Fibonacci Numbers, The Golden Ratio, And Phyllotaxis

Name Instructor Course Date Fibonacci numbers, the golden ratio, and phyllotaxis Fibonacci sequence and the Golden Ratio The Fibonacci series is an infinite sequence of natural numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34. The first two numbers of the sequence are 0 and 1. The other terms are the sum of the 2 previous terms in the sequence: 0 + 1 = 1, 1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8, 5 + 8 = 13. The golden ratio, number or section, is an irrational number and is represented by the symbol φ (phi). It is the ratio or proportion between two segments of a line, which are in the same proportion as the sum of both segments and the longest segment. That is, if the segments are, a and b, and a > b, then φ = (a + b) / a= a / b and the value is equal to 1.618. The Fibonacci appears in many forms of nature, for example where plants are present such as the arrangement of the petals of flowers, the distribution of the leaves on a stem or also in the amount of elements of the spirals or double spirals of the inflorescences, as in the case of the sunflower and many inflorescences of the family. The branch formation, leaf arrangement around stems and seed arrangements on circular seed heads are some of the examples of plants following the Fibonacci sequence and golden ratio (Minarova 9). Each successive level of branches in plant and trees is often based on a progression within the Fibonacci series. The geometric balance in arrangement of braches of the conifers is most apparent and is based on the Fibonacci sequence, new leaves move in a rotating manner as the plant grows, and the strategy guarantees survival by maximizing the distance between the branches and the leaves, looking for angles that do not overlap and in which each leaf receives as much light water and nutrients as possible. A trunk grows to produce a branch, where there are now tow growth points. The main trunk produces another branch and there are three growth points then the trunk and the first branch produce two more growth points, bringing the total to five and the Fibonacci sequence is repeated. Plants position their leaves according to Fibonacci patterns and reflect the golden number. The growth of the plants occurs at the tip of the stem, which has a conical shape. When the plant is seen from above, it is observed that the leaves that grew first, those that are lower tend to be radially farther from the stem. They are also rotated with respect to the axis of the stem so that they do not overlap each other. One advantage of this is that maximizes the space of growth and increase the amount of light that falls on each leaf. In the case of the sunflowers the spirals of these flowers have a number of spirals for one side and another number for the other, and these numbers usually coincide...