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/sci/ - Science & Math

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3822391 No.3822391 [Reply] [Original]

Could someone help with Fibonacci numbers and the golden mean? I was reading up on some sites I found on Google but I'm still confused. This site (http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/phi.html#simpledef)) says that Phi^2=Phi+1. What were the steps they took to get to Phi+1?

>> No.3822419

First, take phi. Multiply phi by phi. Then, math happens.
phi^2 = phi + 1
And you're done

>> No.3822431

>>3822419
umm, ok... how about a serious answer?

>> No.3822454

anyone?

>> No.3822461

Do you mean what steps were taken to get to the <span class="math">\phi + 1[/spoiler] in the equation <span class="math">\phi ^2 = \phi + 1[/spoiler]?

If that's what you mean, well, there were no steps.That's how <span class="math">\phi[/spoiler] is defined!
They say, "Let <span class="math">\phi[/spoiler] be the number such that once you square it, it is itself plus one."
Thus: <span class="math">\phi ^2 = \phi + 1[/spoiler].

It's like if I said, "Let <span class="math">A[/spoiler] be the number such that once you triple it, it is itself plus 4."
So may be able to see that <span class="math">A = 2[/spoiler] just by observation, but we can write the equation in the same way:
<span class="math">3 \, A = A + 4[/spoiler].
Then, solving for A, we get <span class="math"> 2\, A = 4[/spoiler], and therefore, <span class="math">A = 2[/spoiler].

But in the same way, we didn't take any steps to get to <span class="math">A + 4[/spoiler]. It's just the same thing that they did to "get to" <span class="math">\phi + 1[/spoiler].

Hope that helped man.

>> No.3822467

>>3822461
Oh i see. Thanks very much!

>> No.3822482

>>3822467
Yeah, no problem!

The "<span class="math">\phi ^2 = \phi + 1[/spoiler]" is just the starting point. Then the question becomes, "Well, how do we find <span class="math">\phi[/spoiler]?!"
Luckily, that's just a bit of algebra. But that's the part we have to "get to", not the other way around!

Good luck man!