Fibonacci Operations: Uncovering Weird Properties

[willr12]

https://mail-attachment.googleusercontent.com/attachment/u/0/?ui=2&ik=ff063a19b0&view=att&th=148f1c9590566f17&attid=0.1&disp=safe&zw&saduie=AG9B_P-_5uo2y5jplL5o_M_vYWte&sadet=1412805844641&sads=ivFuEkpjW55tmUUptu2J4poEUhA So I've been messing around with the Fibonacci sequence and I noticed a weird property with the squares of the numbers. It is as follows:
Kind of a weird property as the operation on the top changes depending on the value of x.

 

[willr12]

 

[David Carroll]

Very interesting. I have always been fascinated by the fibonacci sequence and the divine ratio.

 

[ModestyKing]

2 is Fibonacci number 4, and 1 is Fibonacci number 2 (and 3, but let's go with 2). Let's try it out:
(2)^2 + (-1)(1)^2 = 3. 3 / 1 = 3. Is 3 Fibonacci number (2*4 - 2)? Fibonacci number 6? No, 3 is Fibonacci number 5.
I 'dunno man, I think it doesn't hold up.

 

[willr12]

2 is Fibonacci number 4, and 1 is Fibonacci number 2 (and 3, but let's go with 2). Let's try it out:
(2)^2 + (-1)(1)^2 = 3. 3 / 1 = 3. Is 3 Fibonacci number (2*4 - 2)? Fibonacci number 6? No, 3 is Fibonacci number 5.
I 'dunno man, I think it doesn't hold up.

Just realized my stupidity. This equation has F1=1, F2=1, F3=2...so it starts with 1 and 1 and then goes onward instead of 0 and 1 as the first two terms. I'm working on a new equation that uses 0 and 1 as the first two. However, this equation does hold up when 1 and 1 are the first terms. When 1 and 1 are the first 2 terms, 2 is fib number 3 and 1 is number 1. Therefore the quotient should be 2*3-(3-1)=4, and 3 is indeed fib number 4 when 1 and 1 are the first terms of the sequence.

 

[willr12]

Very interesting. I have always been fascinated by the fibonacci sequence and the divine ratio.

Me as well.