0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 … Are there just
random numbers? Probably yes for a layman, but not for a scientific mind. Yes,
this is the Fibonacci series. Being the nature’s numbering system, it is a very
popular mathematical sequence that finds its prominent place in fields like
science, architecture, computers, etc. But not many know how this is useful in
those fields. Leonardo Fibonacci, an Italian mathematician, known for his
genius in the area of math was the one who discovered the Fibonacci series.
We observe many things around us. Flowers, honey combs,
trees, etc. Have you ever asked yourself why those are only in that fashion? It’s
not a wonder why math has surrounded us. The Fibonacci pattern can be seen in
many places around us. That’s not it. We can apply another operation to the
numbers in this sequence. Divide every number starting from 2 with its
preceding number. As we proceed further, the quotient gets closer to 1.618033…
This quotient is called “The Golden Ratio”. Phi or The Golden Ratio is what the
nature has formed for itself.
Let’s see a few aspects of this magical sequence.
Fibonacci in
Architecture and Geometry: Ever noticed the values of sides of a
right angle triangle with integer sides? The hypotenuses of all the right
angled triangles belong to the Fibonacci series.
All the historical monuments have their walls built in the
Golden Ratio. It can also be used to create patterns for building structures.
For example, the base of the building can have 89 bricks and its above level
can accommodate 54 bricks. This will have maximum stability.
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| The Pascal's Triangle |
Fibonacci in nature: Did you observe the base that
supports the petals of flower? It is a beautiful sight. And it’s even amazing
to know that all the seeds in that base are arranged according to the Fibonacci
pattern i.e., all the levels of the base contain number of seeds corresponding
to the series as we progress to a higher level.
The number of petals in a flower is fixed. It depends on what
type of flower it is. Whatever it might be, nature is nature. It grows the
flowers all the time to keep the number of petals as one of the Fibonacci
number! This is a fact. We have flowers with one petal – White Lily, two petals
– Euphorbia, three petals - Trillium... twenty one petals – Shasta Daisy … and
the list goes on.
One complete helical structure of DNA, the most basic element
of a human life, has a length of 34 angstroms and width of 21 angstroms. These
are in-turn the numbers in Fibonacci sequence.
The parts of human body are in proportion such that the ratio
of the sizes results in the Golden Ratio. This was explained by Leonardo Da
Vinci through his painting called The Vitruvian Man.
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| Some examples of The Fibonacci Sequence |
Fibonacci in the
universe: How did
the spirals generate? I mean, a never ending not-totally-a-circular object
which looks like a mosquito coil. Squares of area of the Fibonacci numbers are
placed side-by-side. Every square is connected by a curve which covers a
quarter of a circle in every square. This curve emerges out of every square and
enters into larger squares resulting in the ultimate spiral structure.
Once we understand this, we can observe the same pattern in
the spiral galaxies. When hurricanes occurred, and when they were captured from
the satellite camera, it amazed everyone as they resembled the spiral I
described above. This spiral structure is used in the construction of spiral
stair-cases in buildings.
The Golden Triangle, The Golden Rectangle, the pentagram,
honey combs, shells of a snail, the human ear and nose, growth of few plants
and flowers in the spiral, arrangement of leaves of a plant at every level, the
pattern on a wing of a dragon-fly, etc., are the very few examples we have
observed till now in nature.
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| A Hurricane |
This is one proof that science, math and nature are very much
connected. Our universe is a wonder and learning about this wonder gives us
immense knowledge. Here is the link of a small ted talk on Fibonacci numbers.
To know more about it, visit the following link.
http://www.ted.com/talks/arthur_benjamin_the_magic_of_fibonacci_numbers
#Knowing #9D
#Knowing #9D
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