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Old 2004-04-23, 16:06   #1
Bronze Medalist
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Jan 2004

22·33·19 Posts
Default The Golden Section.

The Golden section has been known to the ancient Greeks since antiquity.
It had been worked out geometrically as 1.618033989.... and called phi.
Phi was used in building the Great Pyramid of Giza about 3070 B.C.
They referred to it as the 'sacred ratio'
In the Fibonacci series the ratio of successive terms Fn+1/Fn tends to phi as the series progresses.
In dividing a line x+y In parts x,y such that (x+y)/x=x/y
Then x/y= (1+sqr.rt.5)/2=1.618033989.....

There is a novel way that the ratio can be expressed trigonometrically using the well known constants 'e' and 'i'=sqr.rt (-1)
The Golden ratio can be shown as
2*cos(log ((i^2))/5*i))

Can anyone show that this is equivalent to phi the golden ratio?

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