Mathematics Is The Language Of The Universe
Go down deep enough into anything and you will find mathematics.
â Dean Schlicter
Bonjour! Dear readers. Math looks fascinating when you donât have to solve its problems. Having said that, it occupies the highest pedestal among the brainy giants.
Mathematics is the spirit of Mother Nature. The subject which gave birth to every other. To give you an idea of its immense penetrance in the fabric of our daily lives, letâs bring to light a topic that never fails to mesmerize the general publicâs eye.
An Italian mathematician, âLeonardo of Pisaâ, as he was called, discovered an incredulous, fabulous pattern existing among us â the Fibonacci Sequence.
The Fibonacci sequence is a series of numbers wherein each number is the sum of previous two numbers. Starting from 0, it turns out to be:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144âŠ..
The ratio of every number and its previous number approaches 1.618, aka phi.
If each number is represented as the side of a square, then the resulting squares can be arranged as,
If the opposite corners of the squares are connected, it forms a spiral, as shown below:
This spiral is known as the âgolden spiralâ. The Fibonacci series, and its characteristic spiral can be spotted in a paraphernalia of situations, in our very own Mother Nature. Some of my personal favorites are:
- A flock of birds: My most favorite example of the Fibonacci pattern. If you observe carefully, you can spot the Fibonacci series in a flock of birds flying in the sky. Look at the image below and see for yourself.
( The birds fly in a series of 1, 1, 2, 3, 5, 8, as seen from right to left)
They can also be seen flying in a golden spiral, as captured in the video clip below:
2. Branches of a tree: This is how a tree grows: The single main trunk sprouts a branch. Now one of the resulting two branches remain dormant, and the other splits further into two, resulting in a Fibonacci series of branches.
3. DNA helix: The double helical structure of our DNA has its dimensions according to this magical ratio.
The helix has one full cycle length of about 3.4 nm (34 A) while itâs 2nm (20 A) wide. The ratio approximates phi i.e. 1.618.
4. Human face: Itâs said that the closer the dimensions of a face are to the golden ratio, the more attractive it is. Evolutionary biologists believe that we have evolved to subconsciously perceive the golden ratio as an indicator of good health. Moreover, the most attractive smiles are considered to be the ones which follow the ratio of phi â the central incisors 1.618 times wider than the lateral incisors, which, in turn, are 1.618 wider than the canines, so on and so forth. Plastic surgeons often transform a face keeping in mind this golden ratio, for cosmetic purposes.
5. Hurricanes:
6. Galaxies:
7. Shells of molluscs:
8. Cochlea of ear:
9. Flower petals: Each petal is placed at an angle of 0.61 degrees to maximize sunlight exposure. The number of petals in a lily are three, while butter cups have five. Chicory consists of twenty one petals while daisy has thirty four. Again, the Fibonacci series.
10. A colony of honeybees: If we divide the number of females by the number of males in a colony of honeybees, the answer would approach phi i.e. 1.618. Female bees are produced as a fertilized egg by the fusion of male and female gametes, while male bees are produced from unfertilized eggs of the females by a process called parthenogenesis. Hence, males have one parent while females have two. Thus, male bees have 2,3,5, and 8 number of grandparents, great-grandparents, great-great-grandparents, and great-great-great-grandparents, respectively.
Let me just assume that these many examples would suffice. Next time you wander off on a trip with friends, try to spot the Fibonacci sequence. You shall not be disappointed.
The Unknown Doctor
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