The Golden Ratio

The Golden Ratio

The Golden Ratio1. One of the most alluring discoveries I have made in my journey through this life. I have a keen ability to recognize patterns, both visual2 and numerical3, and the Fibonacci sequence is by far one of my favorites. Each number in the sequence is derived from the sum of the two previous numbers with the mathematical relationship Fn = Fn-1 + Fn-2. A seemingly simple series of numbers that can even be found in various aspects of our culture such as music4, literature, architecture, and even finance.

Even more interesting is the presence of Fibonacci ratios in nature. Phyllotaxis5, in botany, is the arrangement of leaves on the stem of a plant that often form a spiral around the stem at angles equal to different ratios of subsequent Fibonacci numbers. This phenomenon is further observed in the number of petals on numerous flowers6 and even in the arrangement of seeds on a sunflower7.

The ratio of any two consecutive numbers in the Fibonacci sequence has roughly the same value and as the sequence approaches infinity, this value approaches 1.618, known as the Golden Ratio (also known as divine proportion, golden mean, golden section, etc.) and is represented by the Greek letter Phi.

Pinecones, shells, and DNA to hurricanes, the Great Pyramid of Giza, and even the spiral shape of our own Milky Way all follow this ratio. The idea that this ratio 1.618 or its inverse 0.618 (= 1/1.618) are so prominent in the world may not seem rational but ironically that is the crux of this entire premise. The Golden Ratio is the most mathematically irrational number that exists9 and allows for optimal organization requiring the least amount of energy. For example, the seeds on sunflowers are arranged in spirals based on the subsequent Fibonacci numbers such that the angle of turn between the seeds becomes increasingly closer to the Golden Ratio while at the same time the arrangement becomes increasingly closer to being as efficient as mathematically possible.

1The Golden Ratio – Wikipedia
2Visual Pattern Fluid Intelligence Test
3Number Pattern Intelligence Test
4Fibonacci sequence in Lateralus by Tool
5WolframMathWorld – Phyllotaxis
6Flower Patterns and Fibonacci Numbers
7Nature, The Golden Ratio, and Fibonacci too …
8Fibonacci Fractals
9How is the golden ratio the “most” irrational number?