# Magical Maths

Math is magical but beyond it is Logical which makes math a Fun.

Here is one mathematical series, would you like to guess the logic for it.

0 1 1 2 3 5 8 13 21 . . . .

I think its quite easy to crack,

**so here is the logic: the next number is found by adding the two numbers before it**.0

1

1(0 + 1)

2(1 + 1)

3(1 + 2)

5(2 + 3)

8(3 + 5)

and so on!

And we all know that this series or sequence is popular as

**Fibonacci Sequence**. It is named after**Italian Mathematician Leonardo Pisano Bogollo**, his nickname was**Fibonacci**.The numbers in Fibonacci Sequence are known as

**Fibonacci Numbers.**Let

nbe the number upto which we want to write the fibinacci sequence.

Xnbe the Fibonacci number in the sequence

So here we go for fibonacci sequence upto n = 5

n | 0 | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|---|

Xn | 0 | 1 | 1 | 2 | 3 | 5 |

Logic | 0 | 1 | X0 + X1 | X1 + X2 | X2 + X3 | X3 + X4 |

From above table we can clearly write :

Xn = Xn-2 + Xn-1

Where

Xn = Fibonacci Number “n”

Xn-2 = Fibonacci Number “n-2”

Xn-1 = Fibonacci Number “n-1”

Here are the Squares representing a fibbonacci sequence upto n=5.

for n = 0 we have X0 = 0 thus there is no square for it, for n = 1 we have X1 = 1 and thus represented by a unit square and thus X3 = 2 represented by 4 (2 x 2) unit square and so on!

The above representation is made using 8 x 5 unit squares and interestingly we are going to use it as a display of our clock. But How?

**There are some other interesting things about this magical Fibonacci Sequence, Would you like to explore more and let everyone know about it by replying to this thread.**