How to get the golden ratio from a square

Fourth Reflection

A square is drawn, and adjacent to it, a second square is added, forming a double square (rectangular shape) (Steps 1 and 2). Now, a line is drawn from any outer corner to the opposite corner on the longer side, ensuring it does not coincide with any of the figure’s sides. This results in a hypotenuse that defines two right-angled triangles (Step 3). Choosing one of the triangles (ABC) and using a compass, the pivot is placed at the upper angle (BAC), where the hypotenuse originates. The compass is then opened to the length of the triangle's shorter side (AB). Dragging the compass until it touches the hypotenuse divides it into two segments (AD and DC) (Step 4). Now, placing the compass at the opposite corner (ACB), it is opened to the previously determined length on the hypotenuse (CD) and dragged until it touches the longer side of the triangle (Step 5). This creates two segments, where the larger one (CE) is 1.618 times the smaller one (AE), representing the golden ratio.

Steps 1 and 2.

Step 3.

Step 4.

Step 5.