20200114, 12:38  #1 
Jul 2014
3×149 Posts 
problem to do with golden ratio equation
Can anyone explain what's wrong with my logic?
https://www.mersenneforum.org/attach...1&d=1579005470 
20200114, 13:09  #2 
Jun 2003
5,179 Posts 
Golden ratio is an increasing ratio (i.e > 1). The first equation uses x as a decreasing ratio (i.e. x < 1). So you get 1/gr when you solve that.

20200114, 14:45  #3 
Feb 2017
Nowhere
5^{3}×41 Posts 
The usual formulation for x and y being in golden proportion is ; the righthand side clearly is greater than 1. Taking y = 1 gives
An illustration is given by the 727236 degree isosceles triangle. The bisector of one of the 72degree angles divides the opposite side in golden ratio; calling x the length of the base and y the length of the smaller segment of the side opposite the angle bisector, gives the above proportion. 
20200114, 14:54  #4 
Jul 2014
447_{10} Posts 
Thanks very much to both of you.

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