Patricia Marlene Micaller Abalos

Patricia Marlene Micaller Abalos

IV - Photon

The Golden Ratio

I first read about the golden ratio in Dan Browns book The Da Vinci Code. It was when the character Robert Langdon discussed it in front of the people. When he claimed that the golden ratio shows up everywhere in art and nature, I was intrigued.

The golden ratio is a special number approximately equal to 1.6180339887498948482. The Greek letter

Phi () is used to refer to this ratio. Like Pi, the digits of the golden ratio could completely go on forever without repeating. It is often better to use its exact value:

The golden ratio can be found in the Fibonacci sequence (0, 1, 1, 2, 3, 5, 8, 13 ...). In a Fibonacci sequence each term is the sum of the two previous terms (for instance, 0+1=1, 1+1=2 ...). As you go farther and farther into the sequence, the ratio of the term to term before it, will be closer to the value of the golden ratio.

The ratio between any two successive Fibonacci Numbers approaches a limit as the numbers get larger, and that limit is the Golden Ratio. Thus, 6765/4181 (the 20th and 19th Fibonaccis) is 1.618033963, which only differs from the Golden Ratio by 0.000000025.The golden ratio as said above can be found in nature. One example is the head of a daisy. It was discovered that the individual florets of a daisy grow in two spirals extending from the center. The first spiral has 21 arms while the other spiral has 34 arms. The number of arms that each spiral has is a Fibonacci number and their ratio is the golden ratio. The same thing happens to the spirals of pine cones but their spirals have 5 and 8 arms respectively, or if bigger their spirals have 8 and 13 arms. For the pineapple the same thing happens, but the pineapple has 3 spirals, each having 5, 8 and 13 arms respectively.