The Magic of Fibonacci numbers!!
First, let me explain what are Fibonacci numbers -
The Fibonacci sequence consists of numbers such that each number is the sum of the two preceding ones, starting from 0 and 1.
F0 = 0, F1 = 1
And, Fn = Fn-1 + Fn-2 (for n > 1)
The beginning of the sequence is thus –
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597 ……
0+1=1, 1+1=2, 1+2=3, 2+3=5, 3+5=8, 5+8=13, 8+13=21,……..
Now, let’s see the hidden magic of these numbers -
Golden Ratio:
First, take any Fibonacci number, let’s say 89. Now divide it by the previous one (55 in our case). And the result will be 1.6… This result is same for every Fibonacci number like 144/89, 55/34,34/21 all will be approximately equal to 1.6… And this ratio is called the Golden Ratio. Interesting right??
Distance between fingertip and elbow/distance between wrist and elbow is equal to Golden Ratio -
In 12th century, the mathematician Leonardo Fibonacci did an experiment with rabbits and observed that Rabbits breed in the same sequence.
The Fibonacci sequence can also be seen in the way tree branches form or split.
On many plants, the number of petals is a Fibonacci number:
buttercups have 5 petals; lilies and iris have 3 petals; some delphiniums have 8; corn marigolds have 13 petals; some asters have 21 whereas daisies can be found with 34, 55 or even 89 petals.
Take a good look at yourself in the mirror. You’ll notice that most of your body parts follow the numbers one, two, three and five. “You have one nose, two eyes, three segments to each limb and five fingers on each hand”. The proportions and measurements of the human body can also be divided up in terms of the golden ratio.
If we start with two small squares of size 1 next to each other. On top of both of these draw a square of size 2 (=1+1). We can now draw a new square — touching both a unit square and the latest square of side 2 — so having sides 3 units long; and then another touching both the 2-square and the 3-square, which has sides of 5 units. Here is a spiral drawn in the squares, a quarter of a circle in each square.
Here, are a few things which follow the same spiral:
And the list goes on and on…
Happy exploring!!
Thank you!!