Interestingly, another human creation - the stock market - exhibits surprising golden ratio characteristics. What makes these structures feel aesthetically pleasing are the golden ratio proportions of one section to another.įibonacci numbers and the golden ratio play a role in music as well, from musical scales to the foundations of chords to the harmonics created by ratios of frequencies. Similarly, people make use of the golden ratio in architecture, as in the pyramids of Giza, the Parthenon, the Taj Mahal and the Guggenheim Museum. Leonardo da Vinci’s Last Supper, Mary Cassat’s The Boating Party and Georges Seurat’s Bathers at Asnieres are just a few paintings composed using golden rectangles. The swirling pattern of hurricanes and the arms of spiral galaxies are just two examples.Īrtists employ the golden ratio when creating their paintings and illustrations. The golden ratio shows up in some inanimate natural phenomena as well. Likewise, the human body has many elements that show the golden ratio, including the sections of the human finger in relation to each other, the forearm in relation to the hand, facial features in relation to each other, the spiral of the ear and even the spirals of DNA. Some examples of the golden ratio in nature are seen in the spiraling pattern of seeds in a sunflower head, the scales of a pinecone, the unfurling of a growing fern and the chambers of a nautilus shell. The golden ratio shows up in all kinds of natural phenomena but also in human creations like architecture and artwork. That is very interesting math, but what does it mean in the real world?

By drawing arcs through opposite corners of connected golden rectangles, you will get the golden spiral. If you divide a Fibonacci number by the number just before it, you get the golden ratio of 1.618, which is represented by the Greek letter phi.īuilding on the golden ratio, you can make a golden rectangle, in which the lengths of the sides match the golden ratio. Named after Italian mathematician Leonardo Pisano, who was nicknamed Fibonacci, the sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 and so on. But have you heard of the golden ratio?Īlso known as the Fibonacci Sequence, the golden ratio is a proportion based on a sequence of numbers in which each one equals the sum of the two numbers immediately preceding it. Most of us have heard of the Golden Rule, the Golden Age of ancient Greece, the Golden Oldies musical genre, and even the Golden Girls.

What is fibonacci sequence in nature