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
n be the number upto which we want to write the fibinacci sequence.
Xn be 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.
