View Full Version : Alrighty, my brain is fried. need a little help.
07-05-2002, 08:40 PM
Alrighty. I can't remember my algebra.
i'm trying to show that:
( ( x^(k-1) - y^(k-1) ) + ( x^k - y^k ) ) / sqrt(5) = ( x^(k+1) - y^(k+1) ) / sqrt(5)
where x is the golden ratio and y is it's conjugate...
any help... please....
edit: forgot some of the equation...
Yea, that one <--- goes here. And that one ----> goes over there <----.
07-05-2002, 08:47 PM
what the hell kind of algebra is that...
07-05-2002, 09:15 PM
evil, evil, evil algebra
I think my answer is right.
07-05-2002, 09:56 PM
hmmm, maybe i should have paid attention in math class more often.
hey, its summer time, you're not supposed to be doing stuff like that.
07-05-2002, 10:26 PM
If I get a chance I'll work on it. Why are you thinking about this?
Just for definition
The Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, ... (add the last two to get the next)
The golden section numbers are 1803 39887... and 1803 39887...
The golden string is 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 ...
a sequence of 0s and 1s which is closely related to the Fibonacci numbers and the golden section
The Golden Ratio is
(5^1/2 + 1)/2
07-05-2002, 10:44 PM
alrighty I finally figured it out.
we find the golden ratio by solving t^2-t-1=0, right?
well then t^2=t+1. using this, just substitute that in and it goes right to what i need.
why do i need it? damn teacher told me to prove the equation for nth number in the sequence was correct. how did i do that? induction my dear watson.
07-05-2002, 10:50 PM
good... I don't want to waste brain power this weekend anyways
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