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construction 'golden' rectangle

It is possible to draw a Golden Ratio rectangle with rule and a pair of compasses.
Draw a square with side 2 and divide in two equal rectangles. The diagonal in a rectangle has length $\sqrt{5}$ (Pythagoras). Put this length in the side as shown below. The long side length is now  $1+\sqrt{5}$:

construction Golden rectangle

 

 

 

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