There are a couple of errors I noticed. When the author says:
Even if we start with two numbers that are completely unrelated in the Fibonacci sequence – say, 8 and 41 – the simple way that we pick the next number of the Fibonacci sequence will cause us to approximate the golden ratio after only a few iterations:
Why is that? Well, because of the definition of the golden ratio.
He mis-adds in the third step 8+41 ought to be 41+49..
But that's not all. He says "if we start with [any] two numbers...in the Fibonacci sequence" but in fact you can start with ANY two numbers WHETHER OR NOT they are fibonacci numbers.. and perform the Fibonacci operation and divide adjacent numbers and it will converge to the golden ratio. E.g.
The example is showing current=8 previous=41, not current=41 previous=8. I think I did the math right from the those (weird) initial conditions, but maybe not. It converges either way!
Good call on the wording there, though -- changed it from "completely unrelated in the Fibonacci sequence" to "completely unrelated to the Fibonacci sequence" (41 is not a Fibonacci number).
Yeah, if you swap the initial conditions, you get a different sequence of values. You’re starting with 8 41, but the sequence in the article starts with 41 8.
Even if we start with two numbers that are completely unrelated in the Fibonacci sequence – say, 8 and 41 – the simple way that we pick the next number of the Fibonacci sequence will cause us to approximate the golden ratio after only a few iterations:
Why is that? Well, because of the definition of the golden ratio.He mis-adds in the third step 8+41 ought to be 41+49..
But that's not all. He says "if we start with [any] two numbers...in the Fibonacci sequence" but in fact you can start with ANY two numbers WHETHER OR NOT they are fibonacci numbers.. and perform the Fibonacci operation and divide adjacent numbers and it will converge to the golden ratio. E.g.