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View Full Version : Alrighty, my brain is fried. need a little help.

revil
07-05-2002, 11:40 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...

edit: forgot some of the equation...

Hiro
07-05-2002, 11:45 PM
Yea, that one <--- goes here. And that one ----> goes over there <----.

xsiled2
07-05-2002, 11:47 PM
what the hell kind of algebra is that...

revil
07-06-2002, 12:15 AM
evil, evil, evil algebra

Hiro
07-06-2002, 12:17 AM
I think my answer is right.

ribitch
07-06-2002, 12:56 AM
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.

brainsmile
07-06-2002, 01:26 AM

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

revil
07-06-2002, 01:44 AM
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.

brainsmile
07-06-2002, 01:50 AM
good... I don't want to waste brain power this weekend anyways