AUTHOR - Swastika Deb
Well… the title of this article seems pretty simple and easy, basically this is what it is: 0,1,1,2,3,5,8,13,21,34,55,89,...... And it goes on. This is the Fibonacci Sequence. It goes on infinitely and is made up of the series of numbers starting with 0, followed by 1, where each subsequent number is the sum of the previous two numbers.
The ratios of sequential Fibonacci numbers (2/1, 3/2, 5/3, etc.) approach the golden ratio(which is widely known as phi Φ). In fact, the higher the Fibonacci numbers, the closer their relationship is to 1.618. The golden ratio is sometimes called the “divine proportion”.
Golden spiral: We’re about to take this thing to a whole new level here. Imagine the numbers in the Fibonacci Sequence represented by squares like those on a piece of graph paper. Find a starting point somewhere near the center of the page, and color in a single square representing the first number in the sequence (1). Next to it, do the same in honor of the second one. Then, with two being the third number, use a different color to shade in a 2 by 2 square space. From there, find a different hue to color in a space measuring 3 by 3 squares and so on. You’ll end up with a vibrant version of this example:
Now, if you’re following along on paper, grab a pen. Start in the upper corner of your first single square, and draw the first stage of a spiral running to its opposite corner, cutting the square in half. Continue your line across the next single block and on through the following ones, drawing your spiral across the diagonal center of each larger square. You’ll end up with something like this:
Now if you see, the spiral gets bigger by a factor of phi (aka golden ratio!). This spiral is considered one of the beautiful ones too!
Soo yess… till now we know what a fibonacci pattern is, and what a golden spiral is. Let’s see where this sequence appears in our daily life!
Spiraling into Complete Control
Before you read further, make sure you are absolutely ready to make this leap. We are going to check out some really cool stuff about this, let’s get started! The Golden Rectangle generated by Fibonacci’s Sequence has been making appearances around the world for centuries.
Leonardo da Vinci’s Mona Lisa could be considered another display of the near-Golden Ratio at work. Its dimensions are said to be 30 inches by 21 inches. When we take out the ratio, we find it is 1.42857, not an exact match but very close.
Artist Piet Mondrian inserts the Fibonacci Sequence into some of his paintings as well. You can clearly see the puzzle-piece squares making up the Golden Rectangle in certain examples of his work. When you look at it carefully, you could observe the spiral in your head for a while.
These are only a few widely known cases of this pattern being worked into art, architecture and engineering over the centuries. Referring back to the fact you can find patterns in almost anything if you’re looking for them.
Fibonacci and nature:
If you look around yourself, you can find fibonacci in nature too! If you look at sunflowers carefully, you can see that the petals surround a large mass of seeds, but the seeds are not arranged in some random manner, they coil out from the centre and make a spiral in all directions. The angle they make is the golden angle (approx 137 degrees).
Pine cones are another widely used case in point. You’ll notice their spikes are arranged in spirals from both clockwise and counterclockwise perspectives. The same is true of pineapples.There are a lot of examples, including the nautilus shell, the whirlpool galaxy which you can check out on the internet.
The math behind the beauty:
Human physical attraction depends a lot on ratio and symmetry. What is the ratio all about? Well, it’s the golden ratio also known as the divine ratio as a consequence of this. Leonardo da Vinci's drawings of the human body emphasised its proportion. Many have claimed the ratio of the following distances in the above Vitruvian Man image is the Golden Ratio:
(foot to navel) : (navel to head) ≈ 1.618:1
Faces, both human and nonhuman, abound with examples of the Golden Ratio. The mouth and nose are each positioned at golden sections of the distance between the eyes and the bottom of the chin. Similar proportions can be seen from the side, and even the eye and ear itself (which follows along a spiral).
It's worth noting that every person's body is different, but that averages across populations tend towards phi. It has also been said that the more closely our proportions adhere to phi, the more "attractive" those traits are perceived. As an example, the most "beautiful" smiles are those in which central incisors are 1.618 wider than the lateral incisors, which are 1.618 wider than canines, and so on.
There are a lot of examples other than these which you can find in nature by observing some on your own and searching them on the net.
Fantastic work!!!