fibonacci sequence math fibonacci sequence in nature

The Fibonacci sequence and the golden ratio appear in our world in diverse forms. Investors can use charting techniques such as Fibonacci retracements, Fibonacci arcs and Fibonacci fans to inform predictions of price movements in individual stocks or for the stock market. 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. (2017). 15 Beautiful Examples of Mathematics in Nature. (2009) The Math Book from Pythagoras to the 57 th Dimension, 250 Milestones in the History of Mathematics. Whether it maximising sun exposure for a plant, or to maxmise the space within something mathematics makes it beneficial. These findings make it apparent that mathematics is purposeful. It is said that the flowers follow the sequence of Fibonacci to maximise their exposure to sunlight, which is obviously beneficial for the flower. Examples of this is the lily (3 petals), buttercups (5 petals) and daisy’s which have 34 petals. But they don’t.” (Planet Dolan, 2017).įinally, the placement of a flowers petals also follows Fibonacci’s sequence. Subsequently, after a few rotations, spiral arms should start to wind around a galaxy. According to the astronomers, “the radial arms should become curved as the galaxies rotate. After looking into this, I read about how the spiral galaxies does not fit the theories of astronomers. The milky way has several spiralled arms that follow in the Fibonacci sequence. Spiral Galaxies is another example of where Fibonacci’s sequence is apparent. But why do the sunflowers abide by Fibonacci’s theory? It has been suggested that the sunflowers can pack the maximum amount of seeds if it follows this particular sequence.

The spirals of the seed pattern of the sunflower contain Fibonacci’s sequence. Fibonacci discovered that if he used squares with this sequence, it would make the perfect spiral.įibonacci’s golden spiral can be seen throughout nature, sunflowers is a clear example of this theory. This particular sequence starts at 0 then 1 then you add the two numbers before you get the next number in the sequence 0 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and so on. Fibonacci is known for the creation of many sequences, with the golden spiral being his most famous discovery. In our input with Anna, we were introduced to the Italian mathematician Fibonacci. 2017Throughout this module, there has been a reoccurring theme that maths is everywhere.

Fibonacci sequence math fibonacci sequence in nature