How Many Times Have You Spotted Fibonacci in Nature? Here Are 7 Examples for You... - The Stemettes Zine (2024)
Fibonacci sequence is found by adding the previous two numbers of the sequence together. Have you spotted this in nature?
Fibonacci (real name Leonardo Bonacci) was a mathematician who developed the Fibonacci Sequence. The sequence is found by adding the previous two numbers of the sequence together. It looks like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34… And on it goes. This pattern can also be seen as:
The Fibonacci Sequence is found all throughout nature, too. It is a naturally occurring pattern. Here are some examples of Fibonacci in nature…
Tree Branches
Although we all usually see trees everywhere in our day to day life, how often have you looked for the patterns in them? In trees, the Fibonacci begins in the growth of the trunk and then spirals outward as the tree gets larger and taller.
We also see the golden ratio in their branches as they start off with one trunk which splits into 2, then one of the new branches stems into 2, and this pattern continues.
Storms
Your eye of the storm is like the 0 or 1 in the Fibonacci sequence, as you go on in the counter-clockwise spiral you find it increasing at a consistent pattern. This pattern is much like the Golden Ratio. But is a hurricane actually a Fibonacci spiral?? >>
Seashells
When cut open, nautilus shells form a logarithmic spiral, composed of chambered sections called camerae. Each new chamber is equal to the size of the two camerae before it, which creates the logarithmic spiral. This proportional growth occurs because the nautilus grows at a constant rate throughout its life until reaching its full size.
Flower Petals
The petals of a flower grow in a manner consistent with the Fibonacci. Of the most visible Fibonacci sequence in plants, lilies, which have three petals, and buttercups, with their five petals, are some of the most easily recognised.
Galaxies
The golden spiral can be found in the shape of the “arms” of galaxies if you look closely. It can’t be told if galaxies follow a perfect spiral, because we can’t measure a galaxy accurately, but on paper, we can measure it and see the size. Read more on Fibonacci in galaxies here >>
Flower Heads
Most of the time, seeds come from the centre of the flower head and migrate out. A perfect example of this is sunflowers with their spiralling patterns. At points, their seed heads get so packed that their number can get extremely high, sometimes as much as 144 and more. When analysing these spirals, the number is almost always Fibonacci.
YOU!
You are an example of the beauty of the Fibonacci Sequence. The human body has various representations of the Fibonacci Sequence proportions, from your face to your ear to your hands. You have now been proven to be mathematically gorgeous.
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The Fibonacci Spiral is seen in nature in many ways such as the shape of a nautilus (seashell), the arrangement of the spirals of a sunflower, and the arrangement of the scales of a pinecone.
The number of petals in a flower consistently follows the Fibonacci sequence. Famous examples include the lily, which has three petals, buttercups, which have five (pictured at left), the chicory's 21, the daisy's 34, and so on.
The Fibonacci sequence is a type series where each number is the sum of the two that precede it. It starts from 0 and 1 usually. The Fibonacci sequence is given by 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on. The numbers in the Fibonacci sequence are also called Fibonacci numbers.
Specifically five patterns; admittedly, some writings champion greater numbers, with categories slightly different, being more or less inclusive, but five served us quite well. Spiral, meander, explosion, packing, and branching are the “Five Patterns in Nature” that we chose to explore.
The Fibonacci sequence, also known as the golden ratio, is utilized in architectural designs, creating aesthetically pleasing structures. In engineering and technology, Fibonacci numbers play a significant role, appearing in population growth models, software engineering, task management, and data structure analysis.
The notation that we will use to represent the Fibonacci sequence is as follows: f1=1,f2=1,f3=2,f4=3,f5=5,f6=8,f7=13,f8=21,f9=34,f10=55,f11=89,f12=144,…
Divide the spirals into those pointed left and right and you'll get two consecutive Fibonacci numbers. You can decipher spiral patterns in pine cones, pineapples and cauliflower that also reflect the Fibonacci sequence in this manner [source: Knott].
The bones of your finger (including the bone from your knuckle to your wrist) follow the Fibonacci sequence. We have 8 fingers in total, 5 digits on each hand, 3 bones in each finger, 2 bones in 1 thumb, and 1 thumb on each hand. Many flowers also exhibit the Fibonacci sequence.
The 20th Fibonacci number is 6,765. We can find the 20th Fibonacci number by calculating the Fibonacci sequence out to the 20th term, but that would be fairly time consuming.
An octave on the piano consists of 13 notes: 8 white keys and 5 black keys. A scale consists of 8 notes, of which the 3rd and 5th notes make up a basic chord. In a scale, the dominant note is the 5th note, which is also the 8th note of all 13 notes that make up the octave.
The pineapple shows the fibonacci sequence as they possess the fibonacci spirals and also have the fibonacci sequence shown in the number of sections there are. Through this we see that the fibonacci sequence is all around us from sunflowers to the curves of waves, we just need to look for them.
Snail shells, flower petals, pine cones, snakes, storms, DNA, curly hair, even galaxies are spirals—and that's not even nearly all! Why are spirals so abundant in nature?
Sunflowers are a stunning and perfect example of the golden ratio in nature. These beauties have 55 clockwise spirals and either 34 or 89 counterclockwise spirals — all Fibonacci numbers — growing at a constant of the golden ratio.
As plants grow, these fractions often transition according to simple rules related to Fibonacci sequences. This mathematical regularity originates from leaf primordia at the shoot tip (shoot apical meristem), which successively arise at fixed intervals of a divergence angle, typically the golden angle of 137.5°.
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