Dear Learners,

Today we are going to discuss about those numbers which are not known generally but exist in nature and used widely.

Every being living in this world shares a firm pattern. Some mathematician believes, if we look deeply enough, we can find a certain pattern in anything. For this, a man born in Italy namely Leonardo Pisano Bogollo , find a sequence of number which we know by Fibonacci sequence.

In Fibonacci sequence, you start with 0 & 1 and more or from there. Every latter entry in the sequence is produced by adding together the former two entries.
i.e. 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55. . . & so for

Here

0+1=1
1+1=2
1+2=3
2+3=5
3+5=8
5+8=13
8+13=21

The sequence Fn of Fibonacci numbers is define by recurrence relation

Fn = Fn-1+Fn-2,

Where n ∈ N (natural number)

Italian Mathematician Leonardo Pisano Bogollo also known as Fibonacci, underlined Fibonacci Sequence in his first book , Liber  abaci , here he posed a mathematical word problem, which is as follows;

“A man put a pair of rabbits in some place bounded by the walls. How many pairs of rabbits can be produced from the pairs of rabbits in a year?  If it is supposed that every month each pair be gets a new pair from which the second month on became production?” Don’t panic learners, the answer is here—

 Start of Month Number of pairs of rabbits Total pairs of rabbits at start of the month 1 One  pair (original pair) 1 2 There is only a pair of rabbits in the starting of the month. But in the end of this month they have produced one pair to make it two. 1 3 In this month only the original pair can breed, and we get a total number of 3 pairs by the end of the month. 2 4 In this month, the first two pairs can breed and we get 3+2 = 5 pairs by the end of the month. 3 5 In this month the first 3 pairs can now breed and we get 5+3 = 8 pairs by the end of the month. 5

Each entry in the series is produced by adding the two previous entries together.  We can continue this sequence until we got the first 13 Fibonacci numbers:

0,1,1,2,3,5,8,13,21, 34, 55, 89, 144, 233……….

In the starting of the 13th month, (i.e. at the end of the year) we have 233 pairs of rabbits, which is 466 in total!

Fibonacci in Real World:

• The Fibonacci sequence is related to the golden ratio, a proportion (roughly 1:1.6) that occurs frequently right through the natural world and is applied across many areas of human enterprise. Both the Fibonacci sequence and the golden ratio are used to guide design for architecture, websites.

• Fibonacci numbers are various observed in nature. The branching patterns in trees and leaves, for example, the number of petals in a flower consistently follows the Fibonacci sequence. • We can use Fibonacci sequence to convert Miles to Kilometer and vice versa quickly and roughly  (approximately)

Taking any two consecutive numbers from this series as example 8 and 13.

Now smaller number is in miles = The other one is in Kilometer

Greater number is in Kilometers = The smaller one is in Miles (The other way around).

8 Miles = round (12.874752) Kilometers = 13 Kilometers

For distances which are not there in Fibonacci series we can always carry on by distributing the distance into two or more Fibonacci values.

As example, to convert 34 km into miles we can proceed as following:

26 km   =   21 km + 5 km

21 km   =   13.0488 mile = 13 miles

5 km     =   3.10686 mile = 3miles

15 km    =   13+3 miles  = 9 miles