Fibonacci sequence : The beautiful art in mathematics – celebrating 23-Nov – Fibonacci day
Hi all,
Today we are discussing about one of the most amazing series in the world of mathematics. The Fibonacci series.
What is Fibonacci series?
The Fibonacci series is a sequence of numbers in which each number is the sum of the two preceding ones. The sequence starts with 0 and 1, and then each subsequent term is the sum of the two preceding terms.
The series goes like this –
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …
The next number is found by adding up the two numbers before it:
- the 2 is found by adding the two numbers before it (1+1),
- the 3 is found by adding the two numbers before it (1+2),
- the 5 is (2+3),
- the 8 is (5+8)
- and so on!
Here it is longer list :
Formula for Fibonacci series:
The sequence of Fibonacci numbers can be defined as:
Fn = Fn-1 + Fn-2
where:
- Fn is term number “n”
- Fn−1 is the previous term (n−1)
- Fn−2 is the term before that (n−2)
For example :
- F3 = 1 + 1 = 2
- F4 = 2 + 1 = 3
- F5 = 2 + 3 = 5
- F6 = 3 + 5 = 8
- F7 = 5 + 8 = 13
- and so on
Fibonacci Series Spiral
The Fibonacci series spiral is a logarithmic spiral that is formed by joining the corners of squares that have side lengths the same as the Fibonacci numbers in the Fibonacci sequence.
This spiral appears in nature, such as in the arrangement of leaves on a stem, the shell of a nautilus, the spiral arms of galaxies, etc.
When we make squares with area as a Fibonacci number, we get a nice spiral:
We can now see that how the squares fit neatly together
As Fibonacci series is everywhere in nature. Spirals are also found in flowers
Golden Ratio
When we take any two successive (one after the other) Fibonacci Numbers, their ratio is very close to the Golden Ratio which is approximately 1.618034…
It is represented by a symbol called phi “uppercase Φ, lowercase φ or ϕ” . Which is the twenty-first letter of the Greek alphabet.
In fact, the bigger the pair of Fibonacci Numbers, the closer the approximation. Let us try a few:
| A | B | B / A |
|---|---|---|
| 2 | 3 | 1.5 |
| 3 | 5 | 1.666666666… |
| 5 | 8 | 1.6 |
| 8 | 13 | 1.625 |
| 144 | 233 | 1.618055556… |
| 233 | 377 | 1.618025751… |
It gets closer and closer to φ the more we go.
Fibonacci series in nature
Flowers: Many flowers exhibit a Fibonacci arrangement in the number of petals. For example, lilies often have three petals, buttercups have five, delphiniums have eight, and daisies can have 21 or 34 petals.
Spirals in Nature: The spiral patterns observed in hurricanes and spiral galaxies often approximate the Fibonacci spiral etc.
History
Fibonacci was not the first to know about the sequence, it was known in India hundreds of years before!
About Fibonacci the man
His real name was Leonardo Pisano Bogollo, and he lived between 1170 and 1250 in Italy. “Fibonacci” was his nickname, which roughly means “Son of Bonacci”.
Fibonacci Day
Today we are celebrating Fibonacci day so you could explore first 100 digits of Fibonacci numbers.
Download here:
Fibonacci Day is November 23rd, as it has the digits “1, 1, 2, 3” which is part of the sequence. So next Nov 23 let everyone know!
Thank you for reading article and in upcoming articles we would be knowing more about Fibonacci series like “Fibonacci Series and Pascal’s Triangle”, more about golden ratio and many more interesting topics.
Have a nice day!!
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