View Single Post
Old 2004-04-24, 17:18   #5
Bronze Medalist
mfgoode's Avatar
Jan 2004

22·33·19 Posts
Default The Golden Section

Originally Posted by Cyclamen Persicum
Golden Intersection = 2*cos(pi/5)
I am sorry, as I had a nagging doubt, that the way I printed my formula may cause a bit of confusion and this has indeed happened to Jinydu.
I should have clarified that in the expression the numerator is Log (i^2) only and the denominator of this is 5*i i.e. 5*i is not under log with i^2.

Euler discovered the remarkable formula e^(i*pi) = -1. Substitute this in log(i^2) and then divide by 5*i and you will get 2*cos (pi/5) as Cyclamen Periscum has done correctly.

To complete the derivation 2* cos pi/5 ==2*cos36
and cos 36 =(1+sq rt.5)/4 so 2*cos 36 =(1+sq.rt.5)/2 =1.6180339...
=Phi the golden section as given in my thread. or use a calculator.

Mally .
mfgoode is offline   Reply With Quote