grow on each appendage with minimal overlap and the most potential for photosynthesis. This also shows why most plant appendages tend to grow according to multiples of Fibonacci numbers. For example, most flowers grow in multiples of 3, 4, or 5, closely following Fibonacci or Lucas