Saturday, November 19, 2016

Brady numbers. Brady numbers. The title is acting strange. Help me, friend.

I found the general formula for the Brady numbers. It's Bn = 1571.964902Φ^n + 381.0350976(-Φ)^-n.

I know, potoo friend. I was surprised, too.
Here's the series on the Brady numbers:
https://www.youtube.com/watch?v=D8ntDpBm6Ok
https://www.youtube.com/watch?v=dTWKKvlZB08
https://www.youtube.com/watch?v=PeUbRXnbmms
One thing I like about the general formula is that it's clear to see why every series which increases fibonaccily is connected to the golden ratio, because when a term is divided by the previous term it is:
[(a constant)Φ^n + (a constant)(-Φ)^-n] / [(the first constant)Φ^(n-1) + (the second constant)(-Φ)^-(n-1)]
And, because (-Φ)^-n gets closer and closer to zero as n gets bigger, it can be simplified to:
[(a constant)Φ^n] / [(that same constant)Φ^(n-1)]
And then, because [(a constant)Φ^(n-1)] / [(that constant)Φ^(n-1) = 1, this becomes
Φ^(n-(n-1)) = Φ^1 = Φ
YAY!

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