We shouldn't miss two other cases, showing us how the squ­are, yes, the square's perimeter, in addition to starting point, is an in­de­pen­dent con­tain­er of the Golden section, no need of the AB line to set the ratio.

The usual path that is naturally followed to build the golden rectangle that represents so well the ratio among base and height, driving our­selves out of the squared area, does not invite us to validate its au­ton­o­my, but it's time to do it.
In fact in the in­i­tial squ­are we can ob­se­rve that the AC + CB is the same as AC + CE as well as AC + CE is the same as CD + CE; hence that the ra­tio AB/AD is the same as CD + CE / ED.
Here also all sides are involved.

Therefore we ought to con­sid­er the Square like a matrix of the Golden ra­tio in itself, with one curious feature: it is filled four of these triangles!

Turning back to the apex of the DCVO profile [page 15], when the curve will reverse its trend, the vertical OA = 1 can be connected to the mid­point of A1 i.e. ½, to reproduce the basically contained Golden ratio fig­ure into the square.
All this suggests find out the first occurrence of this kind of triangle exactly at the arc tangent =26.56505117707799°, when the sin of the AC radius angle is = 0.50 and the cosin is = 1.
Tap or click the image to page 14 to watch that.

An interesting connection, or only a comparison?