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I do know something about the golden segment but I cannot construct it. I've tried to follow some tips but it was in vain.

Steps for drawing the golden segment:

1. Draw a line L.

2. Choose a point A on the line L. In this point, we'll draw a perpendicular M.

3. We consider one segment [AB], with the length 1, on the line M. (the length 1 is a reference length).

4. We consider one segment [AC], with the length 1, on the line L.

5. We consider one segment [CD], with the length 1, on the line M, so as AD=2.

6. We'll measure in compasses the length BD, and from the point B, with the distance kept in compasses, we'll intersect the line M in the point E.

The ratio AE/AD is the gold ratio.

Construct a right angled triangle with AB =2 units and the hypotenuse 3 units: (On a line AB =2 units errect a perpendicular AY at B.With compass measuring 3 units ,with  A as centre draw the arc to cut AY at C. That gives the right angled triangle ABC)

In the right angled triangle ABC,  BC = sqrt(3^2-2^2)= sqrt5.

Now mark off on the line AB extended with compass measuring  equal to BC with B as centre such that BD= BC.

Draw a perpendicular bisector to AB to find the mid point of AB at say E. Now BE equal to one unit.

Now ED = EB+BD =1+sqrt5 units.

AB =2units

Therefore, ED/AB= (1+sqrt5)/2. That is the golden ratio with proof and with geometrical construction ascertaining the visuality of this irrational ratio, but still being called golden ratio.