Fibonacci Operations: Uncovering Weird Properties

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Discussion Overview

The discussion revolves around the properties of the Fibonacci sequence, particularly focusing on operations involving the squares of Fibonacci numbers and their relationships. Participants explore various mathematical expressions and their implications within the context of the Fibonacci sequence.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant notes a "weird property" related to the squares of Fibonacci numbers, suggesting that the operation changes based on the value of x.
  • Another participant expresses fascination with the Fibonacci sequence and its connections to the divine ratio.
  • A participant attempts to validate a mathematical expression involving Fibonacci numbers but concludes that it does not hold up, questioning the validity of their earlier reasoning.
  • The same participant later realizes an error in their understanding of the Fibonacci sequence's starting terms and proposes a new equation that uses 0 and 1 as the first two terms, asserting that the original equation holds when starting with 1 and 1.
  • Several participants express shared interest in the Fibonacci sequence, indicating a common fascination with the topic.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the validity of the mathematical properties discussed. There are competing views regarding the correctness of the operations involving Fibonacci numbers, and some participants express uncertainty about the outcomes.

Contextual Notes

Participants reference different starting points for the Fibonacci sequence, which may affect the validity of their claims and calculations. There is also a lack of clarity regarding the assumptions underlying the proposed equations.

willr12
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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.
 
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Very interesting. I have always been fascinated by the fibonacci sequence and the divine ratio.
 
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.
 
ModestyKing said:
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.
 
David Carroll said:
Very interesting. I have always been fascinated by the fibonacci sequence and the divine ratio.
Me as well.
 

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