Magical Maths
[justify]Math is magical but beyond it is Logical which makes math a Fun.[/justify]
[justify]Here is one mathematical series, would you like to guess the logic for it.[/justify]
0 1 1 2 3 5 8 13 21 . . . .
[justify]I think its quite easy to crack, so here is the logic: the next number is found by adding the two numbers before it.[/justify]
0
1
1 (0 + 1)
2 (1 + 1)
3 (1 + 2)
5 (2 + 3)
8 (3 + 5)
and so on!
[justify]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.[/justify]
[justify]The numbers in Fibonacci Sequence are known as Fibonacci Numbers.[/justify]
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”
[justify]Here are the Squares representing a fibbonacci sequence upto n=5.[/justify]
[justify]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![/justify]
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[justify]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?[/justify]
[justify]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.[/justify]
