1.61803399…It’s a number that has been given many names – Golden Ratio, Golden Number, Golden Proportion, Golden Mean, Golden Section, Divine Proportion, etc. This number intrigued ancient Greeks and Renaissance artists thousands of years ago, and it does the same to modern scientists and mathematicians today. As well as from mathematicians, it is also a great source of fascination for biologists, artists, musicians, historians, architects and psychologists in their respective fields. What makes this number so special, you ask? You’re about to find out.
The golden ratio, denoted by the Greek letter Φ (Phi), is an irrational number, i.e. it cannot be expressed as the ratio of two integers. Its exact value is equal to (1+√5)/2. The first definition of the golden ratio appeared as early as 300 BC in the Greek mathematician Euclid’s Elements. Since then, numerous books have been written about this number and its properties.
What makes this number so interesting is that this proportion appears extensively throughout nature. Here are a few examples.
- According to the Wikipedia, a golden spiral is “a logarithmic spiral whose growth factor is φ, the golden
ratio, that is, a golden spiral gets wider (or further from its origin) by a factor of φ for every quarter turn it makes”. The golden spiral makes appearances in nature in numerous different places.The largest structure in nature known to exhibit the golden ratio is the spiral galaxy. - Spiral sea shells display the same uncanny shape of the golden spiral.
- Sunflower seeds grow in opposing spirals. Can you guess with what the spirals have a strong geometric relation with? That’s right, the golden ratio. Similar pattern can be observed in many other different kinds of flowers as well.
- The pinecone surface also has counter-rotating sets of spirals, much like the sunflower. And once again, these spirals have the properties of the golden spiral. A pineapple’s outer surface is ruled by the same pattern.
The same is true for strawberry. - Perhaps the most relevant fact to us would be that the Phi proportion can be found throughout the human body. This proportion can be found in the very bones that form our skeleton. For example, the distance from our shoulder to the fingertips, divided by the distance from our elbow to the fingertips equals Phi. The same is true for the distances from the tip of the head to the toes and from the naval to the toes, and also from the hip to the toes and from the knee to the toes. The examples are endless.
These are but only a few examples where Phi appears in nature. Entire books are dedicated to shedding light on nature’s relationship with Phi, yet those only go a small way to doing so. The existence of Phi in nature’s design of the universe is undeniable, but as to why, a satisfactory answer is yet to be found. Some go as far as to believe the number to be divine. Many famous architects, musicians and painters have used this curious number in their work.
Despite discovering the golden ratio’s marvels thousands of years ago, mankind is yet to fully understand and explain its connection with mother nature.