Golden Ratio in Nature

From the beautiful spirals of a nautilus shell and the delicate florets of a daisy to the branching sequence of an apple tree and the pattern of the bracts of a pinecone, the Golden Ratio in nature exists as part of almost everything in the universe.

See more examples of the Golden Ratio

Most people find that things that follow the patterns of the Golden Ratio are pleasing to look at. Scientists have even conducted tests that show that the Golden Ratio appeals to both the human brain and the human eye. However, scientists do not know why this occurs. Some believe that the human brain may be hardwired, or genetically programed, to find the shapes and proportions of the Golden Ratio aesthetically pleasing.

From the times of the ancient Egyptians and Greeks to the modern peoples of today, the Golden Ratio has remained shrouded in a sense of mystique that is yet to be completely understood by science. One thing that most scientists do agree on is that Nature’s perfect number seems to be the Golden Ratio. An infinite number, the Golden Ratio is usually expressed as 1.618.

The beauty of the Golden Ratio is found all throughout nature. For example, if you look closely at the head of a daisy you will see the tiny florets grow in two spirals from the center outward. The number of the florets in the two spirals are 21 and 34, both Fibonacci numbers, which is a Golden Ratio. The Fibonacci number sequence is: 0,1,1,2,3,5,8,13,34,55,89,144. Each number is the sum of the two numbers before it.

Other examples of the Golden Ratio found in nature include:

• The growth points of a tree illustrate the Fibonacci sequence as it grows.
  • The trunk of the tree - 1 growth point
  • The trunk produces a branch -2 growth points
  • The trunk produces a second branch - 3 growth points
  • The first branch and the trunk each produce another growth point - 5 growth points
  • The trunk, the first and the second branch all produce new growth points - 8 growth points

The tree is branching following the Golden Ration with the Fibonacci sequence: 1,2,3,5,8. The growth pattern continues following the Fibonacci sequence as the tree grows.

• The number of petals on many flowers, such as:
  • Lilies - 3 petals
  • Buttercups - 5 petals
  • Delphiniums - 8 petals
  • Corn marigold - 13 petals
  • Black-eyed susan - 21 petals
  • Plantain - 34 petals
  • Michaelmas daisies - 55 petals

The Fibonacci sequence: 3,5,8,13,21,34,55 is illustrated.

• The seed heads of flowers grow in spirals that follow the Golden Ratio
• The leaves of a plant as they grow around the stem
• Plant leaves as they unfurl
• The bracts of a pinecone
• The florets of vegetables such as Romanesque broccoli and cauliflower
• The cells of the human body
• The proportions of the human body
• The proportions of animals and insects

Not all flowers and plants follow the Fibonacci number sequence. There are flowers that have 4, 6 or a different number of petals but these are not as common as those that follow the Golden Ratio pattern of growth.

• A fun resource from Math is Fun has an interactive tool that illustrates how the new cells of a sunflower plant grow in spirals. It allows the user to put in the mathematical amount of the turn the flower should take between the production of each new cell. The flower cells then appear based on the number you enter. Try a few different numbers and see how you would grow as a flower. Then try the Golden Ratio, 1.61803, and see the perfect seed spiral appear.
• In his book, The Golden Section, Hans Walser explores various aspects of the Golden Ratio.
• Fibonacci Numbers in Nature & the Golden Ratio

Examples of the Golden Ratio in nature show up time and time again illustrating the sheer perfection and exquisite beauty that exists all around us.

• Monuments with the Golden Ratio
• Yin Yang Pictures
• Yin Yang Art

• Yin Yang Dragons
• Tiger and Dragon Ying Yang
• Applications How to Place Feng Shui Elephant
• Chinese Dragon Clip Art
• Ying Yang Suns