problem to do with golden ratio equation
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Can anyone explain what's wrong with my logic?
[URL]https://www.mersenneforum.org/attachment.php?attachmentid=21617&stc=1&d=1579005470[/URL] 
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.

The usual formulation for x and y being in golden proportion is [tex]\frac{x}{y}\;=\;\frac{x\;+\;y}{x}[/tex]; the righthand side clearly is greater than 1. Taking y = 1 gives
[tex]\frac{x}{1}\;=\;\frac{x\;+\;1}{x}\text{, or }x^{2}\;\;x\;\;1\;=\;0\text{.}[/tex] 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. 
Thanks very much to both of you.

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