Phy, Phi, Pho, Phum I smell the blood of...Oh whatever! It is all about Fibbonacci!
By Stephanie Britt
Fibbonacci made famous a wonderful sequence that has been used for so many reasons, explained so many patterns in nature and used in many mathematical sequence. One famous math configuration is the golden ratio. The golden ratio is an irrational number that is represented by the greek letter phi. 
The golden ratio is derived from Fibbonacci's sequence in a unique way.
As n approaches infinity the ratio approaches 1.61803 respectively.
If f(0)=1, f(1)=1, F(2)=2, f(3)=3, f(4)=5 and so forth to f(n)=f(n-1)+f(n-2) such as below
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We can see the ratio approaches the golden number.
But what happens if we change our ratio? The Lucas sequence changes the rules a little. The first term is still f(0)=1, but f(1)=3 and so on. So basically the new coniguration is
What does this configuration approach?
It too approaches the golden ratio. I decided to try something else to see what happens when we take Fibbonacci's sequence and find what
What number does this ratio approach?
If figure it out mathematically with a proof we see that
We can also see this using excel.
What interesting sequence can you come up with.