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.
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.
An interesting connection, or only a comparison?